METAL VAPOR VACUUM ARC SWITCHING
by
David Banks Cope
S. B., Massachusetts Institute of Technology
(1979)
and
S. M., Massachusetts Institute of Technology
(1979)
SUBMITTED TO THE DEPARTMENT OF
PHYSICS
IN PARTIAL FULFILLMENT OF THE
REQUIREMENTS OF THE
DEGREE OF
DOCTOR OF PHILOSOPHY
IN PHYSICS
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
October 1983
©
Massachusetts Institute of Technology 1983
Signature of Author ____
Department of Physics
October
Certified by_
14, 1983
..
Peter P. Mongeau
Thesis Supervisor
AcceptedGeorge
F.
K____________________ote___
George F. Koster
Chairman, Department Committee
R 14 '8*
1xCH\ES
L AR~E
R
1
METAL VAPOR VACUUM ARC SWITCHING
by
David Banks Cope
Submitted to the Department of Physics
on 14 October 1983 in partial fulfillment of the
requirements for the Degree of Doctor of Philosophy
in Physics
ABSTRACT
A theoretical
vacuum arc
complete
and experimental
investigation of metal vapor
switching was performed. Establishing a
physical model of vacuum arcs was the
basic principles of operation of vacuum arcs is
goal.
more
The
discussed.
The extension of present theoretical ideas is discussed in
detail
in several areas.
Theoretical
considerations
indicate magnetic field-augmented vacuum arcs have enhanced
construction,
levels.
Design,
performance
of an experimental vacuum arc
interpretation
presented.
2
data, and
device is
Acknowledgments
This thesis is the culmination
would
like to thank the many people who have been ever
helpful in this project.
thank
Most especially,
Davidson, Kenelm
I
so
I would like to
those so intimately involved in the
Acceleration Group,
M.I.T.
of two years of research.
Electromagnetic
(Dr. Henry Kolm, Whitney Hamnett, Lisa
McKinney, and
Scott Clifton) while
at
and, currently, at EML Research, Inc. in Cambridge.
Their curiosity, ability, and natural intellect have aided
me in every aspect of the word "Help".
Every
thesis student
owes a
advisor and I am no exception.
the cold,
was
ready
physicists.
should
tremendous amount
to
his
Peter Mongeau took me out of
that January, and prodded and kneaded me until I
to
rise
into the ranks
Peter has done,
be done:
of
the
professional
for me, everything the way it
directing not by fiat and helping not
pampering.
3
by
Table of Contents
page
Abstract ...............................................
2
Acknowledgements
.......................................
3
List of Figures.................................
I.Introduction to Vacuum Arcs .......
.......
6
............... 10
II. Theory of Vacuum Arcs ..............................
A. Electrodes:
15
Power Balance .................
15
B. Electrodes: Material Considerations..........
37
54
C. Plasma Physics ..................
1. Plasma Processes ...........
54
70
2. Plasma Characteristics.....
D. Interruption Mechanics..............
1. Natural Commutation.............
2. Magnetic Interruption............ . . .. . .
3. Kinematic Interruption Analysis.. . . .. . .
..........
.
72
72
73
77
E. Theoretical Extension
....................... 81
1. Cathode spots: radii and formation time ... 82
2. Ablation theory ..........
89
3. Potential hump theory....
105
4. Arc stability
........
122
.
*----------------
III. Apparatus Issues ..................................
A. Initial Design Requirements...........
B. Magnetic Field Design
.........
130
......... 131
.................
C. Vacuum Considerations...........
1. System Viewpoint............
2. General High Vacuum Issues..
.............
3. Implementation
130
.............
·
·
lll..llllllll
.134
.134
.137
.141
D. Adjustable/flexible Features ..................
1. Gap Variability ............................
143
143
2. Demountable Electrodes .....................
3. Anode/Cathode Interchangeability...........
145
151
4. Flexibility
of Magnetic Field Design .......151
4
Table of Contents
IV. Experimental Work .
(cont.)
.....
............................
154
A. Control System Description ..................... 154
1. Instrumentation
........................154
a) Electro-pneumatic controls ............ 154
b) F.0. Trigger Box
.....
....... 155
2. Diagnostics
..............................
166
3. Implementation.............................
168
B. Data ...........................................
C. Interpretation
........................... 184
D. Summary ........................................
V. Appendices
170
...................
Appendix A: Power Calculations.
.
198
202
..................
202
Appendix B: Applications Considerations
........
205
Mega-Amp Issues...............................
205
a) Electrode Erosion ..................... 205
b) Current Sharing.......................
210
c)
Magnetic
Forces
...
Appendix C: Interruption Calculations
VI. Footnotes
.....
.............
215
.........................222
VII. Bibliography..
........................
225
VIII. Afterword.23..
IX. Biographical Note
....................
2
11
..
...................
231
............
5
2.............232
List of Figures
Figure 1.1
Metal Vapor Vacuum Arc Switch (MVVAS)..... 11
Figure 1.2
Phases of MVVAS Operation ................ 12
Figure II.A.1
Energetic Processes
.......
.......... 16
Figure II.A.2 Potential Hump Form....................... 19
Figure II.A.3
Cathode Energy Balance.................... 27
Figure II.A.4
Open-Shutter Photograph of Cathode Spots.. 30
Figure II.A.5
Cathode Spot Characteristics..............31
Figure II.A.6
Cathode Spot Processes................... 32
Figure II.A.7 Assumptions for Numerical Calculations.... 34
Figure II.A.8 Cathode Power Calculation Results......... 35
Figure II.B.1
Electrode Material Selection Criteria .... 38
Figure II.B.2 Vapor Pressures of Metals................. 40
Figure II.B.3
Cathode Erosion Rates for Vaccum Gaps..... 42
Figure II .B.4
Metal Breakdown Strength Ordering VS.
Young's Moduli..........................44
Figure II.B.5 Critical-Field Ordering for Metal Electron
Emission
Figure II.B.6
................... 45
Average Arc Lifetime as a Function
of Current ............................ 48
Figure
I.B.7
Vapor Pressure as a Function
of Temperature.......................... 49
Figure II.B.8 Arc Lifetime Significance................
. 52
Figure II.C.1 Debye Shielding ......................... 57
Figure II.C.2 Plasma Collisional Processes.............. 60
Figure II.C.3 Collisionless and Collisional
Theoretical
Results
6
..................
65
List of Figures (cont.)
Figure II.C.4
Potential Hump Profile ....................68
Figure II.C.5 Anode Potential Hump Form ...........
69
Figure II.C.6 Vacuum Arc Plasma Parameters.............. 70
Figure II.D.1
Factors Influencing Natural Voltage
Recovery ................................
73
Figure II.D.2
Magnetic-Interaction Configurations....... 76
Figure II.D.3
Simplified Switch Schematic...............
78
Figure II.D.4 Magnetic Field Requirement................ 80
Figure II.E.1
One Dimensional Model for Calculations.... 82
Figure II.E.2 Graph of f(x,t)/F
= erfc(z) .............. 83
Figure II.E.3
Diffusion and Boiling Distances VS. Time:
(One Dimensional Model) .
................
85
Figure II.E.4
Table of Critical Distances and Times
(One Dimensional Model)................. 86
Figure II .E.5
Schematic for Ablation Calculations
Figure II.E.6
Evaluation Parameters for Xth............ 94
.... 90
Figure II.E.7 Enthalpy Changes for Ablation ...........
95
Figure II.E.8 Ablation Comparison: Theory VS.
Experiment ..............................
96
Figure II.E.9 Correspondence of Ablation Theory and
Emitted Electrons Per Atom.
..........99
Figure II.E.10 Quasi-Collisionless Particle Fluxes...... 111
Figure II.E.11 Sample Potential Hump Density Profiles ...119
Figure II.E.12 Critical Density Parameters ...............120
Figure II.E.13 Comparison of Arc Stability Theory for
Metals ..................................
127
Figure III.B.1 Magnetic Field Coil Construction ..........133
Figure III.C. 1 Vacuum Pumping Flowchart
Figure III.C.2 Vacuum System.
.......
7
................. 136
........... 142
List of Figures (cont.)
Figure III.D.1 Slotted Electrodes
..
1..............
147
Figure III .D.2 Slotted Electrode and Coil Geometry ....... 148
Figure III .D.3 Idealined Plasma Model Showing Leakage
Current .
................................
149
Figure IV.A.1
Electrical Schematic for Pneumatic
Valves ..................................
155
Figure IV.A.2
Simplified Control Signal Flow Diagram....159
Figure IV.A.3
Detailed Control Signal Flow Diagram
Figure IV.A.4
Delay Timing Circuit ..
Figure IV.A.5
Arc Discharge and Field Coil Trigger Box..165
Figure IV.A.6
SCR - Transformer Alternatives
......
160
...................
164
.........165
Figure IV.A.7 Overall System Electrical Schematic.......169
Figure IV.B.1
Electrode Polarities.
Figure IV.B.2
Interrupting Current VS. Gap Spacing ...... 179
Figure IV.B.3
Half-Cycles for Interruption VS.
Gap Spacing ............................. 180
Figure IV.B.4
Interruption Current VS. Number
of Half-Cycles ..
.....................
178
........................
181
Figure IV.B.5
Effect of Dielectric Proximity ............ 181
Figure IV.B.6
Arc Re-Strike
Figure IV.B.7
Arc Recovery-Voltage
..................
182
Suppression .......... 182
Figure IV.B.8 Schematic of Field-Caused Deformation ..... 183
Figure IV.C.1
Applied Voltage VS. Current-Gap Product...186
Figure IV.C.2
Electrode Isolation Cylinder .
Figure IV.C.3
Schematic Representation of Pulsed
Magnetic Fields ....
Figure V.B.1
..............
194
...............
196
Material Volume Erosion Characteristlcs...206
8
List of Figures
(cont.)
Figure V.B.2
Critical Current VS. Thermal "Goodness"
209
Parameter...............................
Figure V.B.3
Arc Channel Schematic .....................
212
Figure V.C.1
Simplified Switch Schematic.
Figure V.C.2
Values of Radius Integral ................. 219
Figure V.C.3
Typical Parameters Values for
Interruption...........................220
Figure V.C.4
Graph of Shrinking Plasma Radius
215
..............
as a Function of Time .......
9
2.........220
I. INTRODUCTION
Metal vapor vacuum arc switches have long been used
kiloampere
switch
often
environment
level
currents
than
higher
in
100
voltage
high
a
to
These
kilovolts.
reasonably compact devices feature the ability to interrupt
significant peak current levels at a zero
point
It is this unique
is commonly known as commutation.
which
crossing
aspect which makes them the subject of an intense
research
effort currently being performed at several labs throughout
the world.
device
multi-electrode
vapor vacuum arc device is a
metal
A
housed
in a insulated vacuum
shows a schematic form of a metal vapor vacuum arc
The
conduction
from
the surfaces of the cathode and/or anode. Conduction
surface
electrode
contacts
of
conducting
maintained
breakdown
injects
interelectrode
the
provides the nucleus for an
particles.
trigger
dielectric
the
with
device.
surface
plasma into
plasma blowoff
a
is concerned exclusively
thesis
triggered,
voltage across
high
applies a
latter, three electrode,
When
or
when a third electrode
breakdown
This
surface.
amount
switch.
generated
medium is an ionized metal vapor
is initiated typically by either separating metal
or
1.1
vessel. Figure
The
conduction
region.
small
This
avalanche
medium
by power deposition at the electrode
10
a
is
of
then
surfaces.
I.
Conduction continues
mechanism
Recovery
until some
overwhelms the
is
said
competing
INTRODUCTION
particle-loss
particle-creation
to occur if conduction
mechanism.
ceases
for
an
indefinitely long period of time. Figure 1.2 shows in block
diagram the phases of metal vapor vacuum arc switch.
Figure I.1
METAL VAPOR VACUUM ARC SWITCH (MVVAS)
-
W
I-
-
l
F
I
l-
P
I
I~
-
I
I
!
I CMMDE
1
-
J
CENT
I
.
__
--
I
1
CVAPORDE
L
_
!
IP
11
_I
I
I
I.
INTRODUCTION
Figure 1.2
PHASES OF MVVAS OPERATION
The
situation of
creation
particle-loss exceeding
generally happens
at
a
current
particlezero.
An
alternating current is the most common example of a current
waveform
with
sufficiently
conditions
a
near
for
zero-crossing.
If
the
zero for a sufficiently
current
current
long
interruption have
time
then
is
the
been
satisfied and the chances for actual interruption are quite
good.
The
particle
recombination on
electrode
loss
mechanism
is
that
of
plasma
any surfaces present, particularly the
surfaces. The essential necesary condition
for
current commutation is the elimination of charged particles
from
vacuum
the interelectrode region.
gap,
In an ordinary
the particles are swept clear of the
their thermal velocity.
triggered
gap
by
These conditions are necessary but
12
I. INTRODUCTION
not sufficient for current commutation. Other factors must
be considered before a definitive
ability
may be made.
thermal
heating of an electrode,
insulator surfaces,
statement on interruption
Examples of additional factors
are:
melted metal splatter on
micro-protrusions, the
vacuum gap
dimension, and the applied voltage.
The terminology
An
"vacuum arc" is an unfortunate
choice.
arc necessarily has a substantial number of high energy
ionized
particles;
Similarly,
a
conduction;
it certainly is nt
vacuum
an
arc
will
is
not
a
true
"vacuum".
support
any
in
high
impossible
a
current
vacuum
environment. Rooted in the historical development of these
devices, the terminology persists. We take the word "vacuum
arc"
to
mean
simply that before there was an
arc
there
existed a reasonably good vacuum environment. Yet, like so
many before me,
I,
too, continue usage of the term vacuum
arc.
My thesis is organized according to a
format
which
leads logically from the most general considerations
most
specific.
followed
The
described
exhaustive
theory of vacuum
by a general consideration
specific
designed
An
implementation
of
of
an
to the
arcs
is
apparatus
issues.
experimental
device
according to principles I chiefly established is
next.
intrepretation
Data
I
observed
of the data is given.
13
is
presented
and
my
I. INTRODUCTION
My original,
creative work involved in this thesis is
presented in the particular section which is most logically
determined by the established format.
I have presented the
details of the electrode power balance for the first
(to
my knowledge)
manner.
but
in a coherent,
time
compact and intelligible
Of course, I relied upon prior art of vacuum arcs,
never
before has
such
an
encompassing,
definitive
discussion been published.
In the course of this thesis I derived the mathematical
equations
and elucidated the physical understanding of the
magnetic interruption analysis presented in this thesis.
The
entire
Theoretical Extension
exclusively original work.
offered
The
section represents
increased understanding
by this section is a direct result of my
creative
thinking.
A
further
example of novel work is my design
of
the
experimental device. Innovative features such as the method
of
gap
variation and slotted electrodes
are described
in
detail.
I
have supplemented this whole body of
with the results of other researchers.
original
Thus, I have put my
own work into perspective with work done by others.
14
work
II. THEORY OF ARCS
A
detailed account of the theory of arcs is
presented
in
this chapter.
A. Electrodes: Power Balance
Introduction
The
principal physical
governed
by
an
energy
representation, when
of
basis
an
equation.
In
discharge is
arc
its
most
applied to the cathode,
the
common
energy
equation becomes:
Pcethode
'
N Cp dT/dt.
The notation is as follows:
Pcathode
N
power to the cathode
effective cathode mass
Cp
heat
T
cathode
t = time
capacity
Watts]
kg]
of the cathode
temperature
J/kg K]
K]
ts]
The task is to evaluate Pcathode A list of various energyrelevant
processesappears
processes, according
to
our
in
Figure
present
II.A.l. These
understanding, in
combination with specific material properties, contain the
relevant macroscopic
physics of an arc discharge. It is the
richness of
phenomena which
these
15
makes
for
rewarding
II. Theory of Arcs: A. Power Balance
research.
Convective
Figure
heat
II.A.1.
transfer is notable by its
absence
Shown in Figure II.A.1 is a column
from
giving
the algebraic sign of the effect which the process haa upon
the
cathode
temperature.
A (+) sign indicates
that
the
effect will tend to increase the cathode temperature. A (-)
sign means a tendency to decrease the cathode temperature.
Figure II.A.1
ENERGETIC PROCESSES
Cathode Effect
Process
charged particle bombardment
(1)
(2) neutral particle bombardment
(3)
ohmic (resistive) heating
(4)
plasma radiation
(5)
plasma recombination
(6)
plasma ionization
(7)
bulk metal radiation
(8) bulk thermal conductivity
(9) electrode phase change
(10) work function escape energy
(11)
A
brief
parameters
description
electronic heat capacity
is
given
below
listed in Figure II.A.1.
16
for
each
of
the
II. Theory of Arcs: A. Power Balance
II.A.1
Charged Particle Bombardment
Charged
particle bombardment is simply the result of
deposition of
particles
the
kinetic energy
as they fall down the
acquired by
the
charged
electric-potential
well.
Essentially the particles convert this potential energy to
thermal
energy of the respective electrode.
accommodation coefficient of
delivered
to
the
electrode
unity,
the
Assuming an
total
surface is the
sum
energy
of
the
cathode-fall potential, the kinetic energy of the particle,
and the ionization energy.
The
ionic kinetic energy is greater than the
drop from anode to cathode.
total
voltage
This phenomenon is due to
the
existence of a "potential hump"'. Figure II.A.2 shows
the
form
of a potential hump.
hump
was
Tanberg
The possibility of a
first discussed by Compton
and
Berkey
tTanberg
and
Compton,
Berkey,
recently, researchers in the field have made
measurements
potential
19313
19313.
and
More
experimental
attempting to investigate the structure of the
potential hump
Plyutto, Ryzhkov,
and Kapin, hereinafter
referred to as PR&K,1965; and Davis and Miller, referred to
as D&N,
1969]
19693].
The results of their work
PR&K,
965;
D&M,
show that ions have an energy greater than the anode
potential. The ionic energies vary for different materials,
17
II. Theory of Arcs: A. Power Balance
but range typically from 25 eV
to stainless steel of
we use a value appropriate
our case,
For
D&M].
PR&K] to 70 eV
29 eV. The total energy deposited per ion is
Ei
Vc
Vi
where
I,
Ei
Reece,
1955;
CCobine,
and
1963],
ions,
charged
I
assuming singly
(It should be noted that
D&M, 19693. For simplicity we consider only
1965;
ion,'.) It
that
is important to note
deposition occurs over a very small area at
The
a
fraction of the ionic population is multiply charged
CPR&K,
Z
43 volts.
Vi
ionization
the
I is
Thus,
potential also taken to be 7 volts.
large
taken to be 7 volts
Vc is the cathode-fall voltagce
cathode spot energy fluxes are
this
the
energy
cathode.
indeed, as
quite high
will be discussed later.
The
existence
of
a potential hump is
easily seen
to
be
plausible from two different, but related, points of view.
An
balance performed at
energy
achieved
without
the
a potential hump:
cathode cannot
the
cathode
be
becomes
colder because the material vaporized and ionized requires
a
greet
amount
of
energy.
This
assumes
the
various
parameter values of materials and of the arc discharge
correctly
obtained. Thus,
an
increased input
power
required at the cathode for a balance to be achieved.
increase
in
the ion energy due to the hump
18
is
are
is
The
precisely
II. Theory of Arcs: A. Power Balance
enough for such a balance. The alternative point of view is
one of conservation of current. Again, assuming the various
parameter
values to
be
correctly
obtained,
calculate the electron current leaving the
one
may
cathode. Also
given the plasma parameters, one may calculate the electron
current going
to the anode. The paradox arises that
electron current
leaving the cathode is
arriving at
anode. A potential
the
paradox because
rise
to
an
less
hump
electric
field which
a
accelerates
potential hump has an effect which
ambipolar
Section
diffusion
that
explains the
it generates a space-charge which
retards electrons. From this point of view,
of
than
the
ions
gives
and
the existence
is
similar to
CGunter Ecker, 1980].
II.E.5 presents
a
theory
on
potential
formation.
Figure II.A.2
POTENTIAL HUMP FORM
VA
V~p
v
CATHODE
ANODE
19
hump
II. Theory of Arcs: A. Power Balance
II.A.2 Neutral Particle Bombardment
Neutral
bombardment represents
particle
by
transferred
particle-surface
the
energy
During
collisions.
inelastic surface scattering by neutrals some fraction of
the
initial
surface.
In
neutrals.
ionization
energetic
practical
this calculation we include charge
exchange
reaction
state
is
is
A
indicated
* A -- > A * A
by a
(+)
where
the
and
the
ign
particle is underscored. Note in this case
effect
the
of this factis that the metal surface
a solid angle of 2 7rto the emitting
present
01,
electrode
is optically thick to charge exchange neutrals. The
plasma
scale
The
kinetic energy is deposited on the
depth of this volume is
i.e.
1
1/nd,
volume.
where
The
is dcx
the sum of charge exchange and ionization
cross-
sections.
II.A.3 Ohmic
Ohmic
heating
heating
is the ordinary result of
passing
current
through a body with a finite resistivity.
II.A.4 Plasma Radiation
plasma
The
by
in the inter-electrode
region transafer
several mechanisms. Plasma radiation is one
which
energy
means
energy is transferred from the plasma volume to
20
by
the
II. Theory of Arcs: A.
electrode
surface.
Bremsstrahlung
electrons
volume
and
and
or
The
radiation
line
radiation.
mechaniss
for
recombination.
recombination
one
recombination,
of
to
the
photons which carry away the
The
photons
which
be
Simultaneous
at least three
excess
intercept the
already accounted for by the plasma
recombinetton depends
allowed.
"bodies
of
environments:
conservation of energy and momentum requires
bodies
include
Recombination
ions occurs in two different
near-surface
Power Balance
In
radiative
represented
is
energy
by
momentum.
and
surface are
electrode
Radiative
radiation.
linearly on the electron
and
ion
densities in the volumeof plasma.
II.A.S Plaaa
Three-body
body event.
Radiation
recombination,
In addition to the electrons
recombine as
present
by contrast,
in
is truly a
three
and
which
radiative recombination,
ions,
neutrals are
which may absorb the excess energy and momentum.
The probability,
or rate,
of three-body
is
recombination
proportional to the densities of the interacting species.
There
are
reactions:
three
principal
ion-ion-nutral,
electron-ion-neutral.
The
three-body
recombination
ion-ion-neutral
reaction has
low probability of occurrence under conditions
to
vacuum
arcs;
and
electron-ion-electron
a
applicable
only at extreme ion densities does
this
rate become appreciable. The two latter reactions, however,
21
iI. Theory of Arcs: A. Power Balance
are
significant under
reactions,
in
fact,
extinction. The
discharge
conditions. These
are the most important ones for
arc
electron-ion-electron rate is given
Zel'dovich
and Razier
have
their
used
arc
CZel'dovich and
Razier,
1966].
three-body recombination rate
in
by
We
our
calculations.
Data
for the electron-ion-neutral
However, Kimblin
currents
1971] has measured
to
walls.
Kimblin
be
a result of recombination
measured
approximately 10
used
an
ion
of ions
current
of the total arc discharge
this value
probability
for
in
our
calculations.
wall
condensed
matter,
the
equal
to
current. We
Hence,
density
the
greatly
objects:
(1)
density
is
orders of magnitude higher than
the
where
approximately three
neutral
at
three-body recombination is
enhanced near the surface of two classes of
peak
ion
in vacuum arc discharges. He has suggested this
current
have
Kimblin,
reaction rate is scarce.
in the
the
neutral
plasma,
and
(2)
electron
emitting materials, where the density of electrons is high.
The electrodes satisfy both conditions, while any
exposed
material surface satisfies the former condition. Of course,
all
material
surfaces
dielectric. During
chamber, we
are
included,
conductor
or
periodic cleaning of the glass
vacuum
have noticed metallic build-up in the
inside
22
II. Theory of Arcs: A,. Power Balance
surface.
We
take
care to remove this debri
as
t
would
eventually obstruct our view of the discharge.
IZ;A.6 Plasa
Ionization
Ionization of the plasma tends to have a cooling effect
the
on
electrode. This follows under the assumption that the
same
amount of total energy
transferred
to
electrode.
This
is
plasma means
the
available;
less
more
allocated
This
incident
electrons ionizes a volume of neutral gas;
were
not
to
is exactly analogous to the phase
energy.
gas
energy
occurs,
for
present,
instance,
when
a
the
change
stream
the ionization energy
of
if the
would
be
deposited on the electrode surface as in process II.A.1.
II.A.7 GreX
ody Radiation
As the temperature of the electrode increases,
will
radiate
more
relationship,
surface
which
energy according to
follow,
the
corrected by the emissivity,
will radiate as a grey body.
the surface
black
that
In our
body
is,
the
calculations
we assume the surrounding surfaces
to be at
zero temperature. This assumption is, of course, false, but
it
allows simplification of the calculation and the
introduced
that
of
by
other
approximation
temperature
this approximation
approximations
is certainly
used.
In
becomes better and better as
less
addition,
the
error
than
the
electrode
increases. We also ignore the shape factor, Fij
23
II. Theory of Arca: A. Power Balance
for the solid angle of the opposing electro-..
II.A.8 Thermal Conductivity
Since
energy
surface,
is
bulk
deposited
primarily at
thermal conduction
the
electrode
represents a
cooling
effect of the surface region. Thermal conduction is of most
importance early in the discharge.
rate
is
gradient
proportional to the
is
The
temperature
energy
transport
gradient.
largest before the energy has
had
This
time
to
"spread out" or diffuse. This concept is closely related to
the
existence of cathode spots=
a detailed discussion
is
postponed until more background material is given.
II.A.9 Electrode Phase Cnange
The rate of increase of temperature
precisely steady
temperature rise,
while
phase
the
in time.
At various points during
the local temperature remains
to
phase changes.
ionization.
the solid metal
the ionized phase we have
They are:
Additional
at
the
constant
input power supplies the energy needed
change. Starting with
proceeding
of the electrode is not
for
phase
least
a
and
three
melting, vaporization and singlephase
changes include solid metal
internal changes (e.g. alpha to beta phase transformation)
and multiple
ionization events.
Ionization has been
taken
into account above and so will not be discussed further.
substantial
amount of energy is involved in the
24
A
processes
II. Theory of Arcs: A. Power Balance
of
melting
and vaporization.
The effect is listed
as
a
cooling agent in Figure II.A.1. This is true for the region
of high energy flux.
When condensation occurs, however, on
a material surface the energy "stored" as thermal energy of
a
gas
re-appears
essence,
at
vaporization
the
material
surface. Hence,
in
tends to cool one area but tends to
heat another area.
II.A.10 Work Function Escape Enery
Electrons in a metal are in a quantum mechanical
well.
W,
The
effective depth of the well is the total depth,
minus
function
potential
the Fermi energy,
eF,
and is called
the
work
for the particular metal and is designated by
This effect is a quantum mechanical one,
classical analogies.
One
.
yet it has simple
analogy is that of
the
simple
potential well: a certain amount of energy must be supplied
in
order
amount
to
of
extricate the electron from
energy required varies
with
the
well.
The
the
electron's
kinetic energy (i.e. temperature) and any external electric
field which may be present. The higher the temperature, or
the
greater the electric field,
the less energy
required
and the more likely it is that the individual electron will
escape. The
absence
of
second classical analogy,
an external electric field,
electron evaporation
from the metal.
25
applicable in
is one of
the
simple
The net effect is
to
II. Theory of Arcs: A. Power Balance
the metal;
cool
to
6dI-, where I-
the cooling power is
approximately equal
is the electron current and
the average cooling effect per electron.
Lee (and others),
- i
A
As pointed out by
1931].
Electronic Heat Ca2Ecity
result of
circuit
i
charge neutrality in the
the replacement
closed
electrical
ust
of the electron
the potential well by another electron.
from
[Lee,
numerically different from
1960: Holmes, 1974; and Compton,
II.A.11
- represents
"lifted"
This
second
has a maximum energy equal to the Fermi energy of
electron
particular metal plus kinetic energy corresponding to
the
the bulk metal temperature. The lost electron, however, had
a greater energy because of its higher temperature. Also,
as
mentioned above,
electrons with a greater energy
are
more likely to be the ones which escape the potential well.
Hence
an
energy loss has been experienced
equal
to
the
difference
in kinetic energy
by
of
the
metal
the
two
electrons. This is recognized as simply the electronic heat
capacity. This effect results in a cooling power equal
to
1.5 kB(TH - TC)I-/e, where TH is the temperature of the hot
and TC is the temperature of the cold replacement
electron
electron.
Figure
II.A.3 shows,
in a schematic form,
contributing to the energy equation.
26
the
processes
In Figure II.A.3
the
II.
Theory of Arcs: A. Power Balance
arrowheadindicates the direction of positive energy flow.
Figure II.A.3
CATHODE
(1) charge
ENERGY
particle
(2) neutral particle bc!barkment
(3) ohnic
heating
(4) plasma radiation
(5) plasma recamination
(6) plasma ionization
(7) bulk thermal radiation
(8) bulk thermal conductivity
(9) electrode
phase change
(10) work function escape energy
(11) electronic heat capacity
27
BALANCE
II. Theory of Arcs: A. Power Balance
Pcathode
the
may
be evaluated by writing the expressions
terms and algebraically
individual
summing
them
for
to
obtain a net power transfer.
Pcathode = Pcharged Particle * Pneutrals
* Pradiation
Presistive
Precomb
Pioniz - PBB rad - Pthereal cond
-
- PPhae
change - P
- Pe heat caPacitY
where,
(1)
Pcharged Particle '
(2)
Pneutrals
r En Nn * <dcxtvi> ni nn ei Vs,
(3)
Presistive
2
I1
R
(4)
PPlasma rad '
+
I
v
(Precoab rad
,
PPlasna
(6)
PPlasma ioniz
(7)
PB
(8)
Pthermal cond
%B
recomb
ni n
nn V
E
XI EI/m
dT4 ,
=
(T > Troom temP),
A k dT/dx,
28
(O < r < 1)
PBremastrahlung
Pline)
(5)
rad
Z
II. Theory of Arcs: A. Power Balance
(9)
PPhase change =
Hfusion dM/dt,
T
T melt
HvaPor
T
Tboil
dM/dt,
0,
otherwise
s 6-I-
(10)
p
(11)
Pe heat caPacitY = 1.5 kB(TH - TC)I-/e
where,
three body recombination coefficient cm6 /s]
q3B
nj
number density of species j3 cm-3]
ion, n
neutral)
(e = electron, i
Vs a volume of the near-surface
Vp
plasma volume
interaction
Ccm3 ]
Ccm]3
EI a ionization potential energy [J]
Z a ionization
level of atom.
The above is a generalized framework;
to
the
case at hand,
cathode,
and,
in
we want to specialize
namely that of power balance
particular,
a
cathode
spot.
proceeding we briefly describe the phenomenon of
of
a
Before
cathode
spots.
A cathode spot is a localized region of the electrode where
the
current
A/cm2.
In
density
is very high - of
order
106
- 108
photographs such spots are easily recognized by
the bright light emission. Figure II.A.4 shows several such
cathode spots.
29
II.
Theory of Arcs: A. Power Balance
Figure II.A.4
OPEN-SHUTTER PHOTOGRAPH OF CATHODE SPOTS
On
a microscopic level much remains unknown about
spots.
cathode
What
is known
spots.
Figure
is a
macroscopic description of
II.A.5
characteristics of cathode spots.
30
cathode
gives
several
of
the
II.
Theory of Arcs: A. Power Balance
Figure II.A.5
CATHODE SPOT CHARACTERIISTICS
diameter
10-50 microns
100 amps
spot current
total
Robson, 1978]
current density - 106 - 108 amps/cm2
spot temperature· 3300 K
spot velocity
10 m/s
vaporization rate X
60 ug/C
An
10
(copper)
(copper) CNcGlure, 1974]
Reece,
emitted electrons/atom
1963]
Kiablin, 1971]
(copper)
interesting feature of a cathode spot i
current associated with it.
Figure I.A.4,
This
Kimblin, 19733
(copper)
the
maximum
implies that, refering to
for a 200 amp arc discharge to pass
between
copper electrodes, two (2) cathode spots would be required.
The
This
two
spots would not coalesce
into one-200
amp
spot.
further implies a positive slope of the graph of
voltage across
through
them.
resistance
the electrodes versus the
In
short,
vacuum
arcs
to an increment of current.
current
have
a
Thus
the
passed
positive
vacuum
arcs
will burn in parallel with load sharing among cathode spots
assured.
Gas gaps and SCRs (silicon controlled rectifiers)
are
examples
two
ability.
two
Special
latter
of switches which do not
considerations
possess
must be made
for
this
these
switching elements when parallel operation
desired.
31
is
II. Theory of Arcs=: A. Power Balance
The
existence of cathode spots as areas of intense energy
fluxes prompts
a numerical tabulation of the total
and
flux
the
expressly
power
for
regions that
delineated
into
cathode spots and the
are not cathode spots.
two
power
columns:
other
for
one
similar
Figure II.A.6
lists
those processes confined to cathode spots.
Figure II.A.6
CATHODE SPOT PROCESSES
(1)
charged particles
(6)
ionization
(7)
black-body radiation
(8)
thermal conduction
(9)
phase change energy
(10)
work function escape
(11)
electron heat capacity
energy
Sufficient background material has been given
order
of magnitude calculations to be
to
ade of the
enable
several
parameters of interest. The various assumptions required to
proceed are detailed in Figure II.A.7.
We
calculate
for
the
applicable case of
32
a
10
kA
arc
II. Theory of Arcs: A. Power Balance
current. Given
the current the majority of the
numerical
parameters are available in the published literature either
specifically for vacuum arcs or as a material property. The
other
parameters are a function of geometry or are
simply
derivable from first principles of physics. The calculation
of
ean
free
paths of particles
in
the- interelectrode
plasma for the processes of ionization, charge exchange, et
cetera are first-principle calculations.
33
Theory of Arcs:A. Power Balance
II.
Figure II.A.7
ASSUMPTIONS
I
10 kA
r
0.5
Vi
- 43 volts
FOR NUMERICAL CALCULATIONS
PR&K,1965;
D&N,1969; see
also
Section II.A.1]
0.9 I Kiablin, 1971]
I-
1016 c-
= n
ni
3
[Boxnan, I.974;Kaneda, 1981.]
nn
1017 cm-3
Roece, 19632
na
1022 cm -3
tKittel, 1976]
1 ev
Tev
Vs " 2.5 c
Vp - 25 c
E = 7.7
TH
3
Ccopper,
ev
3300
=
3
Weasst, 197'4]
K
TC " 300 K
Hf = 250 J/g
CTouloukian, 1981]
6..3 kJ/g [ibid.]
Hv
dM/dt
= XI
X · 73 ug/C
.
0.9
k
0.8
Z
1
W/c
Kimblin,
1973.3
K
J = 5 x 106 A/cm2
CCobiae, 1955; Ecker, 19803
vn = 9 x 104 cm/s
6- = 2.6 eV tLee,
1960]
34
II. Theory of Arcs:
The
A. Power Balance
in Figure
of the calculations are presented
results
are given in
II.A.8. The details of the actual calculations
Appendix A. The notations used is as follows: Ptotal is the
Watts] of the electrode
surface power density
Fapot
W/cm 2]
is the power flux
(cathode),
spot,
of the cathode
Fnot is the power flux of the entire electrode
and
surface.
Figure II.A.8
CATHODE POWER CALCULATION RESULTS
Fnot
Fasot
Ptotal
(1)
charged particles(+)
(2)
neutral particles(+) 15_
(3)
Ohmic heating
(+) _2
kW
(4)
radiation
C.) _.3
kW
160 W/cm2
(5)
recombination
(+) 4
kW
____ __
(6)
ionization
(7)
black-body
(8)
(9)
___kW
_
kW
-) _7___kW
rad.
21s__w/_
(-)
100
W
thermal cond.
(-)
3.2 kW
phase change
(-) 6.6kW
620 W/cm2
_.5_MWLca2
200 W/cm2
3.3 MW/cm2
(10) work function
(-) 23
kW
j1.S__W/c m2
(11) e- heat capacity
(-) _3.5_kW
1.8MW/cag
35
II. Theory of Arcs: A. Power Balance
Several
conclusions can
Addition
of
the
total
be
drawn
power
from
column
Figure I.A.8.
indicates
that
approximately 24 kW of unbalanced power heats the cathode.
This
energy gain results in a bulk metal temperature rise
rate
of about 0.2 K/ms of arc duration.
Thus,
of the electrode
any
thermal mass
temperature rise
of
the bulk
prevents
metal. The
the
great
appreciable
cathode
pot
itself, however, is an entirely different case. The thermal
mass
of the cathode spot is,
Because of
in power
always
out
this fact,
of
balance
of
the cathode spot
balance. As an example,
temperature rise
This,
by comparison,
course,
by
a net power of
rate
would be
would
I
kW
quite small.
is
very
nearly
if the spot were
the
resulting
approximately 1000 K/us.
tend to equalize the
input
and
output power to the spot. In fact, this rise rate is of the
order, but less than, the rise rate experienced by the spot
itself during its formation. Early in the discharge, before
the
cooling mechanisms have been activated, the net input
power flux is of order 10 MW/cm 2 .
the
spot
than
kW,
1000 K/us.
This flux multiplied
area yields an unbalanced power gain of
greater
thus the rise rate of the spot is greater
be
than
Grissolm and Newton have conducted experiments
on anode spots with incident energy fluxes estimated at
MW/cm 2.
by
Their
10
observations show the rise time of spots to
of order of 2 us CGrissolm & Newton].
36
II.B Electrodes: Material Considerations
Phenomena
associated with the electrodes can be attributed
to either surface or bulk efects. These effects
criteria
for
material.
A list of selection criteria
II.B.1.
Following
view,
particular
electrode
is given in
other criteria
Figure
of
the
From a more practical point
including material
availability,
cost, machineability, amount of trapped gases, and
purity,
ease
the
Figure II.B.1 is an explanation
of each criterion.
importance
of
selection of
determine
safety of
and
handling,
are
also
important
considerations.
Surface Effects
II.B.1
~V!R2
The
vapor
material
ESSu!RES
pressure
is
the pressure associated with a given
at a specific (uniform) temperature at which
liquid phase and vapor phase
principle
hand,
per unit
the
exhibit detail balancing.
the
The
of detailed balancing, applied to the issue at
is as follows: as many atoms leave
velocity interval per unit
gaseous state
37
time
the liquid state
in transition to
II. Theory of Arcs: B. Material Considerations
FigureII.B.1
ELECTRODE MATERIAL SELECTION CRITERIA
Desired apect
Characteristic
Surface Effects
(1)
vapor pressure
(2) phase
low
transition temperature
(3) erosion rate
(4)
low
heats of transformation
(5) high
voltage standoff
ArMI
high
high
low
Effects
(6)
work function
low
(7)
arc stability
(conditional)
(8)
electrical conductivity
high
(9)
thermal diffuslvity
high
(10)
mechanical strength
high
38
I. Theory of Arcs: B. Material Considerations
as
leave the gaseous state per unit velocity interval
unit time
sense,
in transition
detailed
to the liquid state. In the literal
balance means each microscopic collision
process is balanced by the exact reverse process
and
Pitaevskii,
function
19811.
if
one
temperatures,
The
is
1000 K,
such
only
importance
as
well below typical
the vapor pressure of zinc is
zinc.
a
of
easily
At
a
cathode spot
0.1 atm. Thus,
this is not a vacuum arc
it is, in fact, a relatively high-pressure gaseous
burning in an ambient
capability
high
pressure
[Lifshitz
in regard to vapor pressure is
violation of our assumptions,
at all;
arc
vapor
a considers material
temperature of
in
The
of material and temperature.
material selection
seen
per
of cathode
extinguishing
of a gaseous arc isaseverly impaired due to the
pressure in the arc.
pressure o
atmosphere. The
Figure II.B.2 gives
the
vapor
various metals at temperatures characteristic
spots.
39
II. Theory of Arcs: B. Material Considerations
FigureII.B.2
VAPOR PRESSURES OF METALS
Boiling Point
Metal
Temperature(a)
(760 Torr)
(K)
(10-6 Torr)
(K)
Cd
1040
390
Zn
1185
450
Cu
2840
1120
Fe
3135
1300
Ni
3190
1340
Mo
4880
2080
W
5830
2660
(a) O'Hanlon, 1980
II.B.2 Transition Temperature
A high boiling point will have two related effects:
vapor
i) the
pressure will be lower at a given temperature
(see
above), and ii) a high boiling point means rapid cooling of
the
spot
because the
cooling mechanisms
increase
as
temperatures increase. With respect to the latter, however,
thermionic
electron emission
refractory metals;
too
high.
Rich
limits the utility of
in this case the boiling temperature is
has
noted
that
parameter in vacuum arc operations
(Rich,
scales
1971]. His observations
with
the
increasing
ultimate
is anode spot
limiting
formation
show the critical parameter
phase
40
the
transition
(melting)
II. Theory of Arcs:
.
aterial Considerations
temperatures.
11.8.3 Erosion Rate
The
rate
of
erosion of the
understanding the
Electrode
is
central
generates
to
the
of charge which passes through the switch.
words
each atom ablated from
a
to
performance limits of vacuum switches.
wear appears to be strictly proportional
total amount
other
electrodes
the
characteristic number of
cathode
In
surface
primary electrons
which carry the actual discharge current. At first thought
might seem contrary to expectations. Erosion
thls
determined
because
seen)
II.B.3
is
not
essentially
the spot is such a small thermal mass (as we
that
power;
by the spot temperature. This
is
it
its
is not
determined
by
is approximately at the boiling point.
shows
effective
temperature
experimental
cathodic erosion
have
input
Figure
rates
electrons/atom vaporization ratios for
a
and
wide
variety of metals.
II.B.4 Heats of Transformation
The cooling power per atom ablated is directly proportional
to
the
heat of transformation
of
the
metal.
Hnce,
a
material having a high heat of transformation tends to cool
the
cathode spot more readily than a material with a lower
heat of transformation.
41
II. Theory of Arcs: B. Material Considerations
Characteristics
(l)-(4) are
parameters;
a large extent they dtermine
to
all closely related
quasi-steady state response to a high
Section
in
ore
the material
incident energy flux.
II.E.3 will investigate the steady state
detail
theoretical
by introduction of
material
a
response
relatively simple
odel describing material ablation.
Fig.ReII.B.3
CATHODE EROSION
Met:al
RATES FOR VACUUM GAPS
Erosion Rate (ug/C)
Electrons/Atom
Cd
650
Zn
215
1.8
3.2
mg
35
7.2
Ag
150
Al
120
Cu
115
7.5
2.3
5.2
Cr
40
14
Ni
80
Fe
73
Ti
52
C
16
6.9
7.2
9.6
7.0
No
47
21
W
62
31
CKimblin, 1973;
Plyutto, Ryzkhov & Kapin, 19653
42
II. Theory of Arcs: B.
II.B.5
High yolg
aterial Considerations
S§tandoff
The ability to withstand high voltage can be summarized
measurements of
the
particular material.
upon
which
results
of
electric breakdown
a
strength of
In order to understand the paraneters
breakdown strength
work
by
previously
depends,
published
we
review
CRozanova
the
and
Granovskii, 1956].
Rozanova and Granovskii conducted experiments to
the
of
determine
relati-e ordering of various anode materials in
terms
increasing breakdown voltage. Figure II.B.4 shows
results of their-ordering (starting at the lowest
are grouped
breakdown voltage
together
breakdown
In Figure II.B.4,
voltage and increasing down the figure).
metals
the
if insignificantdifferencesin
were observed. The
interpretation of
their results lead to the widely quoted conclusion that the
electrical
strength
mechanical strength
of
a
vacuum
of the anode,
characterized by Young's modulus.
43
gap
if
depends on
this
strength
the
is
II. Theory of Arcs: B. Material Considerations
Figure II.B.4
METAL BREAKDOWN STRENGTH ORDERING VS. YOUNG'S MODULI
(breakdown strength increasing down the table)
Metal
Young's Modulus(S)
1 x 106 psi
C, graphite
Al
10
Cu
16
Fe, Ni
30
Mo, W
55
(a) Machine Design, 1983 Material Reference Issue, 14 April
1983.
Other work has tended to support this conclusion Erven, et
a,
1970]. Experiments on metals of the same composition
but
differing mechanical strengths have also verified the
above conclusion
stainless
Rockwell
CMcCoy,
1964]. McCoy, et
t a,
steel 304 in the hot-rolled condition
B
condition
scale)
and
the
(92 Rockwell B).
cold
rolled
The harder metal
and
al, used
(76 on the
annealed
consistently
had a higher breakdown strength.
It
should
be
systematically
electron
noted
that
related to
this
the
phenomenon
II.B.5 shows metals
44
not
electric field-enhanced
emission characteristics of
1980]. Figure
is
metals
£Farrall,
listed according to
II. Theory of Arcs: B. Material Considerations
increasing critical field values for electron emission and
the
critical electric fields. It is beyond the
this
thesis
scope
of
to investigate field-enhanced emission; the
results are
listed simply to complete the
discussion of
metal electrical breakdown strength. Note that the relative
order
of Figure II.B.4 has little bearing on the order
Figure 1I.B.5.
Figure II.B.5
CRITICAL-FIELD ORDERING FOR METAL ELECTRON EMISSION
[after Farrall, 19803
Metal
Relative Electric Field
No
1.0
Stainless steel
1.1
W
1.2
Cu
1.3
Ni
1.9
45
of
II. Theory of Arcs: B. Material Considerations
The
above
description applies
to
un-arced electrodes.
Electrodes which have been subjected to high current arcing
will
have suffered asperite formation.
Asperite formation
is an important process because excessive formation implies
a reduced interruption capability. The mechanism is FowlerNordheim electron emission due to surface features with
scale
radius of order 0.1 micron.
microprotrusions is
a
poorly
The formation of
understood
a
these
process. This
surface roughness, however, can be significantly reduced by
electrode conditioning. This is
usually accomplished by ion
bombardment and can increase the initial breakdown
by a factor of 2 or more
protrusion growth
initiated
during
CFarrall,
seems
to
the
arc
be
19801.
a
Unfortunately,
result of
discharge.
As
it
noteworthy
is
process
are
a final word concerning
that the
observed
processes
Consequently
conditioning of repetition-rated devices is not a
matter.
voltage
trivial
high voltage standoff,
results
of
a
conditioning
to deteriorate
in
time
tFarrall,
19803.
Bulk Effects
II.B.6 Work Function
The
work function plays an important role in
spot
large
scenario.
the
cathode
A large work function implies a relatively
cooling effect on the spot during electron
46
emission
II. Theory of Arcs: B. Material Considerations
(assuming
II.E.4,
Section
which
non-thermionic
the
potential.
emmission).
A
we shall
see
in
a model of arc stability is developed
in
work function is related to the
This
minimum
anode
model indicates that an arc will be
more
stable on a material of a lower work function.
II.B.7
Arc Stability
Arc
stability
arc
to
is to be interpreted as the ability of
continue
unstable,
i.e.
continue
the
interrupt,
Vacuum
arcs
become
when they lose the ability
fundamental emission processes which
current-carrying
1980.
carrying current.
the
particles
from
the
cathode
to
supply
CFarrall,
Arc interruption must be controllable to be useful.
Thus,
we
wish
the
arc to be reliably stable until
the
instant of interruption. Associated with arc instability is
a
large fluctuating anode voltage drop.
this
Minimization of
fluctuating voltage is also obtained by a
function
material.
As
closely
intertwined.
mentioned,
More
detail
these two
is
low
work
topics
provided
are
in
the
appropriate section.
Various
experiments have
determining
current.
experiments
the
Figure
average
II.B.6
been conducted with the
arc lifetime as
shows
the
a
aim
of
function
of
results
of
such
Farrall, 1980]. As pointed out by Farrall, the
47
II. Theory of Arcs: B. Material Considerations
metals appear in nearly the same order,
left to right,
they do in the vapor pressure plot,
Figure
plots
stability
related
metal
strongly
to
suggest that
arc
I.B.7.
is
the ease with which vapor is produced
Farrall, 1980].
Figure II.B.6
AVERAGE ARC LIFETIME AS A FUNCTION OF CURRENT
Fsarrall, 1980]
E
9GD
Z
aD
Current (A)
48
as
These
closely
from
a
II. Theory of Arcs=: B. Material
Considerations
FigureII.B.7
VAPOR PRESSURE AS A FUNCTION OF TEMPERATURE
CFarrall. 1980]
1n3
a
0.
0
We
have seen,
1000
0ou
Temperature('K)
in Figure II.B.6,
3000
that the arc lifetime is
strongly dependent on the arc current.
approaches zero in a normal sinusoidal
time
exists
obtained
when
is
Figure II.B.6.
this
4000
As the arc
fashion,
a point in
the time until the sinusoidal
greater
than the arc lifetime
current
as
zero
is
shown
in
Figure II.B.8 shows this schematically.
figure we have drawn a sinusoidal
half cycle
of
In
arc
current with horizontal lines whose length is proportional
to the average arc lifetime at the specific
current
level.
The length of the lines was derived from Figure II.B.6.
49
I]. Theory of Arcs=: B. Material Considerations
On average, when a certain amount of time equal to the arc
lifetime passes,
the arc suddenly interrupts:
that is the
meaning of the arc lifetime. The sudden arc interruption is
the
phenomenon
of
a
current
chop.
In
an
otherwise
sinusoidal current, when the value of the current reaches a
sufficiently low value, the current drops abruptly to zero:
it
chope" to zero,
parameter
lies
hence the name. The importance of this
in the inductive voltage
with a sudden change in current.
V
L dI/dt,
assuming
rise
associated
The inductive voltage is:
values for the circuit inductance of
L = 100 uH and current rate of change dI/dt = 10 A/us gives
a
voltage of V - 1000 volts,
well above the value of
the
anode-cathode drop voltage.
In
the
decay
absence of chopping phenomena,
the
plasma
with the diminahing sinusoidal current.
would
At a normal
current zero, this plasma would disperse due to its thermal
energy and time of flight characteristics.
scenarios can
When
a
subsequently occur;
current chop event occurs,
Two
neither is
a
large
different
desirable.
voltage
can
appear acroas a plasma which has not had time to decay with
the normal sinusoidal
ignition
second
and
current interruption is
scenario
interrupt. This
across
current. The net result is plasma re-
equipment
is
not
the case where the arc
forces
which
achieved.
current
the inductive voltage to
may not
50
have
been
The
does
appear
designed
to
II. Theory of Arcs: B. Material Considerations
withstand
a high voltage.
This,
obviously,
is a
safety
hazard.
The
two important parameters in a chopping event
the electrode material,
For
the
specified material,
the latter parameter
in
allows
discharge
is to be compared to the arc lifetime at the
current
a
(1)
and (2) dI/dt near a current zero.
estimation of the expected time remaining in the
which
are
chosen
level. This process converges to a "chop current"
non-linear fashion due to the
current
exhibited by the arc lietime,
sharp
dependence
on
as shown in Figure
II.B.6. It hould be remembered that the rate of change of
the
current
event;
is
however,
magnitude
of
intimately connected with
for
chopping
estimation purposes,
current
frequency of 60 Hz.
51
is
roughly
the
the
10
chopping
order
A
at
of
a
II. Theory of Arcs: B. Material Considerations
Figure II.B.8
ARC LIFETIME SIGNIFICANCE
I
I
/--
--
…-
tm)+
-- ---- I13----14
INSTANT OF CURRENr
.-
Electrical
11.B.8
power
Resistive
CWOP
Condugctiviy
is
dissipated
proportionately to the reciprocal
in
the
conductivity. Although
is a minor factor in the power balance
this
electrode
for
ordinary
it prevents some more exotic materials from useful
metals,
implementation.
II.B.9
The
the
Thermal
Diffusivity
ability of the bulk electrode internally to distribute
intense
depends
energy
on
the
flux deposited at the electrode
thermal
diffusivity.
surface
Hence, cool-down
between single shots or burst of shots could conceivably be
limited by the diffusivity. A correlation between .a thermal
parameter
and
gross anode melting has been noted by
52
Rich
II. Theory of Arcs: B. Material Considerations
tRich, et al, 1971]. That research group found, for a fixed
geometry
current
and frequency, the critical current
which
caused bulk
to
proportional
the
melting)
increased
"goodness"
thermal
(i.e. that
roughly
parameter
kth
strength
has
Tm/(K )1/2.
II.B.o1 Mechanical Srength
We
have
seen that the electrical breakdown
been related to the mechanical strength through the Young's
moduli. There are,
however, other reasons to use a
high
strength material. Large Lorentz forces may be generated by
interaction of the substantial currents and either self- or
externally-generated magnetic
fields.
In our
particular
device the electrode has been slotted along the z-axis
to
improve the
in
section
carry
interruption characteristics as discussed
III.D.
The result is cantilevered
the current.
material
with
good
In designs such as
mechanical
important consideration.
53
"fingers" which
ours,
choosing
characteristics
is
a
an
II. Plasma Physics
II.C.1 Plasma Processes
To a large measure the arc properties are determined by the
processes and
cathode
material. As
one
increases the
discharge current, however, the plasma, which envelopes the
spots,
cathode
an ever more important role in
plays
Taken
evolution of the arc.
be
by
seen
gas
pressure,
of
an
ambient
current carrying
contribute
even
or
higher
The essential difference is the lack
gaps.
presence)
(or
to an extreme, this can easily
atmospheric,
considering
the
which
environment
(ionized) particles.
can
As
the
desire
and
capability to use greater and greater
current
grows,
the
field
of arc discharges will
renewed
attention.
various plasma
The
in
Therefore,
plasma
this
section we
surrounding
a metal vapor arc has long been
Compton,
discharge work
order to investigate plasma
been done since then,
a
confused state.
transfer
the
from
yet,
Compton,
a
in early arc
19313, performed experiments
properties in an arc.
in
Much has
the field is still in somewhat
The lack of
effective
information
the realm of the physicist to the hands
engineer is,
confusion.
the
consider
properties and processes.
source of experimental uncertainty.
of
enjoy
in my view,
the primary cause
of
of
this
Therefore, to the end of improving the transfer
54
II.Theory of Arcs:
C. Plasma Physics
of information, a rather fundamental viewpoint is
this
section
so
that the salient points
taken in
not
do
become
bogged down in details.
Plasma Definition
A
may be defined as a collection
plasma
which a substantial
A
of
particles
fraction have a net electrical
of
charge.
further qualification of plasma is that there must be
large
number of charge-carrying
radius
equal
discussed
to
particles in a
the Debye length.
shortly. Electric and
forces on
The Debye
a
sphere
of
length
is
magnetic fields
the plasma particles in proportion to
exert
the
net
force.
The
particle charge.
Coulomb Force
Fundamental to
plasma physics is the Coulomb
Coulomb
force
is
particle
(simply referred to as a "charge") as a result
an electric field.
the
force
experienced
by
a
charged
of
This is true whatever the source of the
field: an external source or another charged particle. An
isolated
charge
infinite
space. The
infinite range,
will
affect another charge
Coulomb
that is,
force is said
anywh~r
to
have
charges very far away from
other
can influence one another.
which
causes
This aspect of
long range organized
in
an
each
plasmas,
plasma oscillations,
allows them to behave in seemingly strange ways. Collective
55
C. Plasma Physics
II.Theory of Arcs:
motions of the plasma are
has
of
ubiquitous; much theoretical work
been done in order to understand
It
plasma.
the
present
is
the collective
beyond the scope of
the
results of
work
modes
section
this
concerning
to
plasma
collective modes.
response of charged particles to an electric field
The
is
to
"shield" or cloak the source of the field from the rest
of
the
spatial
scale
plasma.
This
phenomenon occurs
and a certain temporal scale.
scale
ia called the Debye length, which
The
spatial
is,
roughly,
of the temporal scale is called the
reciprocal
frequency:
certain
a
plasma particle.
measure of the sphere of influence of a
The
a
over
plasma
The plasma frequency is the maximum oscillation
plasma;
any slight charge
frequency
of
a
nullified
in
a time of order
imbalance
frequency).
1/(plasma
is
The
product of the Debye length and the plasma frequency is the
characteristic particle velocity.
Even
at
this
early
point
in
the
development
description of plasma there appears to be
of
the
contradiction.
On one hand the Coulomb force is of long range, and, on the
other hand, the Debye length limits the sphere of influence
of
a
charge.
These concepts are
56
not
contradictory,
of
C. Plasma Physics
II.Theory of Arcs:
course,
complimentary. In
but
response to
electric
an
field, caused by a charge imbalance placed in a plasma, an
amount of charge equal in magnitude but opposite in sign to
the
imbalance localizes near the source of the
Hence,
viewed from a distance greater than
when
length from a charge
the
imbalance,
plasma has "shielded" the
schematically shows
this
no imbalance is
need
be
the Debye
detected:
imbalance. Figure
shielding phenomenon.
important to note that we have not depended on
collisions with
imbalance.
any particle of any kind;
aware of each other solely by
the
their pervading electric fields.
Figure II.C.1
DEBYE SHIELDING
1+
00
O
E
57
the
II.C.1
It
is
mechanical
particles
existence of
II.Theory of Arcsa: C. Plasma Physics
The equation
for the Debye length is given below:
LD= _.
We
briefly discuss the parameter dependence of the
length.
shielding
(Because the electrons
Maxwell's
to
discussing
electron
identification of
E
V/LD (we
we
confine
parameters.)
Div E = 4
equations we know
magnitude purposes,
LD). Then
perform the majority of the
function due to their smaller mass
ourselve&
Debye
ne2 .
have
From
For order of
anticipated
the
the scale length with the Debye
length
V/LD 2. Using the equation for LD we find
Div E
the order of magnitude of voltage is V = kT/e.
This
occur
represents
the (scale) voltage variation
over distances of order LD;
which
may
if we attempt to impose
externally a voltage greater than kT/e,
the plasma shields
the
This
voltage
within
a distance of LD.
important implication for
differences which
distance
parameters
order
of
order
shows
10-5 cm.
occur
LD.
vacuum arcs:
in
has
the
a
potential
the arc column occur
Calculation
that LD is quite
for
small
very
in
a
typical
arc
- typically
of
Since the arc column itself is much longer
58
II.Theory of Arcs:
than
LD,
C. Plasma Physics
the ma3ority of the voltage drop occurs
comparatively small
CCompton,
results
seemed quite
only a small
Hence,
field exists over moat of the arc
experimenters
a
distance and only a small voltage drop
occurs over the bulk of the distance.
electric
over
intrigued by
column.
Early
this
result
1931]. A large electric field at the plasma edge
from the concentration of the voltage drop over
a
relatively short distance. As we have mentioned in Section
II.B,
this
emission
The
has implications for
field-enhanced electron
for electrode materials.
other
significant parameter in the
Debye length is the plasma density
Debye length decreases;
formula
n. As
n
for
the
increases the
physically the explanation is
that
more electrons are available in a given volume to take part
in
the
shielding
distance.
As
and so shielding occurs
a parenthetical note
it
in
a
shorter
may be noticed
that
the
charge of the shielding particle enters the expression
for
LD.
Particles with
a
greater charge
shield
more
effectively.
In
summary,
the
plasma
shields
an
externally
imposed
voltage in a distance of order LD.
Ionization
Ionization
occurs
when
an
electron
59
from
a
previously
II.Theory of Arcs:
C. Plasma Physics
neutral particle obtains sufficient energy to overcome
the
ionization potential. The departure of one electron leaves
a
net
charge of
multiple
times
of
charges
1 on the new ion.
in
order to
2 or +3 and so on.
create
Ionization can
particles
Accumulation
occur
with
net
of sufficient
energy to overcome the ionization barrier need not occur in
a
single collision.
In fact,
it can be shown
Zel'dovich
and Razier, 1966] that atoms initially pass through excited
states. Hnce,
with
it is subsequent collisions of excited atoms
energetic
electrons which produce ionized particles
ECompton, 1931]. This
process can be schematically
written
as in Figure II.C.2.
Figure II.C.2
PLASMA COLLISIONAL PROCESSES
A + e
--> A
+ 2e
(ionization)
Am * e
--> A
* 2e
(excited atom ionization)
A+
e
--> A
A*
e * e -- > A + e
A+ + B * e --> A
A
A
--
A
h
(radiative recombination)
B
(ion-electron-electronrecomb)
(ion-noutral-electron
A
recomb)
(charge exchange)
The charge state of the ion is indicated by the (+).
particle is underscored,
and an atom in
energetic
excited state is denoted by an asterisk.
60
An
an
II.Theory of Arcs:
C. Plasma Physics
Recombination
The
process of ionization has a logical
that
of
recombination.
As
reverse
discussed
in
process:
Section
II.A,
different types of recombination are of differing relative
importance
in different regimes of the plasma
Three types of recombination
parameters.
are shown in Figure II.C.2. At
material surfaces the ion-neutral-electron recombination is
most
important and in the plasma volume the radiative
ion-electron-electron recombination are
C^EsThe
and
most important.
Eashaag
charge exchange
process is
schematically shown
in
Figure II.C.2. In contrast to ionization and recombination,
charge exchange does not change the relative populations of
the interacting species.
Instead, charge exchange changes
the energy distribution of the species. As indicated by the
underscore
a
neutral
in Figure II.C.2, an energetic
and
Alternatively,
itself
to
neutral the
ion.
In either event,
energetic neutral and a
an
mention
this
neutrals
the
excess
energy.
an electron leaves the neutral and attaches
the
produce
potential
gives
ion collides with
process
hump
the
because in the
lack of
CDavis and Miller,
the result
low
energy
is
to
ion.
We
discussion of
observed
charge exchange
1969] has implications on
61
the
the
II.Theory of Arcs:
C. Plasma Physics
spatial volume occupied by the high energy ions.
Radiation
The
power
balance aspects of radiation have already
discussed in Section
II.A.
What has not
been
been
discussed
is
the emission process.
Bremastrahlung
particles.
A
is
the
radiation
produced by
charged
particle with a net charge radiates
energy
when accelerated. When two charged particles influence each
other
to
through their Coulomb fields they radiate
their
acceleration. The most common
attractive
force
according
example
between an assumed stationary
is
the
ion and
a
moving electron. The electron is deflected from a straightline
path due to the Coulomb force, hence is
accelerated
and hence radiates energy.
The
existence
specific
neutral
atom.
an
collision
meta-stable
small
implies radiation
This
type
of
radiation
because only specific lines or
emitted. If the
in
excited atoms
wavelengths according to the particular
radiation
not
of
is
excited
called
line
wavelengths are
excited atoms radiate too quickly, they are
excited state long enough for a
to ionize them.
If the excited atom
subsequent
attains
state then the intensity of radiation will
because
at
the transition rate is
62
small.
a
be
Hence, the
II.Theory of Arcs:
significance of
radiation will
vary
characteristics of particular atoms.
originate
at
any
C. Plasma Physics
according
Because
available surface they
to
such
are
the
atoms
frequently
impurities and the resulting radiation is called
impurity
radiation.
Any
material
at
a
finite
temperature
radiates
energy
according to the black-body formula. The plasma temperature
is in excess of 12,000 K.
Thus,
radiation emitted would be quite
the reader may assume the
large.
the arc-plasma is optically thin,
radiation
optically
i
almost
thick,
the amount of black-body
insignificant;
black-body
if the
radiation
significant arc cooling mechanism.
63
However, because
plasma
would
were
be
a
II.Theory of Arcs:
C. Plasma Physics
Collisionless-Collisional Effects
Interruption
quickly when
of
vacuum
arcs is observed
an already
observation is
in
occur
CLafferty,
contrast to
the
very
passes
low current density arc
a zero value of current
through
to
1966].
relatively
This
lengthy
interruption time for gas gap switches.
A
high
pressure gas
gap
arc
must
rely
upon
recombination in order to quench the plasma.
the
charged
particles have a lifetime
milliseconds
long.
Voltage
recovery must
extinction of the charge carriers, else
As
Essentially,
is
several
await
vacuum
the
the arc re-ignites.
stated previously, the metal vapor vacuum arc
relies
for
which
volume
switch
upon surface recombination in order to quench
arc.
Two physically distinct processes must
this surface recombination
the
occur
to extinguish the arc on
a
time scale faster than gas gap extinction.
The
first
extinction
process
is
surface. This
which must
occur
before vacuum
the transport of the plasma to
fundamentally can
happen in
collisional process or it can happen as
process. In the low density plasma
a
arc
a
material
an
ordinary
time-of-flight
(as opposed to the dense
cathode
spot regions) the mean free path for atoms can
greater
than 1 mm.
be
This means that the plasma has roughly
64
II.Theory of Arcs:
ten
collisions
be
described by
theory.
tranversing
the 1 cm electrode gap. This can
either a
collisionless or
Because the number of collisions
of the two
results
Essentially,
then,
theories
do
not
speed
Thus approximately
vacate
the
gap.
collisionless
is
small,
differ
plasmd
1971].
model of the arc
therefore
gap
The
tPR&K, 1965; and D&M,
1 us is required for the
Our
the
greatly.
Miller,
thermal velocity is of order 106 cm/s
to
collisional
particles leave the interelectrode
with nearly the time-of-flight
1969].
C. Plasma Physics
as
accounts
a
plasma
quasi-
for
the
experimentally observed extinction times. Moreover, similar
gas gap calculations clearly show the effect of a diffusion
dominated
process. Figure
calculation for
II.C.3 shows
the
comparitive
a collisionless theory
and
collisional
theory for vacuum arcs,
and the collisional
theory for gas
gaps.
Figure I I.C.3
COLLISIONLESS AND COLLISIONAL THEORETICAL RESULTS
Vacuua Arcs
(n = 1016 cm-3, v
tcollisionjss
' d/v
tcollisional
a d 2 /4D
Gas Gapa
(n
106
6 cm/8)
a 1 us
2 us
1019 cm-3, T = 1000 K)
tcollisional
a d 2 /4D
65
= 1
s
II.Theory of Arcs:
Another
aspect of
C. Plasma Physics
that
interparticle collisions is
of
collisions between different species. We have already seen
Bremsstrahlung radiation as an example
of
inter-species
collisions.
A
logical
question,
then,
concerns the length
between collisions for the plasma particles.
of
time
If we assume,
temporarily, that the plasma is 100l ionized (no neutrals
to
worry
times:
about) then there are three important collision
(1) electron-electron collision time,
collision
time,
(2)
ion-ion
and (3) electron-ion collision time.
The
above times are listed in increasing order. The large mass
ratio
of
mi/me
is
responsible for
the
variation
in
collision times. The time scale of interest determines the
significance of the relative collision times.
The
important
events
of a vacuum arc occur in
times
of
order magnitude microsecond. Cathode spot formation and arc
extinction, as we shall see,
are examples
of events which
occur in a few microseconds.
The electron-electron
and ion-
ion
substantially less
than
collision times
are
a
microsecond for typical plasma parameters. The electron-ion
collision time, however, is of order microseconds. This has
66
C. Plasma Physics
II.Theory of Arcs:
the implication that the electrons and ions have reached an
state
equilibrium
but
individually,
are
they
not
in
equilibrium with each other. The energy and momentum states
of
the electron and ion distribution fungtions are not yet
coupled on these time acales: the different species
not
had time to "know" about the other species.
As
a result,
the electrons and ions have quite
have
different
The electrons have a
very
fast collision time and so are described approximately
by a
energy
distribution
Maxwellian
functions.
distribution function
temperature. The ions,
the
square
with
distribution function. However, it is
distribution
the
ions
function
wel,l-defined
having a collision time varying as
the mass ratio, have
of
a
a
quite
not
a
different
Maxwellian
[PR&K, 1965]. Thus the temperature of
is not well-defined. The average energy per ion is
still a valid concept and it is to this that one must refer
for
meaningful infcrmation concerning the ions.
The
next
section gives approximate collision times in order to give
the reader a feeling for the times involved.
Potential
Tanberg
HumR2
CTanberg,
systematically
1930]
investigate
was
the
the flux of high
from a vacuum arc. More recently, PR&K
and Miller
D&M,
first
researcher
energy
to
ions
PR&K, 1965] and Davis
1969] conducted extensive studies of high
67
C. Plasma
II.Theory of Arcs:
energy
ions.
They
different ions,
also
measured
ionic
of
high
established.
states of
It
energy
ions,
The existence of
therefore,
has been suggested PR&K,
seems
ions.
ions.
a
supplies
The concept of a potential "hump" offers
explanation of the existence of high energy
a
well
1965] that
localized region of high potential exists which
these
several
finding multiple ionization states. They
easured the energy of the ions.
source
Physics
an
A sketch
of the potential hump profile is shown in Figure II.C.4.
Figure II.C.4
POTENTIAL HUMP PROFILE,
CATHODE
As
the
ANODE
current is increased,
potential hump
PR&K
CPR&K,
the formation of
seems possible and has been
1965].
an
anode
suggested by
Figure II.C.5 shows schematically
form for an anode potential hump.
68
the
II.Theory of Arcs:
C. Plasma Physics
Figure II.C.5
ANODE POTENTIAL HUMPFORM
ly,
v
CATHODE
According
voltage
ions
to
is
are
ANODE
Mitchell
[Hitchell,
greater than the
19703,
when
ion kinetic energy,
prevented from
reaching
the
the
arc
cathodic
anode.
"Ion
starvation" results and the arc voltage rises. This creates
a
region of intense ionization
anode. This mechanism would
immediately in front of the
[Mitchell, 1970] cause an anode
potential hump.
We should emphasize that corroborating evidence for
potential
humps
is
required before
their
anode
presence is
assured.
In
some
Section II.E.5 we give a theory of potential
detail.
collisional
Two
cases
of
plasma are considered
69
humps
quasi-collisionless
in that section.
in
and
C. Plasma Physics
II.Theory of Arcs:
II.C.2 Plasma Characteristics
In
section we list the numerical values
this
The rationale for doing this is
vacuum arc plasmas.
the
reader
parameters
some
and
typical
idea of the order of
also
to indicate that
of
t
give
magnitude
of
the
there
a
is
wide
variation of these parameters (orders of magnitude, in some
cases)
in different regions of the arc.
Examples of widely
varying parameters are the neutral density, and the cathode
energy fluxes.
Figure
that,
I.C.6 shows some typical plasma
where
appropriate,
we
parameters. Note
specify the
region of
applicability.
Figure II.C.6
VACUUM ARC PLASMA
PARAMETERS
electron temperature - 2 ev (20,000 K)
ion energy (averaged) - 30 eV
electron-electron collision time - 0.2 ns
ion-ion collision time - 10 ns
electron-ion collision time - 200 na
Debye length - 10-5 ca
plasma frequency - 300 GHz
plasma density - near electrode - 1018 ca-3
- in gap - 1016 cm-3
gap mass density- 10-5
g/cm3
current density - 5 x 106 A/cm 2
Thus,
in a microsecond, an average electron would have had
70
II.Theory of Arcs:
C. Plasma Physics
5000 collisions with other electrons; an average ion would
have had 100 collisions
electron
and
with others ions;
but the
ion would have collided only 5
average
times. Note
that these collision times scale roughly as the square root
of the mass ratio
Braginskii, 19653.
71
II.D Interruption Mechanics
II.D.1 Natural Commutation
Metal
vapor
themselves
vacuum arcz will naturally tend to
interrupt
by a variety of processes unless the plasma
is
continually being regenerated due to power dissipation in
the switch. Some of these interruption processes are:
ion
recombination, surface recombination, gas dispersion, etc.
Once the switch current has gone to zero,
either by forced
or a natural current zero, power dissipation
commutation
in
the switch instantly vanishes. Switch interruption is then
simply a matter of the charge carriers re-depositing on the
electrodes or other surrounding surfaces before bulk
dissipation and subsequent
to
recover. This
inertia problem.
dispersed
plasma
generation has a
can be thought of as a
power
chance
simple
thermal
The thermal inertia of the plasma must be
before a new conduction cycle starts in order to
interrupt successfully the switch.
For precisely the
same
reasons that a metal vapor vacuum switch has low losses,
has
a
very low thermal capacity.
metal
vapor
three
orders
Figure
vacuum
of
This is exactly
why
switch has interruption times
magnitude less than a
gas
II.D.1 summarizes the effects that
gap
a
about
switch.
influence the
innate ability of a vacuum switch to interrupt.
72
it
II. Theory of Arc: D. Interruption Mechanics
Figure II.D.1
FACTORS INFLUENCING NATURAL VOLTAGE RECOVERY
Factor
vapor pressure
Effect
highvapor pressure implies
copious
vapor emission
peak current
increase in erosion products
electrode purity
thermal expulsion of trapped
contaminant gases
current duration
bulk heating of electrode
decreases cooling by
thermal conduction
Tm(kp Cp)1/2
increase of erosion products
time rates of change
of current and voltage
allowable escape time decreases as
rates
of change increase
electrode separation
requiredescapedistance
increases,
condensation solid angle decreases
thernionic emission
emission through current zero,
may provide initial electrons which
re-ignites plasma
asperite formation
enhanced Fowler-Nordheim field
small atomic mass
increased particle velocity
emission
CFarrall, 1980; Kamakshaiah
and Rau,
Farrall, 1965; Rich and Farrall, 1973]
1977,
Miller
and
II.D.2 Magnetic Interruption
Instead of relying completely on passive
73
means for
plasma
II. Theory of Arc: D. Interruption Mechanics
dissipation
one can consider using
removing
the
some active
metal plasma from the gap.
Magnetic
appear to be the ideal way of accomplishing
fields
means
of
fields
this.
Magnetic
can exert extremely high forces in very short
scales. For example, in our lab we have generated
100,000
pounds
thrust in a
five
time
in excess
microsecond period'
CMongeau, 1981]. Furthermore, magnetic fields can
these
forces
obstructing
exert
at a distance thus avoiding the problems of
the
contaminating
electrical
for
arc
the
during
vacuum
normal conduction
environment.
In
or
of
addition,
control allows active intervention with precise
timing.
Most work to date with metal vapor vacuum arcs in
fields
has
£Graneau,
magnetic
involved the use of quasi-steady state
fields
1981; Poeffel, 1980; Heberlein and Gorman, 1980;
Gilmour,
1980]. The background magnetic field is generally
used
spread and distribute the arc
to
over
the
entire
electrode surface area thus preventing intense heat
and
so
postponing
the formation of arc channels
consequent creation of gross melting.
extends
the
spots
and
the
The background field
current-carrying capabilities of
the
switch
beyond passive interruption levels of operation.
A
much more dramatic use of magnetic fields
literal
removal
of the metal plasma from the
74
involves
gap
the
during
II. Theory of Arc: D. Interruption Mechanics
commutation.
the plasma
on
In this
ode Lorentz forces ("J cross B") act
directly,
either simply evacuating the
region or increasing the arc length if there i
gap
a vestigial
current flow and thereby increasing the effective voltage
drop of the gap.
only
Since this arc manipulation
is
desirable
durin! the interruption phase, one must use
pulsed
magnetic fields to achieve the desired interruption time.
All
Lorentz
field.
forces require both a current and a
In a vacuum arc,
current as
the
magnetic
one can use the normal discharge
source current
and
the
self-field
it
generates as the source field. This is the mechanism used
in
the
"instability"
19813. Alternatively,
interrupted
switches
currents can be generated by inducing
an additional current in the switch-plasma
itself contribute
CSchoenbach,
to the switch current.
that does not in
Similarly, source
fields can be generated by external coils which do not rely
on
the
cross
self field of the switch.
Four combinations of
B forces can be generated depending on
whether
current J is an arc current or an induced current,
field
is
either a self field or an external
II.D.2 summarizes these four approaches for
J
the
and the
one.
Figure
the
coaxial
geometry where the electrodes are like two cups facing each
other.
75
r
II. Theory of Arc: D. Interruption
One
should keep in mind from the figure that for the cases
he normal arc or self field,
employin,
will
for
peak.
the Lorentz force
to zero during a natural current
go
useful
current
configuration in
II.D.2 which can operate as a commutator is case
both the source current and field are not
the
main
arc
discharge
we
have
being
This is the configuration
elected to
experimentally
4
dependent
conduction current,
generated by an outside coil.
which
a
is
such a mode of operation is unfeasible for
However,
Figure
where
This
zero.
interrupters which interrupt near
normal commutation. Therefore the only
on
Mechanics
on
concentrate.
Although
there are other geometries which can magnetically
commutate
(such as rectilinear)
be
because of its structural
beat
the coaxial one appears
simplicity
and
strength.
Figure II.D.2
MAGNETIC-INTERACTION CONFIGURATIONS
i
J
If
J
El
76
T extt
®
arc
to
high
II.
Mechanics
Theory of Arc: D. Interruption
II.D.3 Kinematic Interruption Analysis
Given a complete detailed design of the final
configuration and
of
the
An
switch
system
calculation
purposes
of
is
very
contains the
informative
kinematic
exact
to a pulsed magnetic
introduction.
A
II.D.3.
and
is
it
aided
schematic of the magnetically
is shown in Figure
detailed calculation;
is
to analyze the
gap plasma in response
electrical
field.
parameters,
relevant
the
straightforward
relatively
response
all
experimental
is
simplified
presented
Appendix C presents
the present calculation,
for
a more
however,
fundamental physics. Essentially, the analysis
equivalent to finding
the induced current in a
transformer secondary which in our case
Once the current is established
is the
shorted
gap plasma.
we siamply apply the Lorentz
by the pulsecoil to find the time it takes
forcegenerated
for the plasma to be swept clear of the gap
characteristic
region. Using
plasma parameters we find a sweep time of
can be accomplished
lessthan ten microseconds
of about one kiloGauss.
77
with a field
4
II. Theory of Arc: D. Interruption Mechanics
Figure II.D.3
SIMPLIFIED SWITCH SCHEMATIC
I X
L
The
pulse
I K I
RA
7I
coil is driven by an auxiliary capacitor
bank.
The voltage induced in the secondary, which in this case is
the plasma itself, can be expressed a:
V
dd/dt u _
2' dB/dt
C
Assuming a sinusoidal excitation frequency (w = 27tf),
complex amplitudes are:
Vo = fr 2 wB 9 &
This voltage generates an induced current:
VO
Io Z
Z is the complex impedance expressed as:
Z
2
78
the
II.
where
R
and
L
Theory of Arc: D. Interruption Mechanics
are
plasma
the
torus
resistance
and
inductance, respectively. The radial force density acting
on the plasma is:
f
For the
to
a
IB/(s2 c)
J x B/c
back of the envelope".calculation
assume
peak
r
an average acceleration equal to
acceleration.
(Appendix C
assumption;
an
several
of
the
average
acceleration, the
allowance
d
Combining
the
does
one-half the
not
I
t
distance,
a
d,
the
this
of
constant
plasma
is
is:
t 2 /(4r
B
make
is made for radial variation
above parameters.) Assuming
accelerated in a time
magnetic
it is sufficient
2
c).
above equations we arrive
field amplitude Bo necessary to
at
the
minimum
.splacethe
arc
in the specified interruption time:
BO
This
2
t
minimum field
frequency
II.D.4.
At
asymptotic
d
B---'3
c 2yR 2
(L)
r r2 w
2
j
1/2
j
is plotted as a function of
excitation
with interruption time as a parameter in
large frequencies
limit of:
79
Figure
the minimum field reaches an
II.
Bo =
Theory of Arc: D. Interruption
Mechanics
LJ 0 5
d2
Figure II.D.4
MAGNETIC
FIELD
REQUIREMENT
E-
W
in
tr= 1ls
E-,
't~= 2,us
0
.\
, -&-
\
-e
512-
W
PW
U
I-4
10'
6
10
EXCITATION FREQUENCY (Hz)
These asymptotic fields
are of order of a few kilogauss and
are readily generated externally.
80
II.E Theoretical Extension
In
aspects of
chapter we investigate several
this
We
arcs.
theory
of
either
have
phenomena
attempt to explain
not previously been explained or
the
which
provide
we
alternative explanations for phenomena for which confusing
or unphysical explanations exist.
we wish to create
in a particular situation,
Because,
as
simple a model as possible yet retain the essential physics
the situation, we frequently rely
in
inherent
on
well-
established experimental results. An example is our use of
the
experimentally observed average cathode spot
for
metals.
of
usefulness
agreement
We
use this information to
our
by,
model,
demonstrate
instance,
for
current
the
showing
between theoretically predicted results
and
experimental results.
The
topics
which
chosen include one
occurs very early in the
time-dependent phenomenon
discharge,
two
phenomena
which are quasi-static, and a final phenomenon which occurs
during
extinction of
the
discharge.
In
essence, this
section
amounts to examing four special cases of the power
baianc.
discussed in
different
physical
Section
II.A.
conditions
situation.
81
We
which
consider
dominate
the
each
II. Theory of Arcs=: E. Theoretical Extension
II.E.1 Cathode Spot Radius and Formation Time
We
postulate
Adoption
of
adiabatic
heating
of
a simple one dimensional
the
cathode
model leads
spot.
to
the
following equation for energy balance:
U
MsPot Cp
=
V =
scale distance
(i.e.
where,
The
P t
Mspot
II.E.1 shows
T,
A x.
the spot radius)
is
x.
Figure
the one dimensional model. The distance
which a specified temperature is obtained
is denoted by
at
T.
Figure II.E.1
ONE DIMENSIONAL MODEL FOR CALCULATIONS
F= P/A
The
above
initiation;
equation
before
applies
other
82
immediately
loss
after
mechanisms
the
arc
become
II. Theory of Arcs: E. Theoretical
Extenaion
The one dimensional modelis applicable to the
significant.
extent that:
x <
(A "
The heat flux at the spot surface is assumedconstant
to F
equal
Vi J
and
= ViI+/A.
The one dimensional solution for the heat flux is given by
Carlaw and Jaeger
f(x,t)
where,
Caralaw and Jaeger,
= F
erfc(x
1980]:
2
0 - k/* Cp.
This equation shows that at xD
2 /' t'),
f(xD)
0.16 FO.
The scale distance for Diffusion is xD. A graph of erfc(z)
is shown in Figure II.E.2.
FigureII.E.2
GRAPH OF f(x,t)/F
= erfc(z)
N
U
a)
.0
0.5
83
&I
.0
II. Theory of Arcs: E. Theoretical Extension
As
a reasonable approximation to the temperature T we
aterial oiling temperature under
the
pressure:
The
when
T
TB; then XT
condition of adiabatic
include the
atmosphere
of
xB-
heating
imposes the constraint that XB
must
one
use
to the
boiling point
XD. However, if xB > xD we
energy involved in the latent heat
of
vaporization, which is the largest contributor to the phase
change
energy.
We
vaporization in
do
this
not include
the
calculation - we
material up to the boiling point.
latent
merely
In sum,
heat
heat
of
the
our requirement
is:
xB
=
Xcrit ;
XD
this occurs at time tcrit-
Our two equations in two unkowna
xcrit
2
(xcrit and tcrit) are:
tcrit
and
tcritViJ
= xcrit
Cp(TB - Tamb).
These equations are graphed in Figure II.E.3
84
II. Theory of Arcs: E. Theoretical Extension
Figure II.E.3
DIFFUSION AND BOILING DISTANCES VS. TIME
(ONE DIMENSIONAL MODEL)
1'
/
II
I
I
I
I
-CCT
Car
The solution to these equations is:
cri
t
I
22
tcrit 2{TA
f
=
We
identify
Xcrit = rapot;
T
r
that is the
spot
radius
is
determined by adiabatic heating. Beyond the critical radius
(within
metal
it
spot
the
constraints
of a one dimensional
model)
tends to boil away faster than the heat diffuses
- hence
we have adiabatic heating.
formation
predicted by our model
85
The time scale
is
the
to
of
tcrit. Figure
II. Theory of Arcs: E. Theoretical
II.E.4 shows Xcrit and tcrit for a variety of
Extension
metals.
The
input energy flux is that which is experimentally observed.
Hence,
our
analysis
is
self
consistent
experimentally
observed input parameters,
predict
parameters
other
observed.
This
strongly
which are
suggests
we are able
also
that
- given
to
experimentally
our
model
does
actually apply to the real physical situation.
Figure II.E.4
TABLE OF CRITICAL DISTANCES AND TIMES
(ONE DIMENSIONAL MODEL)
Metal
Xcrit
tcrit
Al
10 um
0.6 us
Ag
20 um
1.0 us
Cu
20 u
1.7 us
Fe
5 um
0.4 us
Ni
5 um
0.6 us
15 um
2.0 us
W
The
results
of
this
simplified
calculAtion
allow
significant conclusions in spite of the limitations of
the
model. If the identification of xcrit as the spot radius is
made,
the
agreement
with the experimental
cathode
spot
radii is quite close. (See Figure II.A.5 for characteristic
cathode
spot
identification
parameters.)
of
the
Furthermore,
spot formation time
86
is
if
taken
the
as
II. Theory of Arcs: E. Theoretical
tcrit,
then
Extension
the times listed in Figure II.E.4 are of
correct order of magnitude,
but are too small by a
the
factor
of roughly 2 to 3 compared to observations made by Grissolm
and Newton
Grissolm and Newton,
investigating
of
10
surface
flux
anode spots,
19743. Although they were
they calculated an energy flux
mega-Watts per square centimeter incident upon
of the electrode.
used in our case;
distinguish
This is the same
magnitude
the
of
our one dimensional model does not
between an anode spot (radius of order
1
cm)
and a cathode spot (radius of order 10-3 cm) when they have
the same input energy flux. Agreement to within this factor
is
considered acceptable.
The physical interpretation
of
this
too-rapid
spot formation is the lack of
appropriate
spot
cooling mechanisms. This stems from the
limitations
imposed,
extend
for
simplicity,
the
mechanism,
model
to include
all
If one
time-varying
were
to
cooling
then the spot formation time would certainly be
larger
than
model,
however,
simplicity.
actually
on the model.
that given in Figure
has
validity
Additionally,
in
reasonable
the
II.E.4.
This
physical
and its beauty lies in
results
agreement
of the model
with
its
are
experimental
measurements.
In
summary,
we
consider
the application of
a
constant
energy flux to a localized area. Initially the thermal heat
87
II. Theory of Arcs: E. Theoretical
flux via conduction is large;
the
however,
as time progresses
rate of advancement of heat flux slows:
t
Extension
after a
time
2(, t)0.5.
the flux has diffused a distance XD
total
energy deposited on the area increases
time.
This
The
linearly
in
energy raises the temperature of the thermally
active material to approximately the boiling point. Because
the
of
total energy increase linearly in time but the
heated
time,
time t
4tl
material increases only as the square
volume
root
of
If,
at
the heated volume increases in temperature.
the volume averaged temperature is T1, then at time
the volume averaged temperature is 2T1.
continues
until
the
temperature
f
the
This
process
heated
region
reaches the boiling point. This state is described by xcrit
and tcrit.
A
parallel
occurs
pan.
situation
commonly encountered
in
the
when a stick of butter is pushed into a hot
The
butter
heats
adiabatically
conduction through the mass of butter.
88
- not
by
home
frying
heat
II.E.2 Ablation Theory
We
have developed a simple theory describing material loss
from
the
cathode
due to an intense energy
essentially a steady-state energy balance.
the
model is
the
receding surface.
flux.
It
is
Mathematically,
formulated in a coordinate frame moving
with
This has the effect of producing
temperature profile which appears stationary to the
a
moving
observer.
Analyses
there
is
surface)
of
this type are quite common in problems
relative
motion
of
and a lab coordinate
a
"fluid"
system.
(the
is mathematically identical to the space
entry
problem.
craft
the
occupants or instruments. In the vacuum
arc
the
mechanism
to the cathode spot.
cathode
material
ablates
as
a
As we shall see,
dimensional model predicts the surface recession
surface
effective
re
either
problem,
The
the
In the re-entry problem the heat shield is
to ablate as a cooling mechanism for
spacecraft's
ablating
Specifically,
model
designed
where
cooling
the
velocity.
recession velocity allows calculation
ablation coefficient.
The theoretical
one
of
an
ablation
coefficient may then be compared with experimental ablation
coefficients.
The. ablation coefficient multiplied by
89
the
j
II. Theory of Arcs: E. Theoretical
Coulombs passed through the device
number
of
amount
of removed material.
reasonably
good
refractories.
refractories
In general,
agreement
for
all
Extension
yields
the
the results show
except
metals
The reasons for discrepancies concerning the
stem from the simplifying assumptions of
the
model and are discussed.
We assume an intense energy flux.
as
a
one
dimensional
steady
The problem is idealized
state
model.
The
energy
"reservoir" is the total enthalpy change experienced by the
The total enthalpy change
metal.
rise of the metal,
and
the
includes the temperature
the phase change energies of the metal,
ionization of the ablated vapor from the
cathode
spot.
Figure II.E.5 shows the model used for calculations.
Figure II.E.5
SCHEMATIC FOR ABLATION CALCULATIONS
HEAT
FLUX
Z = Vx/o
a
90
II. Theory of Arcs: E. Theoretical Extension
The one dimensional heat equation is=:
pdj
g =2a (1§ 2a
Zs
In steady state we have=:
TpC,
=
a
Cp
A
Applicable boundary conditions are:
T(xsO)
Tboil ,
dT(x-00/dx
T(xWO)
Tamb
0
Integrating the steady state heat equation once we find:
The boundary condition at x
C1
Tamb
A second integration
where
allows evaluation of C:
yields=:
(T
= k/ Cp.
The boundary condition at x=O allows evaluation of C2:
C2 =
In
(Tboil - Tamb)
91
-
II. Theory of Arcs: E. Theoretical
Extension
The expression for T(x) can then be written as:
T(x) - Tamb
The
net
heat
flux
(T boil - Tamb) exp(-Vax/W )-
is that in
excess
of
the
ablated,
vaporized mass:
FO - pVaHabl
Fnet
This
energy
-k dT/dx - tVaCp(Tboil - Tamb)
conservation equation can be solved
for
the
surface recession velocity Va:
Va = FO/Habl
Hfg + fHI,
Heare Habl
energy,
+
Cp(Tb - Ta)].
where Hfg is
HI is the ionization energy,
the
phase
change
and f represents the
ionized fraction of the evolved vapor.
The
rVais numerically equal
quantity
to
the
number
of
grams of ablated material per square centimeter per second.
Experimentally
cathode,
X,
device.
The
material.
one
per
can determine the mass lost
Coulomb
value
of
charge passed
from
the
through
the
of X is assumed constant for
a
given
This is easily understood when the following
is
realized: (1) several cathode spots burn in parallel with a
certain
maximum
current
per spot,
inertia of the spot is quite small.
total
and (2)
the
thermal
By (1), increasing the
current merely increases the number of active
92
spoba
II. Theory of Arcs: E. Theoretical
Extension
but has little influence on the spots already
established.
Point
than
(2) means
microseconds
the
that
for
times
greater
spot has reached a
quasi-steady
a
few
stat ,
Furthermore, it has been demonstrated experimentally that X
is
approximately a constant for currents less
12 kA
The
Kimblin,
1973; Mitchell,
quantities
1
Va
identical. Hence,
and
XJ
than
about
1970].
are,
then,
conceptually
we can determine a theoretical ablation
coefficient, Xth, and compare it with the experimentally
determined coefficient, XexPt.
The
incident
Kimblin's
energy flux F
result
of
Vi J+
the ratio of ion
O.1 X Vix J,
where
current
total
to
current was used. The equation which determines Xth is:
Xth =
Va/J = 0.1 Vi/ECp(Tb
- Ta)
Hfg
fHT],
or,
Xth = 0.1 Vi/Htot.
Parameters
required
to evaluate Xth are given
II.E.6.
93
in
Figure
II. Theory of Arcs: E. Theoretical Extension
Figure II.E.6
EVALUATION PARAMETERS FOR Xth
Metal
T boil
(K)
Vi (V)
Htot(kJ/g)
Cd
1040
17
3
Zn
1184
13
6
Ag
2436
20
10
Cr
2945
18
33
Cu
2945
20
17
Fe
3135
20
21
Ni
3187
20
22
Ti
3562
20
24
C
4100
20
150
Mo
4880
28
22
W
5828
25
16
94
II. Theory of Arcs: E. Theoretical Extension
Figure II.E.7 details the evaluation of Htot,
Figure II.E.6.
as given in
Figure II.E.7
ENTHALPY
Metal
Cd
Zn
Ag
Cr
Cu
Fe
Ni
Ti
C
Mo
W
Cp T
(kJ/g)
0.2
0.4
0.5
1.2
1.0
1.3
2.9
1.7
1.9
1.2
1.4
CHANGES FOR
Hfg
(kJ/g)
0.94
1.9
2.4
7.0,
4.9
6.5
6.6
9.1
60
6.5
4.7
95
ABLATION
fHI
(kJ/g)
1.5
3.5
6.7
Htot
(kJ/g)
3
6
10
25
33
11.5
17
13.5
21
12.5
22
13.6
24
89
150
14.2
22
9.4
16
II. Theory of Arcs: E. Theoretical
Figure
II.E.8
experimental
compares the theoretical results
results
for
the
ablation
Extension
with
the
coefficients
of
several metals.
Figure II.E.8
ABLATION COMPARISON: THEORY VS. EXPERIMENT
Metal
Xth(ug/C)
Xexpt(ug/C)(a)
Cd
610
650
Zn
225
215
Ag
200
150
Cr
54
40
Cu
120
115
Fe
95
73
Ni
91
80
Ti
80
52
C
13.5
16
Mo
126
47
W
156
62
(a) Kimblin, 1973
Reference
to
Figure
II.E.8 shows
that
reasonably
good
agreement obtains between ablation coefficients
determined
experimentally
and
determined
theoretically,
based
ablation
coefficients
on steady state energy balance.
The
two notable exceptions to agreement are the refractories
96
W
II. Theory of Arcs: E. Theoretical Extension
and
Mo.
It
will alro be noted that the metals
with
the
lowest boiling point, Cd and Zn, exh.bit the most favorable
agreement.
The limitations of the model account for this
discrepancy.
We have neglected the effective work function. Thus, if the
electron
called
emission mechanism for typical metals is the
"T-F",
19603,
and
emission
then
or field-enhanced thermionic emission [Lee,
if
the
temperature
required
for
current increases with increasing work
one
may
refractories
so-
expect the relatively
to
rely on an
electron
high
work
constant
function,
function
emission
mechanism
number of emitted electrons
increased
different than T-F.
Similarly,
if
the
significantly with respect to the number of ions,
then the
cooling effect of the effective work function due to
electrons
can
experimental
emission
no
data
longer
be
[Kimblin,
ignored.
19733
In
we
abbreviation
to
indicate
e/a.
roughly
20
emitted electrons per atom
For
by
the
experimentally-
determined constant ratio of ion current to total
97
to
from roughly
electrons/atom).
In order to retain the
the
electron
per ablated atom for W and Mo to be about two
electrons/atom
brevity,
fact,
indicates
three times that of more typical metals (i.e.
10
these
current,
II. Theory of Arcs: E. Theoretical
the
average
Extension
ionization state of the ions is also
doubled
(i.e.
Because
this model does not account for the cooling effect
of
work
the
coefficients
from
<Z> of about 1 to (Z>
function,
which
it
naturally
the
e/a
from
Figure
coefficients of Figure II.E.8,
between
our
experimental
2).
ablation
are too large for metals which emit
theoretical
ablation
II.B.3
shows
ablation
coefficients,
a
In this case, our
are high by about a factor of 2.
ratio
about
predicts
relatively high proportion of electrons.
predictions
of
roughly
with
Comparison
the
improved
ablation
agreement
coefficients
as
the
of
ratio
and
e/a
decreases.
Figure II.E.9 shows this correspondence between e/a and our
ablation theory.
The figure reveals good agreement between
our results and experimental
7.0. Fair agreement
results for an e/a ratio up to
is obtained for an e/a ratio up to 14.
98
II. Theory of Arcs: E. Theoretical Etension
Figure II.E.9
CORRESPONDENCE OF ABLATION THEORY
AND
EMITTED ELECTRONS PER ATOM
Obviously,
Metal
e/a
Xth/XexPt
Cd
1.8
0.94
Zn
3.2
1.05
Cu
5.2
1.05
Ni
6.9
1.14
C
7.0
0.84
Fe
7.2
1.3
Ag
7.9
1.3
Ti
9.6
1.5
Cr
14
1.4
Mo
21
2.7
W
31
2.5
a
more complicated model could be
constructed
which would exhibit even better agreement with experimental
results.
Thus,
our model clearly has limitations,
but it
also has advantages.
The
first
predict
advantage
of
the
model
is
its
ability
theoretical ablation coefficients and obtain
99
to
good
Extension
II. Theory of Arcs: E. Theoretical
to fair agreements with experimental results.
The
advantage
second
of
the model
in
lies
model
the
The model is analogous to spacecraft re-entry
formulation.
ablation models. By formulating the cathode erosion in this
way, it is hoped that the essential physics is self-evident
and,
that
further,
between
transfered
a useful analytical technique can
the
disciplines of
science
be
and
engineering.
A third advantage is the additional insight afforded by the
For instance,
model.
to
contribution
ionization.
enthalpy
average
The
has
clearly
the
Figure II.E.7 shows that the largest
is
that
due
to
ionization state of
the
plasma
of
the
energy
impact on the
an
change
magnitude
required for ionization.
Kimblin
range
1973] showed that for metals with a wide
Kimblin,
of physical properties,
the ratio of ion current to
total current was a constant roughly equal to, but slightly
He defined an ionized fraction,
less than, 10.
f, of atoms
which are ionized:
I.
Kimblin
from
=
derives
his
efXI/m
.
values of f for a wide variety of
ablation
experiments
100
[Kimblin,
metals
19733.
Extension
II. Theory of Arcs: E. Theoretical
Unfortunately, Kimblin does not pursue this concept, except
to correct f for an average ion charge. The corrected value
fc is:
fc = f/cZ>
Physical
are:
restrictions
<Z>
1, fc
1, 0
<
f < 0.
Specifically, Kimblin does not tabulate I+/I = efX/m. This
would
have
tended
to
reinforce
the constancy of the ratio I/I.
his
point
Moreover,
concerning
the fact that
efX/m = constant can be used for further analyses.
To
the extent that the ionization potential dominates
the
enthalpy change, we can write:
Htot = fHI ,
where HI = EI/m and El is the ionization potential per atom
(7.7 eV for copper) and m is the ion mass (64 x 1.7 x 10 -24
g
for
copper).
Assuming f = 100%,
we have
for
copper,
Htot = 11.5 kJ/g.
Substituting this
equation into our previous
theoretical
result we have:
Xth = 0.1 Vi/fH I
-
Using this in the defining equation for f we get:
101
II. Theory of Arcs: E. Theoretical Extension
I+/I = 0.1 = efX/m = (ef/m)
(0.1 Vi/fHI)
Cancelling terms we find the following equation:
EI = eVi
Thus,
steady
in
state,
incident
ion
creating
another ion.
the
is sufficient
energy
deposited
by
each
to ablate and ionize
an
atom
This is as it should be:
in steady
state the plasma is able to regenerate itself exactly.
The
fact
that Kimblin found the ratio of ion
current
total
current to be constant for a wide variety of
means
that
constant,
the
incident
independent
ion
energy
is
to
metals
approximately
of current. That this is true is seen
as follows.
The
equation
below
expresses
charge
and
energy
conservation:
I./I = constant
= efVi (J+/J)/Emf(EmI/)]
,
or,
I./I = eV i (J+/J)/EI = constant.
Thus,
to
the extent that the ratio of the relevant areas,
A. and A, is constant,
we find:
102
II. Theory of Arcs: E. Theoretical
A+/A = constant
Extension
= eVi/E I
It must be remembered that EI represents a weighted average
of the ionization
potential.
constant
eV i ,
<Z> ),
constant.
the incident ion
Moreover,
for
ionizational potential,
twice
Thus since EI is constant
typical
energy,
metals,
(for
is
the
also
second
E2, is greater than, but of order,
the first ionization potential,
El:
E2 = 2E1 *4E.
Thus, neglecting for a moment the energy4E,
we expect that
up to <2> = 2 the ratio of I+/I will remain
constant.
The
third ionization potential is usually much higher than 3E1,
thus as current is increased we eventually would expect the
production
of
of ions to be reduced relative to the
current.
At this point,
the ratio of ion
increase
current
to
1970]
have
total current would be reduced.
Reece
Reece,
1963]
and Mitchell
Mitchell,
experimentally observed a change in the arc characteristics
and
erosion rate at currents exceeding 12 kA.
current
level
Mitchell
Mitchell,
which
the
current.
required.
arc
The
production
the arc
of
voltage
substantially
increases
the
"ion
concept is the following one:
to increase,
more
this
increases.
1970] has termed the current
voltage
ions
Above
level
starvation"
in order
input
at
energy
for
is
The ions receive the increased energy by falling
down the larger potential well.
103
The increased arc voltage,
II. Theory of Arcs: E. Theoretical
Extension
the potential well in this model, is a direct
which creates
res:-lt of "ion starvation."
In
we
summary,
have
balance
energy
dimensional,
developed
a
model
steady
state,
describing
one
cathode
erosion. The theoretical results are in fair agreement with
results.
experimental
the
energy
balance
Taking note of dominating terms
has
led to
an
explanation
constant arc voltage for modest currents,
phenomenon
of
ion
104
the
and further, the
starvation has been discussed
context of energy balance.
of
in
in
the
II.E.3 Potential Hump Theory
have
Ions
substantially
been observed to attain energies
higher than the anode potential
PR&K,
1965;
D&M,
19693.
One explanation for the origin of these energetic particles
is
the
of
formation
a
hump
potential
the
in
plasma
surrounding the cathode spots.
We
have
predicts
plasma
flux
simple
a comparatively
theory
the existence of a potential maximum
immediately
surrounding
cathode
the
idealized by a one dimensional,
is
problem
model.
developed
which
within
the
spot.
The
state
steady
This model conserves particles and charges. The ion
to
the
cathode
is
by
determined
particular
the
collisional regime.
In
the quasi-collisionless
we assume a particular
theory,
ionization fraction (of neutral vapor).
ion
The
flux is directly related to the ablated neutral
ion
velocity
distribution,
Poisson's
are
In this case,
determined
is
which
is
given
the
flux.
potential
self-consistently
Boundary
equation.
from
the
conditions
from
which
required to form a mathematically complete problem are
explained in the model.
By using perturbation
techniques,
we obtain an approximate analytical solution. Under certain
conditions,
the
results
show formation
105
of
a
potential
II. Theory of Arcs: E. Theoretical
maximum
Extension
in the space charge region immediately outside the
origin of the neutral vapor. In order for hump formation to
occur,
the ionization mean free path for neutrals must
be
less than or of order of a Debye length. This restricts the
allowable
plasma densities which will support a
potential
hump.
The
collisional theory is also based on a one dimensional,
steady
state model.
Particle and charge
obeyed. In the collisional
by
a
balance between the accelerating electric field
determined
The electric field
by the ambipolar condition.
an ion density profile which exhibits
and
is
We give an example
a local
This allows calculation of the perturbed ion
perturbed
is
model the ion flux is determined
the retarding effect of collisions.
of
conservation
maximum.
density.
potential is then calculated and shown to
The
agree
with observations.
Quasi-Collisionlesa Hump Theory
The quasi-collisional theory is based on a one dimensional,
steady
state
obeyed.
The
model.
Particle and charge conservation
ionization
fraction depends on
material
[Kimblin,
utility,
we wish to assume a specific ionization
which
is
1973;
the
PR&K,
19653.
representative of many electrode
106
For
is
cathode
greatest
fraction
materials.
An
Extension
II. Theory of Arcs: E. Theoretical
100.
of the ionization
choice
appropriate
about
such as
of materials
is representative
This fraction
is
fraction
copper, nickel, iron and others.
we assume only
Because this is a quasi-collisional theory,
point deserves some comment.
It is well known
Cobine,
which
temperature
Essentially,
For
to satisfy this
1955] that the electrons have
corresponds to an energy less than
ionization potential of most metals.
well.
This
electron impact ionization must occur.
single
assumption,
ionization
ions.
collisions to produce the required
sufficient
Thus,
single
the
impact
potential
is quite unlikely except deep in the
example,
a
if we assume a Boltzmann distribution
for the electrons, the fraction of electrons which have the
energy E I is approximately
appropriate
of
3
eV
is
electrons
ionize
If E I is the value
(7.7 eV) and an electron
assumed,
then the
is less than 8x.
and Razier,
multiple
to copper
exp(-EI/kTe).
percentage
It has been shown
1966] that formation
temperature
of
eligible
Zel'dovich
of excited atoms
through
electron collisions is the most expedient way
atoms when the electron temperature is too low
to
for
single impact ionization. Hence, this assumption should be
regarded with suspicion and considered a possible source of
error
is
when detailed comparision with experimental
performed.
Nevertheless,
results
for simplicity, we retain the
use of this assumption.
107
II. Theory of Arcs: E. Theoretical
Because
the electron flux from the metal is
Extension
approximately
ten times the neutral flux [Kimblin, 1973], we neglect the
increased electron flux arising from ionization. We assume
the electron flux is roughly constant.
At
this
neutral
point
flux
electrons
In
and
the ionic
flux.
have few collisions,
are determined
- V.
we have established
simply
and V
equality
Since
the
the respective
by the conservation
this equation
total energy,
the
the
ions
and
velocities
of energy:
K is the kinetic energy,
V(x) is the potential
(For the case of ions, U = V
of
K = U
U is
the
distribution.
is the potential at which the
atom was ionized - neglecting the neutral kinetic energy.)
Poisson's equation is the equation which closes the
This
allows
self-consistent evaluation of
the
model.
potential
distribution.
Our methodology may be summarized as follows:
(1) the neutral flux determines the ionic flux,
(2) the
potential
distribution
determines
the
ion
velocity,
(3) the ion velocity
and the ionic flux determine
density,
108
the ion
II. Theory of Arcs: E. Theoretical
(4)
ion
the
the
determines
density
Extension
potential
distribution,
(5)
as
potential
in
an
iterative
distribution
scheme,
a
self-consistent
must agree with that used
in
(2)
above.
The time dependent particle conservation equations are:
by +v r
~-s
Simplifying to one dimension dependence and assuming steady
state conditions
we get:
Direct integration yields the following results:
V~
109
II. Theory of Arcs: E. Theoretical Extension
We assume a neutral density dependence of:
nA(x)
where,
we
=
nAo exp(-x/R),
R is the neutral ionization mean free path.
have
Since
vA
neutrals the neutral velocity
force-free
is
constant.
The particle fluxes are then:
r
=
nAO vA exp(-x/R)
i=
-nao VA exp(-x/R)
e
We
10 nAo
ni(x)
vi(x)
A - nAo VA exp(-x/R).
have used the condition that the electron flux
times
the
=
(assumed)
that
results
total current
Figure
of the ion flux.
of measuring
Kimblin,
II.E.10 shows
This condition is
ion current as
a
is
based
fraction
ten
on
of
1973].
a schematic
fluxes.
110
representation
of
the
II. Theory of Arcs: E. Theoretical
Extension
Figure II.E.10
QUASI-COLLISIONLESS PARTICLE FLUXES
fT
e-
0o
r'
Assuming
10 >> 1),
the
electron
is
flux
roughly
constant
we neglect the second term in the electron
equation:
e
=
10 nAO
A = ne(x)
ve(x).
The electron velocity is given by:
ve = (2V(x)/m)0 -5
and the ion velocity
(kT/m)0.5 ,
is:
v i = (2Z[V
- V(x)J/M)
Then the ion density is given by:
111
0 -5
(e.g.
flux
II. Theory of Arcs: E. Theoretical
ni(x)
n
=
Extension
va ex(-x/R)
Vo - V(x)]0 -5
[2Z
Poisson's equation is:
= d 2 V/dx
V''
Substitution
of
self-consistent
As
=
-417
= -4~7e(Zni
- ne).
ni and ne into the above equation
determination
allows
of n i, ne, and V.
an illustration of application of this methodology,
analytically
technique.
potential:
of
2
solve
the
equations
by
a
perturbative
We use the following boundary conditions on the
V(x=O) = 0, and dV(x=O)/dx
=
Eemission.
The use
the electric field at the boundary x=O is motivated
the
electron
1980;
we
Lee,
emission process.
1959]
have
Several
authors
estimated the necessary
Ecker,
electric
field which provides the observed electron current.
their results here.
by
We use
Numerically, we have Eemission =
-
2 x
107 V/cm = - dV/dx.
The equation for V''(x) may be written as:
V''(x) = -C g(x)
where
C
contains the constants
f,2x)
V(x)/Vo,
C
involved.
then:
4e
nAo VA/(2Vo/M)05 ,
112
If
we
define
II. Theory of Arcs: E. Theoretical
Extension
and,
i7(J7
g(x) =VZ exp(-x/r)/(1-f(x))0.5 - lOiV
where,
ke
z
(kT/Vo) 0
thermal velocity.
from
0 to x,
small.
is
the
dimensionless
electron
We integrate in a straightforward manner
where x is restricted for the present to
Since
sufficiently
5
- ke)),
V(x=O)
small.
=
O,
we
may assume f
We assume, for simplicity,
0
O
for
be
x
Z = 1. Then
we have:
dV/dx
- (dV/dx)x=o = C [tI - 10 (m/M) 0
-5
I23
where,
I1 =
p(-x/R)
dx
= x
,
(x
R)
and,
I2 = fdx/ke
= x/ke
Thus,
V =
dx dV/dx
V = (dV/dx)x=o - 0.5 C x2
This is of the form:
V = Ax - Bx 2 ,
where,
A = V'(x=O).
113
1 - 10 (m/)O-. 5 /ke].
II. Theory of Arcs: E. Theoretical Extension
This
form satisfies our boundary conditions (as it
and furthermore,
p
2osterior
our approximation f(x-O)
for x sufficiently small.
O0 is
Our
must),
ustified
expansion
is
valid for x < R.
As in quantum mechanics,
Bx2
one may now use the form V = Ax -
and iterate to a solution.
The mathematical details
quickly become overwhelming. Resort to numerical methods is
the
usual
recourse.
Discussion of numerical
methods
is
beyond the scope of this section.
In
summary,
we
have
presented
a
simplistic
quaai-
collisionless theory of potential humps. Although it may be
argued that the model is not realistic,
the basic
physics
are more easily understood in a simple model. An analytical
solution
is given which is valid for x < R,
where R is the
neutral ionization mean free path.
In a simple way we can demonstrate conservation of
charge.
The time dependent equation is:
+ V'-J O.
d/dt
In steady state we have:
?-J
=
-Ji
V-Je
=
0.
For arbitrary x we can write the current densities
114
as:
II. Theory of Arcs: E. Theoretical
J
= e
Je
=
Extension
,
and,
-e
The expression
.
for the total current density
is:
Jtot = Ji + Je = -10 e nAo vAHence, we have
r'Jtot=
O and J is less than zero, that is,
to the left, as it should be for electrons
right.
115
traveling
to the
II. Theory of Arcs: E. Theoretical
Extension
Collisional Hump Theory
The
theory
for
dimensional,
particles
balance
the collisional hump is based
steady
and
state
current.
between
model.
The
on
model
a
conserves
The ion flux is determined
the accelerating electric field
one
by
and
a
the
retarding effect of collisional drag. The electric field is
determined by ambipolar diffusion.
For
be
simplicity we assume only singly ionized particles
present.
to
Then the increase in the flux of electrons is
equal to the increase in ionic flux.
Denoting the particle
mobilities by ud and the diffusion coefficients by
D,
we
have the following for the individual fluxes:
ri =
i ni E - Di
ni,
and,
re=
pe no E - De Vne.
The conditionA'
= rj leads to the following
the electric field E:
E
Dl_=_-_Den_....
pjuni- ene
Poisson's equation can be written as:
H'E
where,
'(x) =
dE/dx = 4f,
e ( ni(x) - ne(x) ).
116
equation for
II.
Theory
of Arcs: E. Theoretical Extension
We define nl(x) as a perturbation
to the ion density:
nl(x).
ni(x) = ne(x)
At this point, we make several simplifying assumptions:
Fnl << Vni Fne,
Di << De
Pi << pe
We consider
Neglecting
justified
·
nl/ni < 1. Then we have:
the
gradient
of
the
electron
by the large electron thermal
temperature,
conductivity,
we
get:
(kT/e)d2 (ln n)/dx2 = -fenl(x)
or,
kT/(4fne2 ) nd2 (ln n)/dx2 = -LD2 n d2 (ln n)/dx2 = n(x).
To recapitulate, we use the ambipolar electric field as
a
forcing function. The different diffusion rates of ions and
electrons
the
cause an electric field which tends to
inter-species loss rate.
perturbation,
nl(x).
This gives rise to a density
The above equation,
117
equalize
subject to
the
II. Theory of Arcs: E. Theoretical Extension
assumptions mentioned, allows calculation of nl(x).
As
an example of use of this theory,
let us assume an ion
density profile which exhibits a potential hump.
calculate
hump
shall
nl(x) and show that the existence of a potential
results.
intitial
We
Thus,
density
although
profile,
we have chosen
the fact
hat a
a
special
hump
results
reinforces the theory.
We assume the following form for n(x):
n(x) = no (R/x)0 -5 (1 - exp(-x/R))
The resulting equation for n(x)
-X (')=--X'
Figure
(%)
II.E.11
is:
o
(I -e,
462--;--1
its
shows these two profiles.
quite evident.
118
kS
s
The
3~~~
L5S
humps
are
II. Theory of Arcs=: E.
Theoretical
Extension
Figure II.E.11
SAMPLE POTENTIAL HUMP DENSITY PROFILES
n (x)
x/R
I
We can estimate the height of the potential maximum.
For a
rough approximation we can use the following expression for
V:
V
where,
L2 ,
nl,max = 0.3 no ,
no
L
The result is V
of
4renl]max
1018 cm-3 ,
6 LD
8 x 10-6 cm.
This is the order of magnitude
35 volts.
the experimental results.
119
II. Theory of Arcs: E. Theoretical Extension
Dersity Restriction
The
of intense ionization must be less than or
region
order
of
achieves
Debye
plasma
a
Debye length.
is
This
because
of
plasma
the
quasi-neutrality over distances of order of
the
on
the
length.
density
This
condition puts a restriction
which is a necessary
condition
for
hump
existence. This condition may be written as:
LD
R
is the neutral mean free path,
where, R = vA/(n d ye)
and,
LD is the Debye length.
Our restriction has now become:
n > 4e
2
rVA1.
kT d'2 Lve
Inserting
typical parameters,
as given in Figure II.E.12,
we find the critical density for hump formation to be:
n
6 x 1017 cm-3 .
Figure II.E.12
CRITICAL DENSITY PARAMETERS
kT = 3 eV
c
~ 10-15
vA/ve
c
10-3
120
2
II. Theory of Arcs: E. Theoretical
PR&K
PR&K,
19653 have calculated hump densities of order
of the above critical density.
was
made by Davis and Miller
An interesting
D&M,
19693.
charge
exchange
collisions.
Two
observation
They noted the
lack of low energy ions in the particle flux.
few
Extension
This implies
complimentary
explanations exist which explain this observation:
(1)
the volume of the hump is quite small - it should be
of order LD3,
(2) neutrals and ions do not co-exist;
high (100%)
cathode
potential
formation in the
spots.
collisional
a
we have presented two theoretical models of
hump
collisionless
has
ionization fraction.
In conclusion,
potential
the hump
One
model,
model.
humps
theory
plasma
was
surrounding
based
on
a
the
quasi-
while the other was based on a fully
The
results
can easily form.
shown
indicate
The condition
of
that
hump
formation establishes a minimum plasma density. Approximate
numerical
values of hunp parameters are in good
with observation.
121
agreement
II.E.4. Arc stability
The
vacuum arcs have
advantage
unique
is the
mechanisms
switching
currents
on
equivalent
faster
current
ability
ratings,
and
(2)
alternative
(1)
to:
time scales than other
interrupt
devices
interrupt
with
larger
interruption
comparable
than other devices with
currents
over
time scales.
The
mechanism of arc interruption is not fully
at
present.
We
have
seen
in
phenomenological
experimentation
EFarrall, 1980].
The
been
materials.
pressure
These
conducted
been
different
for
plots have then been compared with vapor
plots [Farrall, 1980].
obtained
that
of this research has
of currents versus average lifetimes
plots
been
product
II.B.2
Section
has
understood
Good correspondence
between the a posteriori
observation
has
that
high vapor pressure materials can withstand a lower current
for
a longer period of time than can a low vapor
pressure
material. No specific model has previously been proposed to
explain this correspondence.
The
basic reason for interruption of the
shrouded
remains
create
a
very
extinguishing
in
phenomenology.
simple
arc.
model of
Our
basic
122
arc,
section
we
transfer
in
an
is
energy
In this
energy
premise
therefore,
that
II. Theory of Arcs: E. Theoretical
Extension
conservation must be obtained in the arc for the arc to
stable.
We
rely
in
introduced
on
Section
the
energy
II.A;
transfer
limit
we
be
mechanisms
to
ourselves
interractions occurring at the cathode spot.
Refering
to Figure II.6 for cathode spots processes yields
the following energy balance equation:
PsPot
Pcharged Particle - Pioniz
-
The
PPhase change - P
-
PBB red - Pcond
- Pe heat caP-
terms in the equation are as defined in Section
Because we are assuming an extinguishing arc,
that
we
II.A.
suggest
moat of the terms on the right hand side of the above
equation are negligible.
Specifically,
change
energy
we neglect residual ionization and the phase
because the arc simply does
not
have
the
a
few
excess energy to vaporize and ionize neutrals.
The
spot
temperature has
microseconds. For
a
time
scale
of
all but the fastest rates of change the
spot is in a quasi-static state.
Thus the spot temperature
falls as rapidly as required by energy conservation. Blackbody
emission,
of course,
falls as the fourth power
and
thermal conduction also becomes negligible. (In fact, in an
123
II. Theory of Arcs: E. Theoretical Extension
arc
which had previously obtained steady state
conditions,
can
thermal
conduction from the bulk to the
occur due to the falling spot
supply
needed
effect.)
energy.
Energy
conduction
Our
temperature;
simple
model
spot
this
neglects
may
this
to replace the electron heat capacity
is
ignored because the spot temperature falls rapidly.
In
essence,
then,
we have an energy balance (PsPot =
0)
expressed by:
Pcharged Particle
The
physics
follows:
function.
expressed by this equation can be
the
sufficient
= P.
incident
stated
charged-particle energy
is
as
ust
to overcome the effective material cooling work
Thus,
the incoming ions carry enough energy
continue the supply of electrons,
to
albeit near-zero initial
velocity electrons.
The
dispersion time for the plasma occurs on a time
of a few microseconds
(D&M,
1969; Farrall,
potential
hump
also
Lafferty,
19663. Other researchers
19803 have found that collapse
occurs on a
scale
time
scale
of
of the
a
few
microseconds. Thus, the cathode spot, plasma, and potential
hump all have roughly the same, quite fast, time scale. The
effect
this
has is (1) the ions impact the cathode
124
(near
II. Theory of Arcs: E. Theoretical
Extension
arc extinction) with not the potential hump energy, as they
do
during quasi-steady state conduction,
the anode potential,
recovery
phase
particles
exit
(2)
after
but with
merely
the plasma is continuously in
a current peak
(i.e. more
the arc than enter the arc per
a
plasma
unit
time
interval after a current peak).
Explicit
representations
the energy
for
fluxes
are
as
follows:
Fcharged Particle
F
Kimblin
the
'
= Vi J+,
eff J-
Kimblin, 1973] has done a rather complete study of
fraction of current carried by ions.
His results show
that approximately 10% of the total current is ion current,
independent of current. Applying his results to the case at
hand
provides
the following relation
between
the
anode
potential and the effective cooling function:
Vi
This
relation
should
work
be
states
9
eff.
that the
minimum
anode
potential
directly proportional to the effective
function.
Furthermore,
higher potentials
cooling
are
more
likely to be unstable than lower potentials. Thus, we would
125
II. Theory of Arcs: E. Theoretical Extension
expect
higher work function materials to be more
with respect to low energy inputs.
unstable
An alternative point of
view is to use the general, non-linear, V-I relationship to
determine
V
continuation
at
a given I.
is energetically
9
If this V <
unfavorable
eff
then
arc
and the arc
will
spontaneously interrupt. For a positive V
relationship, a
material
function
with
extinguish
a
more
larger
quickly
effective
work
than a material with
a
will
smaller
effective work function.
Lee
Lee,
function
1960] has determined the effective cooling work
as a function of
temperature,
field,
and
work
function.
His results show that the effective cooling work
function
is approximately 2 eV less than the ordinary work
function under representative conditions.
Figure
II.E.13
comparison
shows
a
tabulation
of
the
results
of
of the above simple theoretical explanation for
arc chopping at low currents - and hence low voltages.
126
II. Theory of Arcs: E. Theoretical
Extension
Figure II.E.13
COMPARISON OF ARC STABILITY THEORY FOR METALS
Arc Voltage (a )
Metal
deff(b)
(Arc Voltage)/6eff
Cd
11 V
2.1 eV
5.2
Zn
13 V
1.8 eV
7.2
Cu
20 V
2.4 eV
8.3
Ag
20 V
2.3 eV
8.7
W
25 V
2.55eV
9.8
Mo
25 V
2.6 eV
9.6
The theoretical model
(Arc Voltage)/deff
9.
(a) Kimblin, 1973
(b) after Lee,
1960;
Although
the
experiment
described
eff
agreement
is,
at beat,
in
the
text
predicts
6 - 2 eV
of
this
simple
approximate,
theory
with
it does suggest an
energy balance is intimately involved with arc instability.
Furthermore,
the
agreement
effective
reveals
used.
examination
of
work function column in Figure
the metals are again in rough order
agreement
with the above
It
is
model
however,
for
models
are useful to a
true understanding to
127
the
II.E.13
of
arc
possible
would
if a more accurate work function correction
Phenomenomological
extent,
An
as indicated in Figure II.B.6.
improved
obtained
with observation.
cooling
that
stability
that
a more detailed model is justified to improve
be
were
limited
occur,
more
II. Theory of Arcs: E. Theoretical
Extension
physical modeling is necessary.
There
is
an additional consideration which has
not
been
mentioned in the vacuum arc literature. There is a minimum
characteristic
size
required for existence
phases. Essentially, the
of
interface
transition
creation
to
occur
of
different
energetically unfavorable process
must
be
overcome
(Lifshitz and
for
a
phase
Pitaevskii,
1981].
Surface tension is perhaps the most obvious example of this
phenomenon.
former
If
cathode
energy,
a
phase transition
spot does not persist due to
emission.
field-induced
mind
changes
to pure (quantum mechanical)
The current densities
emission decrease quite
increasing effective work function.
in
a
Lee, 1960], also know as the field-
enhanced thermionic emission,
field-induced
of
insufficient
then the entire electron emission process
from the "T-F" process
from
at the location
obtainable
rapidly
with
The reader should keep
that the plasma density decays on the
same
time
scale as the temperature of the cathode spot, hence a space
charge-enhanced
seems
degree
improbable
electric field is not
likely.
Thus,
that the field can intensify to
to produce significant currents,
observed to extinguish.
128
such
it
a
and so the arc is
II. Theory of Arcs: E. Theoretical
In summary,
Extension
a physical model has been used to obtain rough
agreement with observed low-current instability trends
different
energy
metals.
The
conservation,
model is a simple
and
improved
expected with a more involved model.
129
for
one,
based
on
agreement
could
be
III. APPARATUS ISSUES
III.A Initial Design Requirements
Initial design characteristics were chosen to satisfy
conflicting
requirements
understanding
of
arcs
in
budget.
of
achieving
and advancement
a reasonable
the
significant
in the field
amount of time and within
of
vacuum
a
finite
A compromise between practicality and idealism was
therefore made. Practicality won. Theoretical analyses were
performed to determine the minimum range of magnetic fields
which
would significantly interact with the arc in a metal
vapor vacuum arc switch.
kiloGauss.
was
This range was found to be a
few
A preliminary configuration for the field coils
then established which was subsequently
substantially
modified as the total design evolved.
The very name of metal vapor vacuum arc switch implies some
pressure
vessel
pressure
in the arc itself during conduction is
Torr,
thus,
to contain the conduction
initially
material.
of
The
order
it was thought a thermal vacuum of
10-4 Torr would be adequate. The requirements on the vacuum
system,
however,
extend
system,
and
merely on the pressure during
short
not
throughout the lifetime of
lifetime of the arc.
trapped
gases
on
the
the
very
This is due to the build-up of
the exposed
surfaces.
If
the
vacuum
pressure is not sufficiently low, contamination effects due
130
III. Apparatus
to
Issues: A. Initial Requirements
impurities internal to the switch will prevent
performance.
Thus,
we determined
optimum
that operation at a base
pressure of less than 10-6 Torr was desirable.
As an experimental
device,
we designed a most flexible and
adjustable
device in order to optimize the performance of
the
vapor vacuum arc switch.
metal
To this end
we
seemingly endless design modifications while we were
working on paper.
made
still
In the final analysis we produced a unit
which is very versatile as an experimental device.
III.B Magnetic Field Design
Having previously determined that magnetic fields of
of
a
few kiloGauss were sufficient
plasma,
which
with
the
we performed analyses to determine a configuration
met
produced
this
to interact
order
this
requirement
and
additionally could
from our present stock of equipment.
be
Essentially
meant the various available capacitor banks presented
another design constraint. A design consisting of dual twoturn
coils
of
11
cm
radius
was
chosen.
independent coils allowed the possibility of
two different resulting magnetic fields:
parallel
excitation
geometry);
of
the
(the z-direction
investigating
in
cylindrical
excitation
The resultant coils have an inductance
131
two
an axial field by
and a radial field by anti-parallel
coils.
Having
of
III. Apparatus Issues: B. Magnetic
1.6
micro-Henries
each.
excited by a 90 microfarad capacitor bank,
and
parallel
in
When connected
Field Design
a period of
54
microseconds results. Ideally this period is much less than
the
will
period of the arc discharge so that the arc
discharge
appear "frozen" at the instant of application
of
the
magnetic field. This is necessary for maximum effect of the
magnetic field. The apparent limitation on the frequency of
the
is of
discharge which will be interrupted
arc
A 20 kiloHertz arc discharge is difficult
concern.
little
indeed
to extinguish!
Initially
diameter
later,
the
coils
were
constructed
bare stainless steel wire.
problems
arose
from
As will be
associated
with
the
1/8"
inch
discussed
lack
of
insulation on the wires. An alternative construction called
for
Teflon
insulated wires of the
cross-section. See Figure III.B.1
132
same
current-carrying
III.
Apparatus Issues: B. Magnetic Field Design
Figure III.B.1
MAGNETIC FIELD COIL CONSTRUCTION
133
Issues: C. Vacuum Considerations
III. Apparatus
III.C Vacuum Considerations
III.C.1 System viewpoint
The
of the metal vapor vacuum arc switch.
limit the performance
For
ultimately
cleanliness of the vacuum environment may
this reason it is important to understand the pressure
vessel
a system point of view.
from
are
there
pressure
desired
In addition
many
the
to
sometimes
other,
issues to be considered when designing a high
conflicting,
performance vacuum system from the very beginning.
Of foremost interest,
of course,
is
pressure
our
for
defined,
pressure.
The
purposes,
as the pressure below which tests, or shots, are
conducted.
rise
above
groundrule
operating
is the desired operating
The pressure may, immediately following a shot,
operating
pressure,
consistent
results
the
for
but as an
shots
no
a
priori
be
would
initiated while the pressure is above some minimum pressure
- the operating pressure.
and
Flexibility
system
which
is
experimental
is provided
expediency
capable of being pumped
to
a
by
a
pressure
substantially below the actual operating pressure. The fact
that the pressure decays in time roughly as an
exponential
function means an ultimate pressure less than one-third the
operating
pressure
is
desirable
134
for
the
device.
The
III. Apparatus Issues: C. Vacuum Considerations
ultimate
pressure
chosen
implies a
restriction
suitable types of vacuum pumps to accomplish the
on
the
task.
As
mentioned above, we determined an operating pressure of 106
Torr
to be an acceptable.
Accordingly
we designed
the
system to achieve, under worst case conditions, an ultimate
pressure of 3 x 10 - 7 Torr.
There
are several types of vacuum pumps which will achieve
the above requirement O'Hanlon, 1980].
diffusion
pumped systems,
and ion pumped systems.
We considered
turbomolecular pumped
systems,
We had available at essentially no
added cost either a turbomolecular pump or an ion pump.
chose
the
ion pump for reasons of experimental
ease
We
and
mechanical simplicity.
Figure
II.C.1 is a vacuum pumping flowchart.
It shows the
logical order of the vacuum components from bottom to top.
A mechanical
pump is required
approximately
milliTorr.
minutes for our system.
be
turned
on
to rough the pressure
This process takes
down to
about
At this pressure the ion pump
and the pressure
will
rapidly
45
can
fall.
The
phenomenon
of backstreaming prevents one from turning
the
mechanical
roughing pump on and then allowing the pump
to
work,
say,
overnight.
Oil from the
135
mechanical pump will
III. Apparatus Issues: C. VacuumConsiderations
FigureII.C.1
VACUUM PUMPING FLOWCHART
136
III. Apparatus Issues: C. Vacuum Considerations
traverse
the
pumping lines upstream and
contaminate
very vacuum chamber one is attemping to evacuate!
the
The
oil
can accomplish this travel most easily when the pressure is
the
lowest. This is
because the oil
essentially free flight.
The
watch
over
are
Thus it behooves one
the mechanical pump pressure
the
to
gauge
thermocouple gauge) in order to close the high vacuum
valve
in
molecules experience no drag
effect due to ordinary viscosity.
stand
molecules
(a
gate
at the earliest possible moment and then to turn
ion
pump once the mechanical pump has
been
on
isolated
from the pumping circuit.
II.C.2 General High Vacuum Issues
One
of
the issues which must be taken into account
in
a
device such as this one, is the choice of various materials
to be employed inside the high vacuum environment.
In view
of
of
the
requirements of the device and in
light
the
physical model of a hot plasma dissipating in the electrode
gap, and condensing on the surrounding surfaces, it is very
important to use materials with a low vapor pressure under
the anticipated conditions.
importance
We have seen in Chapter II the
of material selection for the
electrodes.
The
same problems occur with all surfaces exposed to the plasma
environment.
The vapor pressure of metals such as
silver, tungsten,
copper,
and stainless steel 304 are low enough at
137
III. Apparatus Issues: C. Vacuum Considerations
encountered
typically
commonly
In a specific
materials.
used
be
the
application
the
for these to
temperatures
requirements
metal chosen will depend on other
particular
to be satisfied.
Examples
of
materials
not to be used in
environment environment include zinc,
lead.
vacuum
sulfur and
cadmium,
Zinc is a component of brass, cadmium
sulfur are found in some types of steels and stainless
steels,
and lead is a component of most soft
shown in Figure II.B.7,
function
must
high
The problem with these materials is their relatively
high vapor pressure.
and
a
be
if
As
vapor pressure is a rapidly rising
Therefore,
of temperature.
avoided
solders.
they
would
above room
be
the above
materials
to
subjected
temperature;
even
room
at
temperature
rise
temperature
these materials should not be used except
exceptional
reasons.
Fortunately
there
exist
any
for
suitable
replacement materials for the above materials.
Diffusion is the transport of one material through another.
Gaseous diffusion through the bulk materials which form the
sidewall
of
the
vacuum
device
is
one
factor
ultimately limits the minimum pressure achievable.
pressure
on
concentration
one
side
gradient
of
the
surface
The gas
establishes
through the material.
138
which
It is
a
this
III. Apparatus Issues: C. Vacuum Considerations
gradient
which forces gas atoms and molecules through
the
solid. Since the internal pressure is negligble compared to
the
external
pressure,
approximately the
same
pressure
difference occurs in most high vacuum systems. Hence, using
a
thick-walled
vacuum
vessel will
concentration gradient,
reduce
the
and this, in turn,
particle
will result in
decreased diffusion transport through the vessel walls.
Permeability
systems.
1980]
another
Permeability
Gas
vessel,
is
first
consideration
for
high
is a three-step process
adsorbs on the outer wall
vacuum
O'Hanlon,
of
a
vacuum
diffuses through the bulk of the solid and finally
desorbs from the interior wall.
Steady-state permeation is
physically similar to a small, constant leak.
Outgassing
is
the continous evolution of gases
from
the
vacuum surfaces. The gases become trapped on the surface in
a
thickness
several
molecular
layers
thick.
Whether
acquired during metal fabrication or exposure to air during
assembly,
industry
material outgassing has historically plagued the
unless
special precautions
were
taken.
Simple
triggered vacuum gaps became a reality once the problem
outgassing
was solved by vacuum melting the metal for
electrodes.
eliminate
The
as
central
idea of vacuum
melting
much gas as possible from the
processing.
139
metal
was
of
the
to
during
III. Apparatus Issues: C. Vacuum Considerations
Other
solutions to the outgassing problem include a vacuum
bakeout
The
of the entire system while under vacuum
rate
of
outgassing
is
dependent.
At
elevated temperatures the outgassing is increased over
low
temperatures. The
possible
during
idea
temperature
pressure.
is to "bake off" as much
the limited time of the
bakeout
gas
as
thereby
"cleaning" the system. After cool down, the outgassing rate
will presumably be much reduced.
be
used
A cryogenic cold trap can
to expedite this bake-out process
by
preventing
back-streaming.
Hence
the three concepts of diffusion,
outgassing
are
all
different
but
permeability,
related
aspects
achieving and maintaining a high vacuum environment.
three processes occur over over the blk
We
and
to
These
of solid material.
now investigate the sealing problem at the
atmosphere-
vacuum interface.
Various
access
electrical
ports were installed in
order
to
supply
power to the trigger and coils located interior
to the vacuum vessel.
The cost of electrical
feedthroughs
was
substantial for the voltages and currents involved
in
our
system.
number
of
ports without reducing the flexibility inherent
in
access
Thus
we
designed for a
140
minimum
III. Apparatus Issues: C. Vacuum Considerations
the overall design.
The seals for the vacuum environment received much thought.
If one wanted the highest performance system
is
solution
an
use
obvious one:
If,
however,
available, the
as
copper gaskets
one merely wants a
the
"good"
sealing
method.
system,
while subject to the restriction of a budget, then
the answer is not so obvious.
The alternative to expensive
metal seals is to employ re-usable rubber gaskets.
Of course,
throughout the design period we constantly kept
in mind the end use for our product. This had the effect of
keeping things simple from an implementation point of view,
and
insured
a reasonable compromise
between
conflicting
requirements.
III.C.3 Implementation
The
vacuum
cylindrical
system
glass
in
the present
vacuum
vessel of
form
18
consists
inches
of
a
diameter
capped at top and bottom by a one-half inch thick stainless
steel plate 24 inches in diameter.
operates
lower
The 200 1/s Vacion pump
through a four inch opening in the center of
flange.
See Figure III.C.2 for a schematic view
the vacuum system.
141
the
of
III. Apparatus Issues: C. Vacuum Considerations
Figure III.C.2
BELLOWS
HIGH
VOLTAI
PULSE COIL!
ELECTRODES
GROUND FLA?
VACION
PUMF
VALVE
ROUGHING
The
PL
small diameter access ports are sealed
Varian-style
electrical
copper
gaskets.
feedthroughs
were
with
Commercially
selected for
standard
available
the
magnetic
field current and the arc discharge trigger lead.
The large (18") diameter vacuum seals are made with Viton-A
rubber boot gaskets.
These gaskets have proven quite
good
from a vacuum standpoint, easy to install, and economical
because of the ability to re-use them.
We have achieved
system,
ultimate pressures of 3 x 10 - 8 Torr in our
indicating
outgassing
and
good system cleanliness,
acceptably low permeability of
walls.
142
low material
the
glass
III. Apparatus Issues: C. Vacuum Considerations
III.D Adjustable/Flexible Features
Adjustable
features
evaluate.
A
constructed.
way?",
are
device
of
both
difficult
maximum
to
flexibilty
design
was
to
and
be
However, questions such as "Flexible in which
"What needs to be adjustable?",
et cetera continue
to assault the designer.
In fundamental terms, an experimental device is constructed
because
the
advanced
Rational
set-up
knowledge
in
a
particular
field
has
to the stage where all relevant facts are
udgment is required to produce
an
not
known.
experimental
in which flexibility and adjustablity are preserved
in all the proper areas, and yet the device
is not unwieldy
to use.
We determined the essential elements which must be
allowed
to vary for the full range of interest
in
vacuum
arcs to be explored. These elements are described in detail
in this section.
III.D.1 Gap Variability
The
ability
vacuum
to
vary the electrode gap
was a central design issue.
without
breaking
The design chosen
was
one in which the gap variability is derived from the welded
metal bellows attached to the top, cantilevered, electrode.
This allows the gap to be varied in excess of 2 inches. The
method
of alignment is four corner
143
threaded
rods.
Three
III. Apparatus Issues: D. Adjustable Features
rods
are
required for movement in three
fourth rod serves as a locking rod.
creep
when
dimensions.
This prevents any slow
of the electrode and also serves as a positive
aligning
the electrode.
144
The
stop
III. Apparatus Issues: D. Adjustable Features
III.D.2 Demountable Electrodes
Demountable
electrodes
the
provide
ability
to
use
interchangeable materials and/or geometrical configurations
in
the
Initial experiments have been
device.
stainless steel electrodes,
of
done
however, we anticipate the use
The lower
copper electrodes in the fututre.
electrode
bolts into position with four stainless steel bolts.
The upper electrode is soldered
its mounting station.
place with Indium.
into
insertion
contact
through
the
These
electrode
bolts insure good electrical contact between the
and
with
The soldering is performed
adjustable
bellows.
is assured by the Indium oint.
after
Electrical
These
electrodes
can easily be mounted and demounted in a matter of minutes.
is another,
There
the
quite unique,
pulsed
aspect of our particular
application
of
the
primary
design.
During
current
(in the magnetic field coil) the plasma acts as
single
turn
effect.
A
cylindrical
primary
transformer secondary.
leakage effect
lip
with
the
occurs because
is also a transformer
current.
circumferential
This is
In
this
the
the
secondary
configuration
the
a
desired
electrode
to
the
induced
plasma current is electrically in parallel
induced electrode lip
current.
This
parasitic
effect at best dilutes the effort of the pulsed field, and,
at worst,
may actually make interruption more difficult to
145
III. Apparatus Issues: D. Ad3ustable Features
achieve due to the additional Joule deposition of energy in
the current carrying electrode.
The electrodes are specifically designed for increased lipcircumferential
impedance.
This has been accomplished by
the use of axial slots in the electrode. These slots are 21/2 inches deep,
that is, the slot root is approximately a
three inches from the center plane of the
total
of
coil.
Figure
field
III.D.1 shows the geometrical situation for
the electrodes.
146
III. Apparatus Issues: D. Adjustable Features
Figure III.D.1
SLOTTED ELECTRODES
f
147
III. Apparatus Issues: D. Ad3ustable Features
Figure III.D.2 is an assembled view showing the geometrical
arrangement of the field coil and slotted electrodes.
Figure III.D.2
SLOTTED ELECTRODE AND COIL GEOMETRY
148
III. Apparatus Issues: D. Ad3ustable Features
At
this point we digress slightly to review the
issues
at hand.
Calculations were performed to
technical
determine
the severity of this leakage current and its effect on
desired
plasma current.
The problem may be idealized
the
as
shown in Figure III.D.3.
Figure III.D.3
IDEALIZED PLASMA MODEL SHOWING LEAKAGE CURRENT
plasma model
-
J
C
L
driving circuit
The
voltage
closed
electrode lip model
on the capacitor bank after the switch
S
is given by (resistance and lead inductance in
is
the
primary circuit is neglected for simplicity):
V = L dI/dt + d(MlIl + M2I2)/dt
The notation used is the following: unsubscripted - primary
current
parameter;
subscripted
149
1
- plasma
parameter;
III. Apparatus Issues: D. Adjustable Features
subscripted 2 - electrode lip parameter.
If we assume flux conservation (i.e.
interest
plasma
are
less
circuit
assume that times
than (L/R)I or (L/R)2
of
(for
both
the
we
find
the
and the electrode circuit),
following results:
-- O=MtI+L±
1+Mulz
Simultaneous solution of these two equations yields:
L 44
The
important
plasma
point
current.
-Msz
1
here is the effect M12
has
The coupling between the plasma
on
the
and
the
electrode lip actually serves to reduce the plasma current.
Because of this effect,
we have attempted to substantially
reduce M12 by our slotted electrode design. Essentially, we
force the current to traverse a path which is far away from
the region of good coupling.
150
III. Apparatus Issues: D. Adjustable Features
III.D.3 Anode/Cathode Interchangeability
The Vacion pump is connected to the chamber via a four inch
diameter
the
formed-bellows tube.
pump to the lower flange.
This electrically
Thus,
connects
the lower flange and
lower electrode must always remain approximately at
potential
for
safety reasons.
restricts
the
polarity
electrode
may be either positive high voltage or
high
of
This in no
the
upper
flange.
voltage - in fact in the half cycle
upper
electrode
way,
The
however,
The
top
negative
discharges
the
in the final state has approximately the
same magnitude voltage but opposite in sign to the
state.
ground
essential
initial
point is the interchangeability of
anode and cathode in our design.
III.D.4 Flexibility of the Magnetic Field Design
Our design included two autonomous magnetic field coils and
a
trigger electrode.
minimum
added
Thus three vacuum feedthroughs are a
for this system.
A fourth vacuum access port
to insure experimental flexibility.
experiments to
"blanked
Throughout
date this port has simply been
off." However,
closed
was
all
or
we anticipate the possibility at
some later date of instrumenting the
electrodes,
and,
at
attempted
to
that time, we will require a fourth access port.
By
using
such
a
large vacuum
1'51
vessel
we
III. Apparatus Issues: D. Adjustable Features
mitigate
any possible influence of the end effects in
device.
few
our
An additional advantage of the large vessel is the
geometrical
constraints
imposed by
the
surrounding
walls.
The
flexibility of
our approach
is
emphasized
incorporation of the magnetic field coil design.
that
we
had
sufficient
flexibility
by
the
Confident
to implement
a
coil
subsequent to the initial tests, we essentially assembled a
triggered
vacuum
design
allowed
device
much
gap.
The
flexibility inherent
us to gain valuable
ealier than otherwise
experience
possible.
in
our
with
the
Of
subsequently the field coil has been designed,
course,
implemented
and suitably modified within the same fixtures.
As
mentioned
vessel.
and
above,
Aside
we have implemented a
glass
from the vacuum considerations of
permeability,
the
use
of
glass
has
vacuum
outgassing
far-reaching
implications. First, as a dielectric the glass is sufficient
to hold off the full voltage of the electrodes
with a large
safety margin. This allows the vacuum flanges to be used as
the current feedthroughs. In addition, excellent visibility
is
afforded
electrical
by the glass chamber.
feedthroughs
and
The expense
indeed in the
saved
large
in
vacuum
vessel itself is substantial.
6
152
III. Apparatus Issues: D. Adjustable Features
Safety
when
provided
This
but
by
working around the glass
an encircling piece of
vacuum
Lexan
chamber
is
polycarbonate.
not only protects against accidental glass
breakage,
also serves as a mechanical support for the top flange
should the glass ever break.
153
IV.
EXPERIMENTAL WORK
IV.A Control System Description
IV.A.1 Instrumentation
In
addition to the basic systems described in the previous
chapter, various control systems are required for effective
implementation of the concept of synchronous application of
a current-interrupting magnetic field.
a) Electro-pneumatics
Primarily
these systems are
timing is of importance.
electronic,
We employ,
systems which are not electronic.
manual
shorting
capacitor
charging
banks
valves
for
however, several sub-
capacitors,
control
independently
when
These systems are: a)the
crowbars for the
electro-pneumatic
especially
and
of
for
and
b)the
charging
isolating
supply from high voltage surges during an
two
the
actual
discharge.
The
manual crowbars operate in a self-evident way
and
so
will not be discussed further. The electro-pneumatic valves
also
operate
safety
in
issues
experiment,
it
a straightforward way.
involved
and
ease
of
Because
use
of
during
is felt worthwhile briefly to discuss
valve operation.
154
the
the
the
IV. Experimental Work: A. Control System Description
The
electrical
schematic
is
shown
in
Figure
IV.A.1.
Features of interest include the master safety switch
the
indicator
light
pneumatic valves.
nitrogen
tank,
condition
and the
independent
electro-
Supplied with air pressure from a common
all electrical
connections
in the event air pressure is
issues go beyond one operator;
to
four
with
go to a "safed"
lost.
The
other workers having access
the experimental cell are assured as to their
under all conditions.
Figure IV.A.1
ELECTRICAL SCHEMATIC FOR PNEUMATIC VALVES
MASTER
SWITCH
bank #2
155
safety
security
IV. Experimental Work: A. Control System Description
The
master
security
wired
safety
switch
as loss of air pressure.
in
series
the
same
sense
of
The indicator
light
is
with the master switch.
is not activated,
switch
provides
If
the
master
connections
all electrical
are
"safed." If the indicator light fails for internal reasons,
The indicator light has a logic
all connections are safed.
which
if lit something ay be in the
means the following:
"live" condition,
exercised;
if
grounded.
Note
grounded
under these conditions caution is to
be
the system
is
the
light is extinguished,
the system could very well
even if the indicator is lit,
be
completely
but it serves as a
visible warning that care is to be exercised.
The
four
SPST
other toggle switches control
air solenoids.
circuit
independent
One of the solenoids is for the
circuit on each of the capacitors,
charging
four
for
each
dump
and one is used for the
capacitor.
The
utility
of
independent control is the ability to charge the capacitor
banks to different voltages.
to
independently
Thus,
we have the capability
vary the arc discharge current
and
the
magnetic field current.
b) Trigger Boxes
The
events
waveform
to
be
synchronized
are
the
arc
discharge
and the application of the pulsed magnetic field.
156
IV. Experimental Work: A. Control System Description
currents are initiated by trigger pulses delivered
The
respective
the
associated with either gap,
be
taken
account
into
Any
triggerable gaps.
to
the
determine
delays
timing
if significant,
to
would have to
delay
actual
required for synchronous operation.
Providing
synchronous timing pulses proved to be
no
Many methods were investigated and pursued.
task.
mean
Perhaps
the easiest method is to use a simple timing delay for the
trigger
pulses.
Advantages
This
is
in
fact
the
approach
taken.
of this method include the ability to introduce
the desired synchronization at an arbitrary time in the arc
discharge waveform.
may turn out that the field-producing current can
It
more
accurately or reliably be produced by an electrical circuit
which is capable of determining,
in real time, the optimum
time to initiate the delayed current. For example, a simple
circuit
This
to
could
search for a current or
voltage
extremum.
type of circuit would not add any qualitative ability
the
over
all performance, but
it
may
improve
the
reliability.
A simplified control system flow-diagram is given in Figure
IV.A.2. A
detailed timing diagram indicating the
various
intrinsic delays associated with the various components is
157
IV. Experimental Work: A. Control System Description
shown in Figure IV.A.3.
an
passive
that
of the complexity of
understanding
latter
figure
delay.
From either diagram one can obtain
more
readily
For instance,
shows the
the
The
process.
advantages
even if it were
of
a
determined
the field should be triggered at a particular
moment
in the remainder
of the
in time, the time delays inhererent
system must be taken into account for synchronous operation
to actually occur.
In short,
difficult to achieve.
158
true real-time operation
is
I
IV. Experimental Work: A. Control System Description
Figure IV.A.2
SIMPLIFIED CONTROL SIGNAL FLOW DIAGRAM
14GER
THAN
T I GGE P.
II
1
MAaErTc
D*iRGb
FIELD
+
159
IV. Experimental Work: A. Control System Description
Figure IV.A.3
DETAILED SIGNAL TIMING DIAGRAM
Ii
)
A
6Ius
I
65'"
,
r·
__,_--~~~~~~~~~~~~~
I
0
5
10a
160
IV. Experimental Work: A. Control System Description
Figure IV.A.3 (cont.)
DETAILED SIGNAL TIMING DIAGRAM
©
©
ARC
DISC
or
.ACGE
CULREwr
161
IV. Experimental Work: A. Control System Description
presence of fiber optics throughout the control system
The
deserves
concerns,
comment.
the
ease
them
makes
a
ignored.
As
the
omnipresent
of implementation of
practical
to
answer
safety
optical
the
fibers
problem
of
delay
generating
electronics.
safety issue,
as always,
should not be
with
communication
Furthermore,
In addition to the
the
the high voltage
indicated in Figure IV.A.2,
region is isolated from the instrument bench by either,
least, a one megaohm resistor or optical fibers
about five
feet
long). The instrument bench can be further
from
the
fiber.
from
operator by approximately six
Thus,
any
battery,
feet
at
isolated
of
optical
the operator is provided an environment safe
hazards of electrical shock.
A nine volt
which operates the optical emitter,
is the
radio
only
source of current within about eleven feet of the operator.
The circuit implemented for the delay generator is shown in
Figure
IV.A.4.
It shows two outputs which
timed with respect to one another.
delay
is
precisely
The first output of the
box goes to the arc discharge trigger box.
shown
second
are
in electrical schematic in
Figure
This box
IV.A.5. The
output of the delay box goes to the field-producing
trigger box. This box is operationally identical to the arc
discharge
trigger box.
162
IV. Experimental Work: A. Control System Description
In essence,
the operation
1.
The
is as follows:
hand held trigger emits an
optical
signal
which is detected by the timing box.
2.
The
timing box gives an output at t=0,
and
an
output some finite time later at t=TD.
3. Each of these outputs,
emitter.
in turn, powers an optical
This signal is detected at the respective trigger
box.
4.
The
receiving
Darlington-type
resulting
photodetector
manner
current
with a
is arranged
standard
in
a
transistor. The
is supplied by a capacitor
(introduced
for fast response), which triggers a high current SCR.
5.
The SCR then shorts one side of the
transformer
one may wonder about the wisdom
having
the
the primary voltage (600 volts) until
the
to ground.
At
first
transformer
at
of
SCR conducts to ground. The reader may be assured that many
transistors
otherwise.
have
Two
been
in
to
Figure
to
IV.A.7.
in the Darlington array.
The typical breakdown
volts.
Presumably,
inductance of the transformaer primary caused the
rise
high
do
we frequently destroyed the second
voltage of a transistor (2N3904) is 30
the
attempts
alternatives are shown in
When option B was used,
transistor
destroyed
enough in voltage to
163
exceed
the
SCR
reverse-
I
IV. Experimental Work: A. Control System Description
voltage
rating of the transistor.
breakdown
Option A
is
presently implemented and no problems have arisen.
Of
course,
there are many different ways to
triggered delay results.
the
It must be said,
trigger pulse provided
example
of
its
utility,
produce
one.
the gas gap triggered
magnetic field has a minimum recommended breakdown
(6
KV)
operate
far above the value at which we can very
(2KV). We
this
attribute
circumstance
particular triggering method.
Figure IV.A.4
DELAY TIMING CIRCUIT
+9 volts
optical emitter
W
164
that
however,
is quite a robust
the
As
for
an
the
voltage
reliably
to
our
IV. Experimental Work: A. Control System Description
Figure IV.A.5
ARC DISCHARGE AND FIELD COIL TRIGGER BOX
+600 volts
*
Figure IV.A.6
SCR - TRANSFORMER ALTERNATIVES
+600 volts
transformer
R
tgger
device
under
test
to
trigger
R
B.
A.
165
IV. Experimental Work: A. Control System Description
IV.A.2 Diagnostics
In
this section we review the type of diagnostics employed
through the course of this investigation.
We were primarily interested in gross, macroscopic results.
The
interruption
on
of a current of order kiloamperes
the
Thus
first half cycle is the type of event we anticipated.
our most important diagnostics were standard tools such
Tektronix
shutter
high voltage probes,
Rogowski coils,
photographs. The high voltage probes
banks,
open
the
showed
the final charge on
initial charge on the capacitor banks,
the
and
as
The Rogowski coil,
and the voltage waveforms.
when integrated, showed the current as a function of time.
In
addition
to
the
obvious use
of
the
measuring
arc
discharge characteristics, we also conducted control tests
with
the
installed
steel
the
wire.
We
arc-discharge
Rogowski
determine
the
example,
when
we
magnetic field coil it was
bare
stainless
diagnostics.
coil
the
parasitic
As
an
suspected a discharge was occurring
electrode
to
coil
wire.
and high voltage probe,
By
we
use
were
in
the
from
of
the
able
to
magnitude of the short-circuit current
voltage deposited
first
and
field-producing
capacitor bank. The effect was actually first noticed on an
open
shutter
photograph
which showed
166
tell-tale
cathode
IV. Experimental Work: A. Control System Description
spots on the field coil.
As complimentary diagnostics, we employed photodetectors to
get
an
idea of the time history of
the
light-production
from the arc discharge, and Vacion current as an indication
of the amount of liberated material from a given shot. Both
of
these diagnostics aided us tremendously throughout
investigation.
supplied,
As
however,
only
the
qualitative
information
usefulness of these
methods
our
was
was
limited.
Often
over-looked diagnostics,
the human visual and aural
devices are quite indispensible. Visual indicators
from
indicator
lights to inspections for loose
faulty connections.
existence
first
performed
electrode gap.
existence
from
was the standoff
One of
ability
At 40 KV corona was observed.
voltage of 20 KV produced
wires
in a darkened room,
of corona can visually be detected.
tests
operating
Furthermore,
ranged
of
no visible corona.
definitive conclusions from an
photograph, as
the
the
the
The maximum
of a small amount of ambient light prevented
making
or
open
The
us
shutter
in performing lower bound measurements
on
emitted light.
Aural
detection
of very small arcs due to
aided
us very much during one particular experimental run.
167
bad
grounding
IV. Experimental Work: A. Control System Description
One must exercise caution,
sensitive
to
pressure
acoustical energy,
bank
however. The human ear is quite
disturbances.
When
converted
the energy of a high voltage
capacitor
can easily permanently deafen an unprotected operator
- or anyone else who happens to be in the area at the
of
to
time
an experimental shot or a fault condition.
IV.A.3 Implementation
Figure
IV.A.7 shows an overall electrical schematic of our
system.
Shown
are
the
pnematic safety
valves
for
the
capacitor banks, the hand-held trigger, the optical fibers,
the pulse delay box, the two trigger boxes, the vacuum gap,
the field coil, and a Rigowskii coil as a current probe.
A
variable
inductor
has
been
constructed
satifactory time-dependent waveforms.
heavy
obtain
It is constructed of
cable wrapped on an insulating mandrel 12 inches
diameter.
will
to
Typically,
we
produce an inductance
use 20 turns of the cable.
of 70 uH.
capacitor bank, the system has a Zeff
168
in
This
With a 37 uf driving
of 1.4
IV. Experimental Work: A. Control System Description
Figure IV.A.7
OVERALL SYSTEM ELECTRICAL SCHEMATIC
;coDe
C =
- 100
169
IV.B. Data
In
this section we present data obtained from the
various
diagnostics over the course of the experiment. The data can
be conceptually divided according to the type of diagnostic
used:
prompt
monitored
is
on
used to describe diagnostics
a shot-to-shot basis;
which
periodic is
are
used
to
describe diagnostics which are meaningful over a relatively
long time period.
It
should be noted that no external circuit elements
added
to
enhance
Typically,
the
interruption
were
characteristics.
it is common practice for vacuum switch-circuit
designers to include capacitors in parallel with the vacuum
switch
These
and saturable inductors in series with the
elements improve the interruption performance of the
switch.
They
physics
of the vacuum switch.
do
not,
however,
have any effect
Therefore,
were conducted which explored these
obtaining
below
switch.
areas.
maximum results were a concern,
could
no
be improved upon by addition
on
experiments
Obviously,
the data
of
the
if
given
appropriate
external circuit elements.
IV.B.1 Prompt Diagnostics
The high voltage probe,
open
shutter
Rogowaki coil,
photograph
are
170
all
photodetector, and
prompt
diagnostics.
IV. Experimental
Phenomena
arc
such
as asymmetry exhibited by
initiation
characteristics
It
is
polarity"
the
and
discharge, 9
interruption
are measured by prompt diagnostics.
importnat
concerning
the
(triggering) effects
Work: B. Data
to
electrode
note
the
polarity.
following
We define
definitions
the
"standard
to be when the upper electrode is the anode
lower
polarity,
electrode
we
have
is the
the
cathode.
"inverted
Upon
and
exchange
polarity"
of
situation.
Inverted polarity has the anode as the lower electrode
and
the cathode as the upper electrode.
Aaymsetrx
A
striking asymmetric effect was observed to occur in
arc
discharge.
Out
of the several
hundred
the
experimental
shots, the vast majority had a preferred current half-cycle
after
which interruption would occur.
operating under the standard polarity,
occur
almost
half-cycles.
when
interruption
would
exclusively after an odd number
When
interruption would
cycles.
Specifically,
Figure
the
electrdoe polarity
occur
IV.B.1
after an even
schematically
of
was
number
current
inverted,
of
half
illustrates this
situation.
An effect related to the interruption half-cycle
171
asymmetry
I
IV. Experimental Work: B. Data
is
the
arc-voltage-waveform
standard polarity,
cycle
has
asymmetry.
Operating
under
the beginning of an even-numbered half-
a much larger transient voltage rise
beginning of an odd-numbered half-cycle.
than
Similarly,
the
under
inverted polarity, the beginning of the even numbered halfcycles
exhibits
a
relatively
large
transient
voltage
waveform. A necessary condition for interruption is the
transient
applied.
voltage
must exceed the voltage
which
is
re-
Essentially, the breakdown strength of the vacuum
gap must exceed the applied voltage.
TrIggsegAg
Another asymmetric effect observed was the operation of the
trigger
under anode-cathode inversion.
initiate
a
The trigger
discharge in both circumstances.
It
would
required
much less energy and current to achieve arc initiation when
the
trigger assembly was adjacent to the cathode (the so-
called
"cathode
supplied
discharge
anode
to
mode").
the
when
An
increased
trigger box in
order
voltage
to
must
initiate
the trigger assembly was adjacent
("anode mode").
The amount of increased
required to trigger the discharge depended upon the
electrode
gap.
The
design
voltage of
the
to
be
the
the
voltage
inter-
trigger
box
represented a limitation on the maximum allowable gap which
would reliably trigger in the anode mode. This circumstance
is
consistent
with the interruption asymmetry
172
discussed
IV. Experimental
above. Other researchers
similar
asymmetry.
Work: B. Data
[Warren, et al, 1981] have noted a
They
also
report
a
difference
in
operating characteristics for reversal of tAigger polarity.
have noticed such effects.
The trigger polarity
We,
too,
was
significant in terms of operating characteristics only
under inverted electrode polarity.
Because arc
was
quantitative
not
our
emphasis,
little
initiation
data
was
recorded.
Interruption
Interruption of AC vacuum switches can be characterized
the
peak
the
actual
current in the half-cycle immediately preceding
following
interruption.
this
On
basis
we
noted
the
occurrences:
(1)
as
overwhelming
number
by
of
mentioned above,
tendency
the current exhibited
to interrupt after an odd
half-cycles,
depending
upon
the
or
an
even
electrode
polarity, see Figure IV.B.1;
(2)
influence
the inter-electrode
gap distance
interruption of
on
peak
had
current
a
marked
immediately
preceding interruption, see Figure IV.B.2;
(3)
required
gap
to
interruption
size influenced the number of
interrupt a given current (the
after
an
odd
number
standard electrode polarity persists,
173
of
half-cycles
condition
half-cycles
of
for
and, of course, Nmin
IV. Experimental
= 1), see Figure
(4)
interrupt
Work: B. Data
IV.B.3;
smaller
discharge
frequencies
greater currents (within a modest
experiments
tended
range),
to
[our
did not emphasize this particular aspect, but
the tendency was noted];
(5) in multi-half-cycle discharges,
number of half-cycles,
the greater the
the smaller the peak current which
immediately preceded interruption, see Figure IV.B.4;
(6)
dielectric
surfaces
in the vicinity
of the
gap
aided interruption, see Figure IV.B.5;
(7) arc re-striking was occassionally observed for
temporary interruption times from 1 us to 1 ma,
see Figure
IV.B.6;
(8) the magnetic field had an effect which tended to
reduce the arc recovery-voltage,
(to be discussed shortly)
see Figure IV.B.7.
(9) for our device and circuit,
recovery
parameters
dR/dt
/us.
=
1
of
dV/dt
174
=
we have measured
0.6
kV/us,
and
IV. Experimental
Work: B. Data
IV.B.2 Periodic Diagnostics
An
can
various
estimation of the lifetimes of the
determined by inspection of the
be
substantial
testing.
components
inspection must,
This
components
after
by its
very
nature, occur only periodically and is somewhat subjective.
The
shows
trigger
serious
effects
the
of
plasma
environment. Each trigger pulse expels, from the dielectric
surface, only a minute quantity of material. The subsequent
interaction with the plasma,
the
however,
certainly dominates
actual arc intiation event in terms of material
loss.
The dielectric cylinder surrounding the tungsten pin shows,
quite evidently,
signs of deterioration and mass loss.
must
however,
be
exhibited
shots)
said,
that
the
dielectric
thus,
any subsequent erosion was
small by comparison.
Because the trigger has
performed
is difficult
estimate
the
material
deterioration very early in its life (first
and,
well,
it
to make
the trigger assembly lifetime
of
trigger
assembly
appears
to
have
a
It
50
considered
consistently
quantitative
at this
an
time;
indefinite
lifetime. This is likely to be a result of the regeneration
of
the
conductive
originates.
layer
from
which
discharge
This regeneration occurs primarily as a result
of metallic condensation from the previous
tungsten pin,
the
discharge.
The
which is the actual trigger electrode, shows
175
Work: B. Data
IV. Experimental
little
very
effect
the
of
exposure
This is to be expected:
environment.
to
plasma
the
we selected tungsten
its
as the trigger electrode material precisely because of
low erosion rate.
electrode lifetime is also expected to be
The
long.
No
noted.
of bulk or localized
evidence
The
has
melting
been
is
effect noted on the electrodes
major
cathode tracks,
familiar
indefintely
the
also known as Lichenstein tracks
[Graneau, 1981]. These tracks mark areas of the electrodes
through
which
substantial
current has passed,
as
in
a
cathode spot.
The individual cathode spots, of course, are much too small
to
observe
with the naked eye.
One can
easily
observe,
however, the result of repeated arcing. The arcing tends to
wear-away
on
any suface impurity which may have been
the electrodes.
The areas which have been
present
effectively
"scrubbed" in this manner are demarcated by a smooth, shiny
surface.
The area on the electrode adjacent to the trigger
assembly, especially, is smooth and shiny.
Metallic condensation occurs as a result of each discharge.
As mentioned previously, the un-monitored metallic build-up
can
accumulate
until
interrupter. The
the
surface
device
nearest
176
is
inoperable
the arc
serves
as
as
an
a
IV. Experimental
Work: B. Data
convenient location for condensation for the metal vapor.
A quick order of magnitude calculation shows that, assuming
approximately
500
approximately
1021 metal atoms have been ablated from
electrodes.
means
that,
central
Wiping
large surface area of the
for
region
monolayer
the
The
C have been passed through the
vacuum
of
the
vessel
walls,
the
vessel
a quasi-uniform spray of vapor over
the
approximately a
of metal atoms has formed.
the inside of the vacuum vessel revealed residue of
arcing process.
were
device,
the
shield
Teflon,
metal atoms,
likely components of the residue.
was
installed
immediately
and impurities
When a
glass
surrounding
the
electrodes, the available surface area for condensation was
decreased.
Hence,
if
not
periodically
cleaned,
the
thickness of the atom layer could become appreciable within
the lifetime of the electrodes.
An
the
additional important observation was the deflection
magnetic field coils.
of
After dissipating approximately
15 kJ in the field coil (while the coils were
electrically
connected
electrically
in
parallel),
the
coils
were
connected in the anti-parallel mode.
Subsequent
of
approximately
the
coils
at current levels of
177
operation
50
kA
IV. Experimental
Work: B. Data
caused a substantial,
permanent, yielding of the material.
Figure
an
IV.B.8
observed.
field
The
should
deformation.
shows
illustration
of
yielding
the
ability of the coils to produce a
not
be
by
impaired
this
magnetic
noticeable
The deformation of the coils provides graphic
evidence of the existence of a powerful magnetic field.
Figure IV.B.1
ELECTRODE POLARITIES
Initial State
Final State
II
Standard
Polarity
Inverted
Polarity
I
Lrmmu
__r-J
N
odd
-Lsi
G--li
I
-~~~~~~~~~~~~~~
even
LFsi
T-1
-il
178
IV. Experimental
Work: B. Data
Figure IV.B.2
INTERRUPTING CURRENT VS. GAP SPACING
o
ED'
0u-
In-
.
t-
Z
Co
E-
z
Es
Cv-
U
0)
o
--
o
vc]
-
I
0. 0
1. 0
~~~~~~~~~)2.0
GAP SPACING (cm)
------------
179
3.0
3. 0
IV. Experimental Work: B. Data
Figure IV.B.3
HALF-CYCLES FOR INTERRUPTION VS. GAP SPACING
o
U;
o
I = 4 kA
u
U
I
C.
:3:
0
I =
o
3 kA
N-
Z3
z
Co
.4-
c~
-
0.0
_
~~I
--I
I-
1.0
_
I
I
2.0
GAP SPACING
180
--
3.0
3.-0
(cm)
4.
IV.
Experimental Work: B. Data
Figure IV.B.4
INTERRUPTION CURRENT VS. NUMBER OF HALF-CYCLES
cl
IC.
GAP SPACING = 1.6
I
I
cm
.
mu I
I
Z
co
z
-
P:
u
U
o
o
I
c-
.1
-0. 00
J
l
I
J
2.00
I
J
-
J
4.00
6. 00
-Jl
,
8. 00
I
-
Io1~~
NUMBER OF HALF-CYCLES
Figure IV.B.5
EFFECT OF DIELECTRIC PROXIMITY
Electrode-Glass
Shield Distance
Peak Current Preceding
InterruRtion
2.9 kA
16 cm
5.4
4 cm
181
kA
IV. Experimental
Work: B. Data
Figure IV.B.6
ARC RE-STRIKE
I
_t%2waw
Figure IV.B.7
ARC RECOVERY-VOLTAGE SUPPRESSION
V
Ac.VOTM6
0
V'
-
_
\h
0<
I
0ca
182
IV. Experimental Work: B. Data
9
Figure IV.B.8
SCHEMATIC OF FIELD-CAUSED DEFORMATION
.
m
K
I
IL
1_
_L
1
-'
r
L
1
CN
liii
I
I
L
C
·
-.. d-
C
-
--
C
--.0000'
W_'
j
I
1 NL _o
ssb-,l
%~~~
A
i
l
P
ff
183
I
IV.C Interpretation
This
section
experimental
discusses
data
the
presented
in
interpretation
Section
IV.B.
of
the
In
this
section, we focus on the data presented in the figures.
Current dependence on Ga2 S2Ping
Figure
IV.B.2
observed
cycle
illustrates
data
representative
trend of the dependence of maximum,
current
on
the gap
spacing.
In
of
the
single half-
accordance
with
intuition, beyond a certain gap~spacing, increasing the gap
increases the maximum interruptable current.
results from the well known (Mitchell,
This increase
1970;
Reece, 19633
increase in arc voltage at larger gap spacing.
An
increase in the maximum current also occurs as the
gap
is
reduced
two
distinct
related
The
below
a certain gap spacing.
mechanisms at work here.
are
The first mechanism
is
o the condensation time of metal vapor in the gap.
condensation time is the time required for
vapor
to condense on a surrounding surface.
reduced,
the
condense
mechanism,
mechanism,
the
metal
As the gap is
electrode surfaces represent a larger
angle from the point of view of the plasma.
to
There
on
such
occurring
is
similar
surfaces
is
to
the left hand
184
Thus, the time
reduced.
simultaneously
solid
with
The
second
the
first
branch
of
the
IV. Experimental Work: C. Interpretation
As the gap
Paschen Voltage-pd curve.
free
path
Hence,
become harder to satisfy.
conditions
avalanche
for ionization becomes greater
ionizing
Townsend
decreases,
than
The
mean
the
gap.
particles simply traverse the gap
before
initiating an ionization event.
Aa shown by Boxman
Boxman,
1974],
the plasma density
is
proportional to the arc current. The plasma pressure is, of
course,
at
fixed
directly related to the plasma density.
require higher voltages.
of
higher
circuit parameters (L,C) means
Justification for
Operation
currents
interpretation
Figure IV.B.2 as a Paschen-type phenomenon is given
by
plotting the voltage against the product of the current and
the
gap
spacing.
In
Figure
IV.C.1
such
a
plot
is
diagrammed. When interpreted in this light, the terminology
"vacuum arc" is quite misleading, indeed.
185
IV. Experimental Work: C. Interpretation
Figure IV.C.1
APPLIED VOLTAGE VS. CURRENT-GAP PRODUCT
8
7
6
5
-4
4
.'
3
-W
>2
1
2
4
6
8
10
12
14
I x G (kA-cm)
Interruption-Current dependence on Half-Cycles
Increasing
the
current
for
ignition
to
current
the
particular gap spacing
with
interruptable
causes
zero.
another two half-cycles (and
number remains odd numbered).
immediately
decrease
maximum
occur at the first current
executes
half-cycle
which
current beyond the
arc
e-
Thus,
the
the
total
The peak current
precedes interruption
is
observed
an increase in the number
of
half-cycles.
to
IV. Experimental Work: C. Interpretation
Thermal
effects
reduction
IV.B.3,
the
in
this
actual
spacing
occurring
to the electrodes
interruptable current.
cause
As shown
in
this
Figure
reduction effect is roughly proportional
number
noted.
of half-cycles executed
for
the
to
gap
(We observed different characteristics for
different gap spacings.)
Each
subsequent
full period of conduction
energy on at the electrode surface.
This heats the
and causes an increased ablation rate.
increased
of
deposits
metal,
The presence of the
neutral gas impairs the interruption
the switch.
more
capability
The plasma density must be proportionately
reduced if interruption is to occur.
This interpretation is
ustified by Section II.E.2. In that
section it is demonstrated theoretically that the number of
ablated
to
same
atoms depends linearly on the energy input.
Thus,
the extent that the energy input per full-cycle is
for
subsequent full-cycle
conduction
periods,
the
our
theoretical and experimental models are consistent. Because
the
arc
assumption
current
of
is
actually
constant
a
damped
energy input per
sinusoid,
the
period
not
is
strictly true and must be taken as approximate. The current
decays only a few hundred amps per period (less than 10
of
the total arc current), however, the approximation is quite
187
IV. Experimental Work: C. Interpretation
accurate.
Presence of Dielectric Surfaces
We
mechanism
effect
of vacuum arcs.
of
interruption
of
this
the
method
from
the
arc
discharge.
in a triggered vacuum
gap
mode,
a
circumstance
field coils
the
operated
A clear demonstration
of
as
occurred
isolation
When
quenching
emphasized surface condensation as the
have
capabilities
were
observed
a second glass cylinder
installation
of
electrodes.
This
cylinder
of
improved
fol lowing
surrounding
the
separated
the
physically
electrodes from the field coil.
the nearest vertical surface,
Originally
could condense,
on which
was the vacuum vessel wall.
The
plasma
distance
from the electrodes to the chamber wall is approximately 16
cm.
We
installed
an
additional
effectively isolated the electrodes
on
are
which vapor might condense.
discussed shortly.
dielectric
glass
cylinder
rom the other surfaces
The reasons for doing this
The net result of this
isolation-
surface closer to the gap resulted in
interruption characteristics.
improved
Figure IV.B.4 shows a
comparing the electrode-glass shield distance and the
single-half-cycle
currents
interrupted.
188
which
which
were
table
peak
subsequently
IV. Experimental Work: C. Interpretation
Teflon
has
many qualities desirable from an
experimental
viewpoint.
Easy machinability, good dielectric properties,
acceptable
vacuum
products
properties,
and
lack
of
carbon
are all characteristics which make Teflon a
attractive material.
byvery
Accordingly, Teflon was employed as a
material for several key components in our system.
Contact
of
Teflon.
This phase change is preferred to carbonization, a
process
which occurs to most
leaves
a
Teflon
with the plasma tends
conductive
into
volume.
interruption performance,
of
the
glass
carbonization
the release of ionizable material
the
shield,
Thus,
A
the
this
is
residue.
as
ablate
of
transformation
discharge
plastics,
to
we
disadvantage
believe
the
improved
associated with the installation
may
partially
be
a
result
of
separation of the plasma from contact with Teflon.
Arc-Restrike
Occassionally,
temporarily
us
it
has
been
observed that the
arc
will
interrupt for a period of time ranging from
to 1 ms,
although it may subsequently
re-strike.
1
The
exact breakdown mechanism is not known. It is believed that
thermal processes and T-F electron emission play a role
breakdown
of the temporarily recovered gap.
shows a typical arc re-striking event.
189
in
Figure IV.B.5
IV. Experimental Work: C. Interpretation
It
has
been
mentioned that no
melting has been observed.
however,
there
evolution
region
of
metal
which
residual
Alternatively,
either
rule-out
hot
vapor from a
previously
gas
unity;
accomodation
The
this
surfaces.
implies
a
Thus,
there
of
continued
surface
spot.
cathode
be
may
coefficient
reflection
exist.
localized
may have been
trapped
the
from the actual electrodes or from the
surfaces.
macroscopic
Cathode spots certainly
no reason to
is
of
evidence
outgassing
surrounding
not
is
vapor
exactly
from
are several sources of
solid
extraneous
vapor which may occupy the gap volume.
Microprotrusions,
spots,
have radii of only a few
electric
be
resulting from solidification of cathode
microns.
Hence,
average
fields of only a few kilovolts per centimeter can
to values which
magnified several thousand times,
cause substantial electron emission current.
may
This emission
of
the
emission current may directly ionize the residual
gas
current
will
be greater for higher
temperatures
emitting region.
The
in the gap volume.
electrode
evolved
Alternatively, energy deposition at the
may cause gas to evolve from the
gas
may
subsequently
190
become
surface.
ionized.
This
IV. Experimental Work: C. Interpretation
It
is
important
to recall that the
polarity in an AC discharge.
(electron
emitter)
electrodes
That is,
the former
is the new anode (electron
Thus,
microprotrusions
cycle
are
formed during the
field-enhanced
"targets"
exchange
cathode
receiver).
previous
during
the
halfensuing
cycle.
Magnetic Field Effects
Before
we
detail
field,
we
describe some of the problems experienced as
the observed effects
of
the
magnetic
a
result of our unique mode of operation.
We
observed unanticipated interactions of the
and
the
exposed
magnetic field.
wire
of the
coil
which
arc
plasma
produced
These interactions produced an
electrical
short
of the high voltage electrode to ground through
field
coil
winding.
In
open
shutter
the
photographs,
the
we
observed
several brightly illuminated cathode spots on the
magnetic
field coils.
These photographs prompted
a
more
thorough investigation into the phenomenon.
The
results
currents
of the investigation proved that
substantial
were indeed flowing through the coils to
ground.
We tested the coils under two conditions: both sides of the
field-coil-capacitor shorted to ground, and one side of the
capacitor
electrically
floating,, In the former
191
case
we
IV. Experimental Work: C. Interpretation
observed a current of 200 Amps to ground.
The latter
case
showed a short circuit current of 400 Amps. Although we did
not observe a turn-to-turn short of the coil, we considered
it feasible and so we re-designed the coil.
The
new
design called for 8 gauge
copper
wire
inserted
through 7 gauge Teflon tubing. The Teflon tubing was chosen
to have a thickness sufficient to prevent recurrence of the
short circuit.
A
continuous length of tubing was used for each of the two
coils.
amounted to a tubing length of
This
approximately
two meters per coil. This represented an engineering tradeoff between good electrical isolation and good
practice.
of
The
vacuum pump had to evacuate the full length
effective.
tubing if this design were to be
between standard 7 gauge and 8 gauge items.
was
approximately
in
of the difference
one-half
effectively
After an
20 mils.
The
mid-
The pumping aperature
point was one meter from either end.
was
high-vacuum
diameter
This aperature
appropriately
long
vacuum pump-down, it was determined that the implementation
was ready to be tested.
The
tubing
longer
worked precisely as designed.
shorted
to
the coil
wire
192
itself.
The
End
plasma
no
effects,
IV. Exerimental
essentially, took
plasma shorted
path
irectlv to tne wire,
field-coil
obviously,
:of a vertically
rinot g- ing
were
ri.urited
to
work.
cylinder ttally
of the electrode volume.
of
separation
significantly
elements
glass
An
It
electrodes
suIrrounrding
increased
oef any potential
the
vacuum
This almost total
from the rest
all-
consist ed
with exceptions being allowed for
electrodes,
pumping
tne
J.nt
erlea late
designr review.
encompassinrg so 1 ut ion was f i nally imp 1ement ed.
the
least
:..f next
to the exposed end connections.
This prompted a total
so lut i onrs,
the
Instead of shorting
resistance.
ion
ersisted in supporting a short circuit. The
however, still
plasma,
Work:C. I nteroretat
of
the
physical
chamber
impedance between different
short
circu it.
Figu.re
IV. C. 2
shows a schematic drawing of the solu,tir i r, oleent e.
Another possible explanation for the aarent effect of the
rmag
netic field was the actual reak.dowr,of tne coil leads.
This effect was periodicailly checked and the usual
was
negative:
no
We no,:t iced,
effect.
n owever,
imourit ies have accumulated at the coil junct ions.
th
latest
1e
eoeri
o'f tese
ilurit ies.
rlents demorst atea high-volt age
tAiri,-ugn
the periodic
result
cec..s
One of
reakdwn
rul.e out
this effect f,-, all experimental runs, the possibility
sour i -us
discharoe
caused by impurity breakdown must
193
that
fa
be
IV. Experimental
Work: C. Interpretation
taken into consideration, especially at higher voltages.
Figure IV.C.2
ELECTRODE ISOLATION CYLINDER
I
- -
-
194
IV. Experimental Work: C. Interpretation
A
mounting
allowed
ig was arranged which held the
for vertical movement of the
necessary
due
condensation
to
on
periodically
the
the
effect of
glass
adjusted
up
the
to
discharge
is
also aided by
but
This
expected
The
down
dielectic surface for condensation.
the
cylinder.
walls.
or
cylinder,
was
metallic
glass
can
provide
a
fresh
Visual observation
moving
the
be
of
obstructing
condensed material out of the gap line-of-sight.
As
mentioned
parameters
in the data section,
we
observed
recovery
of dV/dt = 0.6 kV/us and dR/dt = 1 S/us.
figures apply in the absence of an applied magnetic
Application
of
surprising
the
effect
magnetic field
on
the
observed
a
accompany
interruption
phenomenon
reduction
is
in
produced
interruption
the
parameters
in Figure
field.
somewhat
parameters.
when the field was
illustrated
a
These
which
We
would
applied.
IV.B.6;
the
This
field
decreased the breakdown voltage.
It
appears
plasma.
behind
our
confined
the
Magnetic confinement of plasma is the central idea
many experimental fusion devices.
device
confinement
Tokamaks.
consider
as if the magnetic field better
resembles
schemes:
Because
a
particular
the torodoidal
of
this
class
fusion
topological
it possible that the applied
195
The topology
field
of
of
magnetic
devices,
or
similarity
we
is,
indeed,
IV. Experimental Work: C. Interpretation
acting
to
confine
the plasma.
Figure
IV.C.3
shows
an
idealized representation of the magnetic fields.
Figure IV.C.3
SCHEMATIC REPRESENTATION OF PULSED MAGNETIC FIELDS
J4
0
(
0
/
i0
0
0
i
I
I
a
F
0
0o
-I
/
rl--
~
\,j
PRESENT DEVICE
TOKARAK
plasma current
J8e
B8
torodial field
H
vertical magnetic field
z
196
I
~~~~~
U
_
IV. Experimental Work: C. Interpretation
Our
interpretation
the Lorentz force,
the plasma ring,
of this phenomenon is
the
following:
which acts to constrict the diameter of
also acts to confine the plasma while the
contraction occurs.
However,
the possibility of spurious,
parasitic discharges must be considered.
Hence,
we
mechanism
together
have
that
while
an
ironic
moves
twist
of
the plasma also
it is being moved.
events:
holds
The
the
same
plasma
Simply increasing
the
magnitude of the magnetic field does not produce any change
in this chain of events.
Although a greater force acts
the plasma, a greeter confining force is also present.
197
on
IV.D. Summary
This thesis has investigated the physics of vacuum arcs
and
examined
how
characteristics
applicable to vacuum switches.
of
vacuum
arcs
are
Specifically, four distinct
areas have been discussed in-depth. They are the following:
(1)
Theory
of
vacuum
arcs,
including
several
new
theoretical approaches; (2) Description of our device, this
amounts
to a transfer of technology from our group to
public domain;
some
(3) Data obtained by the device,
interesting
data,
which
results;
including
and (4) Interpretation of
binds together the theory,
the
device,
and
the
the
data.
Theory of Arcs
A
generalized
examined
been
in detail.
provided
power balance of vacuum arcs
has
been
Original theoretical extensions
have
in four separate areas.
The
cathode
radius and formation time were theoretically predicted
these
predictions
agreed
well
with
spot
and
experimental
observations. The quasi-steady state phenomena of electrode
ablation
and plasma potential hump formation were examined
in detail. These original theoretical results again were in
good agreement with experimental results. The phenomenon of
arc stability during arc extinction was also
It
was
found
that
a model
198
based
on
investigated.
electrode
energy
IV. Experimental Work: D. Summary
conservation
fit
the available
model
more-appealing
physically
model
heuristic
previous,
experimental
of
is
arc
in
This
data.
to
contrast
stability
based
a
on
electrode material vapor pressure.
In
each of the above cases,
theoretical
were
models
emphasized
the
Good agreement
was
obtained between predictions of the theoretical models
and
developed
physics
were
which
of
quite
simple
the particular situation.
results.
experimental
however,
improve the agreement,
extended
to
the essential physics
is
theory
The
and
could be
clearer in a simplified presentation.
The
characteristics
such
materials,
as
vapor
outgassing rate, and erosion rate, which must be
pressure,
considered
Because
of
for
there
use
in
vacuum
switches
are
is such a wide variation in
discussed.
properties
of
materials, various engineering trade-offs must be made. For
instance,
dielectrics
machining
Another
and
trade-off
undesirable
must
be
good
commonly do not exhibit
vacuum
outgassing
example is provided
thermionic electron
both
good
characteristics.
by
emission
Tungsten.
The
characteristics
considered as well as the desirable high
melting
point of Tungsten.
Basic
plasma physics has been included to provide
the
fundamental knowledge necessary to understand the issues of
vacuum arc switches.
This type of transfer of
199
technology,
IV. Experimental Work: D. Summary
and information from theory to practice is an
methodology,
important result of solutions to applied physics problems.
been
interruption have
of
mechanics
The
discussed.
constant
a very simplified kinematic model with
of rigor:
levels
aided interruption was covered on two
Magnetically
and another, more complete, model which
plasma properties,
took into account radial dependence of plasma parameters.
Device
The team at MIT/EML has helped me in the formulation of
design
several
for
criteria
the
device.
experimental
Details of design and construction of our particular device
Many
given.
been
have
of
implementation
the
Teflon
gaskets.
and
structures
We have
built
rubber
vacuum
device
that
imposes
few restrictions on
itself.
The
ability
to
intermediate
results
has a value which
modify an
and
materials
of
include
Examples of such uses
have been used.
techniques
uses
unique
an
re-usable
experimental
experiment
the
based
experiment
cannot
be
on
over-
estimated.
Data and Interpretation
The device has been operated in two modes:
vacuum
mode.
with
gap
The
the
(TVG) mode,
and a magnetically augmented
results for the TVG mode are in good
results
of
a triggered
other
200
researchers
(in
TVG
agreement
terms
of
IV. Experimental
interruption times,
baseline
for
the
currents,
Work: D. Summary
and voltages) and present a
magnetically
augmented
results.
The
results
of magnetic augmentation show that magnetic fields
can
used to manipulate the
be
further show,
however,
arc
plasma.
The
results
that the plasma is quite difficult
to control precisely. We have been able to apply a magnetic
field
which
becaused
constricts
and
confines
the plasma is confined,
the
plasma,
yet
arc extinction does
not
immediately occur.
Over 200 experimental shots have been fired.
Benchmark
results are: single-half-cycle peak current interruption of
5.2 kA,
recovery voltage of 7 kV, and an interruption time
of approximately
10 us.
Future Work
The
idea
of a plasma baffle was
construction of the device.
conceived
It was decided,
prior
however, that
for simplicity the device would be constructed without
Surface
metal-vapor
condensation
will
application to improved field-augmented
Baffles
can
likely
have
plasma
extinction.
The baffle design
resemble that of ordinary gas-arc chutes.
cylinder-electrode
design
of
installation of such a baffle.
201
the device will
it.
immediate
be installed on which the field-confined
field-driven plasma will condense.
to
and
will
The open
allow
for
Appendix
A
Numerical Power Calculations
In
this
the numerical details
appendix
in Figure II.A.8 are given.
presented
the
of
results
Descriptions of the
various processes can be found beginning in Section II.A.1.
necessary
assumptions
numerical
Other
these
for
calculations are presented in Figure II.A.7. P is the total
power
Watts/cm2 .
area
and F is the
Watts
in
is
the
spot
cathode
density
"spot" indicates the
subscript
The
power
surface
area;
the
in
effective
subscript
"ave"
indicates the effective area is the entire surface area
of
cathode.
(1)
charged
particles:
P = ZViI+
= 1 x 43V
x 0.1
x
lOkA
P = 43 kW,
FsPot
= ZViJ+
= 1 x 43V x .1 x 5x10 6 a/cm
2
FsPot = 21.5 MW/cm2.
(2) neutral
P
= .5
particles:
3.8x10-
20
P
(r[En rnA + <cxvi>ni
x 3x10
2 1 cm- 2 s - 1
nn E
A dl]
x 25
10-16 cm 2 xlO 6 cm/sxlOl 6 cm- 3 xlO 1 7 cm- 3 xl.6xlO-1 9 Jx25cm2 x.07cm]
P = 15 kW
Fave = P/A = 620 W/cm2 .
(3) ohmic
heating:
P = I2 R; R = 73x10
202
-6
x 7cm/ 25 cm 2 ;
V. Appendices: Appendix A Power Calculations
P = 2 kW.
(4) radiation: Prad = ZC[Prad recomb
Precomb
=
PBrem + Pline3
r ne ni Vp E = 6 kW; Frec = 240 W/cm 2 ,
Kr = 10-11 cm3 /s,
PBrem
= 1.7x10-
32
n e n i TO. 5 Vp = 425 W;
FBrem = 20W/cm2 ,
Pline = bZ
Anm
Enm
Nn = 4 kW; Fline = 160 W/cm2 ,
L= 0.3 strd,
Prad = 3.3 kW;
Fave = 130 W/cm2.
(5) recombination (three body): P3B = 3B
(ne)2 ni VE
P = 4 kW,
E
= 1 eV
K3B = 9 x 10-27 T -4 5 cm 6 /s = 10-26 cm 6 /s,
Fave = 160 W/cm2.
(6) ionization:
Pioniz
= XI E/m = 7 kW,
FsPot = 3.5 MW/cm2 .
(7)
grey
+
body rad.:
PBB = Ld(Tspot)4 Aspot +
4 AbulkL
(Tbulk)
P = 100 W
FsPot =
(8) thermal
d(TsPot 4
conduction:
Tbulk
4 )
= 200W/cm 2 .
P = AsPot k dT/dx
203
= 3.2 kW,
V. Appendices: Appendix A Power Calculations
FsPot = P/A = 1.6 MW/cm2 .
(9) phase
FsPot
change:
P = (Hfusion
+ HvaPor)
XI = 6.6 kW,
= (Hf + Hv) XJ = 3.3 MW/cm 2 .
(10) work function
FsPot =
cooling:
P-
=
-I- = .9
- I = 23 kW,
- J- = 11.5 MW/cm2.
(11) electron heat capacity: P = 1.5 kB(TH - TC) I-/e
P = 3.5 kW,
FsPot = 1.5 kB(TH - TC) J-/e = 1.8 MW/cm2.
204
Appendix B Application Considerations
V.B Mega Amp Issues
As in most fundamental experimental investigations, we were
in
interested
performance
level
vacuum
a metal vapor
of
we
increasing
the arc discharge current.
question is whether operation at
levels
could
is
switch
arc
for
level it would be a very attractive device
is
program
of
an
before
achieve
undertaken to
characteristics
operating
several limiting
However,
carefully
considered
be
must
current
mega-ampere
and interrupt at the mega-ampere
conduct,
of applications.
by
specifically,
More
If a metal vapor vacuum
feasible.
trigger,
current
number
switch.
arc
were concerned with limitations imposed
Primarily,
the
the
limit
the parameters which ultimately
areas
experimental
capability.
this
a
vacuum arcs offer
so
The
many
unique advantages (rapid commutation, low losses, very high
voltage operation) that in the future such an effort should
certainly be considered.
Electrode Erosion
erosion
Electrode
current
caused
is
operation.
by
the
This
very
concern
the most serious
is due to bulk
great
currents
and
metal
of
high
removable
deposition
on
surrounding surfaces. Because lifetime considerations imply
a
volume
erosion,
Figure
205
V.B.1
shows
erosion
V. Appendices: Appendix B Applications Considerations
characteristics
of
several in terms of
cubic
centimeter
eroded per Coulomb of current passed.
Figure V.B.1
MATERIAL VOLUME EROSION CHARACTERISTICS
Metal
Erosion rate
(ucm3 /C)
Cd
76
Zn
30
Mg
20
Ag
14
Al
44
Cu
13
Cr
In
Ni
11
Fe
8
Ti
11.6
C
7.6
Mo
4.6
W
3.2
addition
however,
plasma
5.6
to
overall
cycle
lifetime
consideration,
erosion has other implications. As mention above,
condensation on surrounding surface
206
occurs
during
V. Appendices: Appendix B Applications Considerations
interruption.
current
Unless the switch has been properly
designed to take this condensation into account, the buildup
of metal may lead to an internal short circuit
and subsequent disposal of the inoperative
device
of
the
device.
If this build-up occurs un-monitored, one must consider the
as disposable after a certain number of cycles
devices
or
catastrophic failure of the device once the condensed
risk
reaches
metal
critical
a
level.
It
is
design
common
practice to shield critical components from condensation of
low
current
erosion by blocking the solid
angle
of
the
component as seen from the eroding metal. However, for high
shield
it is not sufficient to merely
operation,
current
components from the line of sight of the electrode in order
to prevent exposure to condensation.
in
Erosion
researchers
al,
19783.
condensation
Daalder,
on
of
the
by
several
Tuma, et al, 1978] have observed
parts of their apparatus which
In particular,
cathode received a flux of
subsequently
which
observed
1976; Jenkins, et al, 1975; Tuma, et
et al
Tuma,
has been
to the eroding surface.
exposed
side
form
droplet
condensed in
suggested by Jenkins,
situ.
metal
Two
were
not
the
back
particles
explanations
et al [Jenkins, et al,
arise.
One,
1975],
is that macroparticles of the eroding surface
been
eected
with a substanial velocity in
207
an
have
arbitrary
V. Appendices: Appendix B Applications Considerations
As the macroparticle continues along its flight
direction.
it continuously emits vapor (as when boiling). This results
if present) along
in sending neutral atoms (and molecules,
of sight.
line
another
The second explanation relies
Tuma, et al
collisions to re-distribute the particle flux
Essentially, then, the metal atoms have executed an
19781.
run"
"end
on
shields installed for
around
the
purpose
of
protecting build-up of metal condensate.
At high current levels anode spot formation is observed. In
to
contrast
metal
spots represent a more difficult
than cathode spots.
extinguish
of
Typically of a few centimeters in
areas.
anode
the
anode spots are bulk
cathode spots,
diameter,
challenge
to
This is primarily a result
large thermal inertia of the
the
liquid-
gross
area
melting
which continues to release vapor during a current zero, and
partly
in
because,
becomes
the
an AC
the
discharge,
mentioned
anode
spots.
frequency
the
Lee,
He
found
situation,
The
II.B)
of
Rich, 1971] experimentally investigated
that
for a
given
peak
geometry
metals differed widely according
and
to
anode
spot
current achieved without anode
spot
peak current which could be drawn without
formation.
to
19603.
in the materials section (Section
Rich
this thesis,
anode
new cathode and as such it is susceptible
electron emission by the "T-F" mechanism
As
former
208
V. Appendices: Appendix B Applications Considerations
formation is called the critical current. He correlated the
critical
current
dependence
5
parameter Tm(kr Cp) 0 - .
appear
with
a
thermal
goodness
His results for a variety of metals
in Figure V.B.2.
(Rich used electrodes 5.7
cm
in
diameter.)
Figure V.B.2
CRITICAL CURRENT VS. THERMAL "GOODNESS" PARAMETER
[Rich, 1971]
Critical Current
Tm(kr Cp)0 .5
Sn
2.3 kA
57
Al
6.8 kA
383
Ag
9.7 kA
723
Cu
10.3 kA
954
Mo
13.6 kA
1204
W
13.8 kA
1693
using
the same material in a
Metal
By
configurations,
Rich
further
variety
found
of
geometrical
geometry to
make
a
significant difference in the critical current. Kamakshaiah
and
Rau
arcing
Kamakshaiah and Rau,
time,
electrode surface
1977] concluded
conditions,
and
separations also factor into anode spot formation.
209
that
the
contact
V. Appendices: Appendix B Applications Considerations
Thus,
a variety of guidelines
designer
which
enable
are available to the switch
him to design
higher
performance
switches.
Current Sharing
The
Introduction contains a list of vacuum arc properties.
Included in this list is the condition of positive voltagecurrent relationship.
mentioned
The discussion of cathode spots also
this feature of vacuum switches.
The
practical
implication of a positive voltage-current characteristic is
the
stable parallel operation of vacuum arcs.
gaps,
Unlike
gas
the voltage across the electrode gap of a vacuum arc
increases
these
roughly linearly as
devices
share
current
increases.
current evenly among
all
Hence,
available
arcs.
Since most of the cost of
vacuum
vessel
feedthroughs,
electrode
same
and
it
pairs
is
a vacuum
switch is
associated
high
quite possible
to
the cost of a
voltage/current
combine
in the same vacuum vessel all
high current feedthrough.
using
On a small scale,
exactly what occurs for cathode spots.
several
this is
As interest in
commercial application of high current devices grows,
activity
is
expected in engineering improvements such
the above extrapolation.
210
the
the
more
as
V. Appendices: Appendix B Applications Considerations
Magnetic Forces
The
introduction of a large current into
implies
Even
the
though
through
the
significant.
existence of a rather large
the
current executes
device,
the
Present-day
a
confined
device
magnetic
field.
simple
single-pass
forces generated can
railguns
are an
be
example
quite
o
a
single-turn large-current device. The performance levels of
these
devices
illustrate
the existence of
which switches must contain.
will
even
forces
Moreover, the field generated
exert large forces on all current
Hence,
large
carrying
if interior to the vacuum vessel the
divides into parallel segments,
members.
current
proper design must account
for the forces generated.
The plasma-current interaction also is a consideration. The
plasma arc channel must be in quasi-equilibrium; hence, the
internal
plasma
pressure must be
equal to
the
magnetic
field pressure generated by the current. Figure V.B.3 shows
a schematic of the arc channel.
211
V. Appendices: Appendix B Applications Considerations
Figure V.B.3
ARC CHANNEL SCHEMATIC
The field at the surface of the arc channel is:
B = uI/2
r.
This field produces a pressure:
P = B 2 /2uo.
If
the
the magnetic field pressure were greater than
plasma
decrease.
greater
tend
(P
If,
=
nkT),
the
arc
increase
equilibrium
is
radius
of
would
on the other hand, the plasma pressure were
than the magnetic pressure,
to
channel
that
in
radius.
frequently
The
called
the arc channel would
condition
the
of
quasi-
Bennet
pinch
condition.
We can use this simple analysis to predict the arc
radius. The resulting expression for the radius is:
212
channel
V. Appendices: Appendix B Applications Considerations
r = I
___
2rV
·
nkT
For
copper at an oberved arc channel current of 100
amps,
the
critical channel radius is about one millimeter.
This
value
agrees with experimental observation
[Reece,
1963;
Mitchell, 1970; Heberlein, 19803.
As
the
current
magnetic
in the
pressure
I2:
this
conditions
kT
must
This
has
that
nkT W. 12.
it is observed that
n
BZ
the
12.
For
nI,
Under
quasi-
present-day
thus as the current
must increase faster than
increase approximately linearly
important
resulting
the plasma pressure must also scale
means
increases either
increases
will increase as
equilibrium to obtain,
as
device
implications for the
linear,
with
or
current.
overall
energy
balance of vacuum switches, in general, and the surrounding
vacuum
vessel
walls (which presumably
must
receive
the
increased heat flux), in particular.
Summary
In
with
addition
metal
to the actual performance
vapor
vacuum
arc
levels
switches,
more
considerations will be necessary for effective,
implementation of them.
213
attainable
practical
widespread
V. Appendices: Appendix B Applications Considerations
There
appears
vapor
vacuum
no fundamental current limitation to
arc switches.
However,
because
metal
there
are
current density limits (even at present-day current levels)
proper design engineering will be required to reach desired
interruption
several
feasible,
current
but
accomplished
magnetic
performance
carrying
levels.
arc
Parallel
channels
operation
seems
of
entirely
there has been little experimental research
in this area.
Containment of
the
increased
forces as a direct result of an increased current
will require a suitable mechanical support structure.
214
V. Appendix C
This
appendix
Interruption Kinetics
presents
a
mathematically
more
detailed
analysis of the interruption kinetics introduced in Section
II.D.3.
We
assume the magneto-hydrodynamic
equations
are
valid.
For
in
completeness we repeat the introductory analysis given
Section
schematic
II.D.3.
Figure V.C.1 is a
simplified
showing the physical parameters needed for
switch
this
analysis.
Figure V.C.1
SIMPLIFIED SWITCH SCHEMATIC
--
-
-0
l
I
The
pulse coil is driven by an auxiliary
capacitor
bank.
The voltage induced in the secondary, which in this case is
the plasma itself, can be expressed as:
215
V. Appendices: Appendix C Interruption Calculations
V = dd/dt = 7rr2 dB/dt .
Assuming a sinusoidal excitation frequency (w = 27rf),
the
complex amplitudes are:
V0 = 7rr2 wBO.
This voltage generates an induced current:
VO = Io Z
.
Z is the complex impedance expressed as:
2 + (w)2 ,
Z =
where
R
and
inductance,
L
are
the
plasma-torus
respectively.
resistance
and
The radial force density acting
on the plasma is:
f =
This
given
is
in
magnetic
excitation
a = J x B/c
= IB/(c
the point of deviation with
Section II.D.3.
flux:
we
are
frequency.
s2
)
the
simpler
We assume the plasma
in the asymptotic
This
conserves
limit
means the plasma
theory
of
current
the
is
given by (B is the driving field):
I
We
= -
AB/Lc
solve these equation for the plasma acceleration
function of radius:
216
as
a
V. Appendices: Appendix C Interruption Calculations
dZ
~L~-
-r2
B2
2
s2 L c
a =
For
/
modest
changes
=oro/r,
in
r
3G ~~T~.
we can
assume
L
=
rLo/rO,
= constant, and B = constant. The resulting
second order differential equation is non-linear and can be
written as:
d 2 r/dt2 = -pr2
where,
B 2 /( ,
p =
This
2
Lc 2 )
equation can readily be solved by forming a system of
two simultaneous first order differential equations:
dr = v
dt
and
dv = -pr2 .
dt
The initial conditions are v(t=O) = 0, and r(t=O) = r.
Re-
arranging we obtain:
dr
v
(Note: a somewhat different derivation leading to identical
results consists of multiplying the expression of
first
law
by
the velocity
v
and recognizing
differential.) In any event, the result is:
217
Newton's
an
exact
V. Appendices: Appendix C Interruption Calculations
v 2 /2 = p(r03 - r3 )/3 .
This
equation
may
then be solved for the
time
rate
of
change of the radius:
dr = v = -
2(rQ3_-
dt
3
egative value of the square root was
Note that the
Physically
<
dr/dt
r3 )
this corresponds to a shrinking
radius,
taken.
(i.e.
0).
Separating exact differentials we get:
3
j^3ic,-
After the substitution u = r/rO has been made, reference to
the
integral
Gradshetyn
tables of Gradshteyn and Ryzhik
and Ryzhik, 1965) yields the solution for the time required
for
the
plasma current-ring to move
under
the
magnetic
force to the dimensionless radius u = r/rO we have:
t
3
F(d sin 75)
V 2pro
where,
F(O\k) is the Elliptic Integral of the First Kind,
and,,
218
V. Appendices: Appendix C Interruption Calculations
= arccost[tl
- 1
1 - u.
u/[(/
solution,
Because of the awkwardness of the analytical
is
frequently
convenient
more
directly
numerically
I(u) is given by:
I(u), where
integrate
to
it
I
I(u)
When
I(u)
is
dx
(1 - x3 )0 . 5
defined as above,
identical
with
3
F(O\k=sin
75)/
A
table of the values of
short
I(u) is
I(u) =
F(d\sin
given in Figure V.C.2.
Figure V.C.2
VALUES OF RADIUS INTEGRAL
u = r/ro
I(u)
= F(\sin
0.9
27.
0.37
0.8
37.5
0.53
0.7
48.4
0.66
0.5
56.5
0.89
0.3
64.9
1.10
0.1
70.
1.30
0.0
74.5
1.40
219
75)/
75/
s
V. Appendices: Appendix C Interruption Calculations
In
order to illustrate application of the above formalism,
we
assume typical values for the relevant
given in Figure V.C.3.
parameters,
The resulting radius as a
function
of time is shown in Figure V.C.4.
Figure V.C.3
TYPICAL PARAMETERS VALUES FOR INTERRUPTION
= 1 cm
s
Lo = 0.1 uH = 1.11 x 10-19 s 2 /cm
ro = 6 cm
0
=
10- 5
g/cm 3
Figure V.C.4
GRAPH OF SHRINKING PLASMA RADIUS AS A FUNCTION OF TIME
U:
O0
B =
5
10
15
t, us
220
20
500
as
G
25
V. Appendices: Appendix C Interruption Calculations
This
graph
microseconds
kiloGauss.
shows
are
These
that
possible
fields
extinction
at applied
times
fields
levels are readily
practice.
221
of
order
of
a
produced
10
few
in
i
FOOTNOTES
1. Boxman,
R. L. 1974. J. Appl.
Phys.,45,
p. 4835.
2. Braginski, S. I. 1965. Reviews of Plasma Physics
Vol. 1 (New York: Consultants Bureau) p. 220.
3. Carlsaw, H. S. and Jaeger, J. C. 1980. Conduction of
Heat in Solids, Second Edition, (Oxford, Britain:
Oxford University Press) p. 75.
4. Conbne,
J. D. and Burger,
26, p. 895.
E. E. 1955.
5. Compton,
Rev. 37 p. 1069.
K. T. 1931. Phys.
6. D&M: Davis,
W. D. and Miller,
J. Appl.
H. C. 1969.
Phys.,
J. Appl.
Phys. 40 p. 2212.
7. Ecker, G. 1980. Vacuum Arcs: Theory and Applications,
ed. Lafferty (New York: Wiley) p. 228.
8. Erven, C. C. et al 170. Proc. of the Fourth Intern'l
Syn. on Discharges and Electrical Insulation in Vacuum,
(Waterloo, Ont., Canada) Sept., 1970, p. 219.
9. Farrall, G. A. 1980. Vacuum Arcs: Theory and
AppRications, ed. Lafferty (New York: Wiley) p. 188.
10. Gilmour, S. 1980.] "The Present State and Projected
Capabilities of Vacuum Arc Opening Switches", SUNY,
Buffalo].
11. Gradshetyn I. S. and Ryzhik, I. W. 1965. Table of
Integral§, Series and Products (New York: Academic
Press) p. 229, integral 3.139, #2.
12. Graneau, P. 1981. private communication.
13. Grissolm
J. T. and Newton,
J. C. 1974.
J. Appl.
Phys.
45 p. 2885.
14. Heberlein,
J. V. R. and Gorman,
J. G. 1980. IEEE
Trans. on Plasma Science PS-8 p. 283.
15. Holmes,
A. J. T. 1974. J. Phys.
D: Appl.
Phys.
7
p.1412.
16. Jenkins,
J. E. et al 1975.
222
J. Phys.
D 8 p. L139.
17. Kamakshaiah S. and Rau, R. S. N. 1977. IEEE Trans. on
Plasma Science PS-5 p. 1.
18. Kaneda, T. et al 1981. Physica, 104C, p. 124.
19. Kimblin, C. W. 1971. Proc. IEEE 59 p. 546.
20. Kimblin, C. W. 1973. J. Appl. Phys. 44 p. 3074.
21. Kittel, C. 1976. Introduction to Solid State Physics,
(New York:
Wiley)
p. 32.
22. Lafferty, J. M. 1966. Proc. IEEE 54 p. 23.
23. Larmar, E. S. and Compton, K. T. 1931. Phys. Rev.
37 p. 1077.
24. Lee, T. H. 1959. J. Appl. Phys. 30 p. 166.
25. Lee, T. H. 1960. J. Appl. Phys. 31 p. 924.
26. Lifshitz E. M. and Pitaevskii, L. P. Physical Kinetics,
(New York: Pergamon Press) p. 6.
27. McClure, G. W. 1974. J. Appl. Phys. 45 p. 2078.
28. McCoy, F. et al 1964. Proc. of the First Interna'ct'l
Sym. on Insulation Strength in Vaccum, Cambridge, MA,
October 1964, p. 259.
29. Miller H. C. and Farrall, G. A. 1965. J. Appl. Phys.
36 p. 1338.
30. Miller,
H. C. 1971.
J. Appl.Phys.
43 p. 2175.
31. Miller, H. C. 1977. IEEE Trans. on Plasma Science PS-5
p. 181. 1977.
32. Mitchell, G. R. 1970. Proc. IEE 117 p.23 1 5 .
33. Mitchell, G. R. 1974. J. Appl. Phys. 45 p. 2078.
34. Mitchell, G. R. 19 . "The Influence of Vacuum Arcs on
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35. Mongeau, P. 1981. AIAA/JSASS/DGLR, Fifteenth International
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36. O'Hanlon, J. F. 1980. A User's Guide to
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223
Vacuum
37. PR&K:
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V. N. and Kapin,
A. T.
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38. Poeffel, K. 1980. IEEE Trans. on Plasma Sci. PS-8
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39. Reece, M. P. 1963. Proc. IEE 110 p. 793.
40. Rich J. A. and Farrall, G. A. 1964. Proc. IEEE 52
p. 1293.
41. Rich, J. A. 1971. Proc. IEEE 59 p. 539.
42. Robson, A. E. 1978. J. Phys. D: Appl. Phys
11
p. 1917.
43. Rozanova, N. B. and Granovskii, V. L. 1956. Sov. Phys. - Tech.
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1 p. 471.
44. Schoenbach, K. et al 1981. Third IEEE International Pulsed
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45. Tanberg, R. 1930. Phys. Rev. 35 p. 1080.
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47. Touloukian, Y. S. 1981. Vade Mecum ed. Anderson (New York:
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48. Tume, D. T. et al 1978. J. Appl.Phys. 49
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49. Weast, R. C. ed. 1974. Handbook of Chemistry and
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51. Machine Design, 1983 Material Reference Issue, 14
April p. 65.
224
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230
VIII. Afterword
A
doctoral thesis has a multitude of goals:
are
achieved
represented
goals
and
by
some
of
which
are
some of which
not.
The
this thesis has accomplished many
set by the author,
by external agencies.
work
of
the
as well as the goals established
From an academic point of view,
the
author feels several important theoretical issues have been
clarified
and/or explained in this work,
which previously
have not received attention.
From
a
practical
constructed
but,
Interruption
of
It
of
view,
a
device
has
which not only provides an excellent
experience,
merit.
point
must
additionally,
performs
be remembered that no
learning
quite
5 kA in 160 us is the present
been
well.
figure
external
of
parallel
capacitors or series staturable inductors have been used to
achieve this performance level.
The
author
has
thoroughly
associated with his study;
the
enjoyed
the
camaraderie
the other graduate students and
excellent staff of professionals have made the
experience especially rewarding.
231
entire
IX. Biographical Note
The
was
author
born
and
raised
Canton,
in
Ohio.
In 1975 he graduated from Glenwood High School. During high
a self-paced mathematical program and courses at a
school,
local
institution,
College,
Malone
were
important
in
M.I.T.
In
providing some of the necessary preparation for
in
variety
a
of
author
particpated
extracurricular
activites
including
related events.
His extended family had (and still has) an
the
addition,
and
sports
church-
influential effect on his development.
What is not widely recognized,
institution,
great.
the people behind the scenes who keep MIT
is
When
concerning M.I.T. as an
the
author experienced a very
the Rpeple
injury due to a fall from a substantial height,
at
back
serious
MIT made it possible for him to continue
academic
his
program, even if it was an abbreviated schedule.
Prior
AVCO's
I.B.M.
At
concerning
Systems Division and a
Inc.
the
application
of
vacuum
of
further
and
acceleration
of
at
research
fields
magnetic
including
matter,
arcs
group
development
the author will continue
EML,
acceleration
involving
Launch
Electromagnetic
(EML) Inc. of Cambridge, Mass. the author worked
Research,
for
oining the staff at
to
to
research
metal
with
applications to national security.
The author currently lives in Medfield,
Collie,
wife
and
has
assisted
Ginger.
with
the
Mass. with his
Elizabeth Anne
Bernhard
artwork
the
for
Master's/Bachelor's Thesis and this work.
232
Cope
combined