)CUMENT OFFICE 26-327
.SEARCH LABORATORY OF ELECTRONICS
,SSACHUSETT$ INSTITUTE OF TECHNOLOGY
,MBRIDGE, MASSACHUSETTS 02139, U.S.A.
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i
DIAGNOSTIC EXPERIMENTS IN A MAGNETICALLY
DRIVEN SHOCK TUBE
JOHN B. HEYWOOD
TECHNICAL REPORT 428
DECEMBER 31, 1964
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
I
RESEARCH LABORATORY OF ELECTRONICS
CAMBRIDGE, MASSACHUSETTS
The Research Laboratory of Electronics is an interdepartmental
laboratory in which faculty members and graduate students from
numerous academic departments conduct research.
The research reported in this document was made possible in
part by support extended the Massachusetts Institute of Technology, Research Laboratory of Electronics, by the JOINT SERVICES ELECTRONICS PROGRAMS (U.S. Army, U. S. Navy, and
U.S. Air Force) under Contract No. DA36-039-AMC-03200(E);
additional support was received from the National Science Foundation (Grant GK-19).
This report will also be issued as Fluid Mechanics Laboratory
Publication No. 65-1. Additional support for this work was provided by the Advanced Research Projects Agency (Ballistic Missile
Defense Office) and the Fluid Dynamics Branch of the Office of
Naval Research under Contract Nonr-1841(93).
Reproduction in whole or in part is permited for any purpose
of the United States Government.
SCALES FOR OSCILLOGRAMS
Fig. 8.
VE scale 2 kv/cm; I scale 125 kamp/cm; time scale
2 jisec/cm.
Fig. 18.
Vertical scales in wb/m2; time scale 1 sec/cm.
Fig. 19.
Vertical scales in wb/m2; time scale 1 isec/cm.
Fig. 21.
Vertical scales in wb/m2; time scale 1
Fig. 24.
Vertical scale 67 volts per cm/cm; time scale
1 sec/cm.
Fig. 26.
Be scale in wb/m 2 ; Er scale in volts per cm/cm; time
sec/cm.
scale 1 sec/cm.
Fig. 28.
Deflection in 1014 watts/m,
0. 5 ,usec/cm.
m3, sterad; time scale
I.
d
MASSACHUSETTS
INSTITUTE
OF TECHNOLOGY
RESEARCH LABORATORY OF ELECTRONICS
December 31, 1964
Technical Report 428
DIAGNOSTIC EXPERIMENTS IN A MAGNETICALLY
DRIVEN SHOCK TUBE
John B. Heywood
Submitted to the Department of Mechanical Engineering,
M. I. T., September 12, 1964, in partial fulfillment of the
requirements for the degree of Doctor of Philosophy.
(Manuscript received November 4, 19 64)
Abstract
This report describes the results obtained from a series of experiments in Hydrogen
in a magnetic annular shock tube with an applied axial magnetic field. Measurements of
the front speed were made over as wide a range of initial gas pressure, initial drive bank
voltage, and axial magnetic field as possible. These results are compared with the predicted speeds obtained from the Kemp and Petschek solutions and the snowplow model,
and reasonable agreement is obtained.
Measurements were also made on the front properties with magnetic and electric
field probes inside the annulus, and with phototubes. It was found that a substantial fraction of the drive current always flows in the front and no shock wave preceding the current sheet was observed. A detailed picture of the current distribution inside the annulus
is obtained, and a current loop was found to flow behind the front. It is shown that electric field measurements substantiate this picutre. It is also shown that when the Alfv6n
speed ahead of the front is comparable with the front speed, the flow pattern changes
significantly.
9I
TABLE OF CONTENTS
I.
II.
III.
IV.
V.
VI.
INTRODUCTION
1
1. 1 General Considerations
1
1. Z2 Magnetic Annular Shock Tube
1
1.3 Experimental Program
2
THEORETICAL MODELS FOR THE OPERATION OF A MAST
4
2. 1 Kemp and Petschek Solution
4
2.2
5
"Snowplow" Model
2. 3 Comparison of the Two Models
6
2. 4 Validity of the Assumptions
6
EXPERIMENTAL APPARATUS, MEASURING TECHNIQUES, AND
INSTRUMENTATION
8
3. 1 Description of the Experimental Apparatus
8
3. 2 Measuring Techniques and Instrumentation
13
EXPERIMENTAL RESULTS
17
4. 1 Summary
17
4. 2 Measurements on Azimuthal Uniformity
18
4. 3 Measurements of the Front Speed
19
4. 4 Internal Measurements with B 0 , E z , and E r Probes
24
4.5 Absolute Light-Intensity Measurements
39
INTERPRETATION OF THE RESULTS
43
5. 1 Summary of Front Properties
43
5. 2 Momentum Balance
43
5. 3 Internal Flow Pattern
45
CONCLUSIONS
47
6. 1 Summary
47
6. 2 Suggestions for Further Work
47
APPENDIX A
Diffusion of the Current Sheet into the Shock-Heated Gas
49
APPENDIX B
Equation for the Flux Speed
50
APPENDIX C
Drive-Bank Performance with the Shock Tube as Load
52
APPENDIX D
Calibration of B
54
Probes and Magnetic Search Coils
Acknowledgment
56
References
57
iii
I. INTRODUCTION
1.1
GENERAL CONSIDERATIONS
Interest in the dynamics of gases at very high temperatures and velocities has
stimulated the development of devices that permit experimental investigation of the
properties of such ionized gases or plasmas. One such device is the shock tube. In it
the undisturbed gas is accelerated and heated as it passes through a strong shock wave
that is driven down the tube. The attraction of this type of device is that the gas compressed between the shock wave and the driver interface (called the homogeneous gas
sample) has properties that can be accurately calculated from the state of the undisturbed gas and the conservation laws.
A discussion of the conditions attainable in
various types of shock tube and some of the limitations of these devices have been
given by Kantrowitz.
The temperatures and velocities attainable in conventional pressure- or combustiondriven shock tubes are limited by the speed of sound in the driver gas. These limits can
be raised by adding the energy from a condenser bank to this driver gas (arc-driven
shock tube); but to obtain shock velocities high enough to completely ionize the gas compressed behind the shock wave (of order 10 7 cm/sec for Hydrogen gas) it is necessary
to resort to electromagnetic forces to propel the shock down the tube.
This type of
driver (called a magnetic driver) involves the interaction between the current obtained
from a condenser-bank discharge and the magnetic field that this current creates behind
it to drive the current down the tube.
If the gas temperature,
and thus the electrical
conductivity in the current sheet, is high enough (magnetic Reynolds number effect) the
current sheet will act as a piston and drive a shock wave in front of it. Shock speeds 1
of up to 6 X 107 cm/sec have been obtained with this type of device.
1.2 MAGNETIC ANNULAR SHOCK TUBE
One useful type of device that has been developed has coaxial geometry, in which
the driving condenser bank is discharged between two concentric metal cylinders. The
radial current sheet that is produced is driven down the annular spacing between the
cylinders by the azimuthal magnetic field which it sets up. Two types of test-gas distribution in this annular space have been considered.
In one the gas is released at the
driving end of the tube from a fast-acting valve. This type of device is usually called a
"Plasma Gun" or "Plasma Accelerator." 2 '3 In the other, the initial test-gas pressure
is uniform; this is called a "Magnetic Annular Shock Tube" (MAST) 4 - 8 and it is designed
to produce a slug of shock-heated gas whose properties are uniform and can be calculated.
To achieve such a uniform shock-heated gas sample, magnetic containment in the
form of steady magnetic bias fields parallel to the walls of the shock tube must be
applied, to prevent the hot ionized gas from condensing on the walls. These bias fields
1
will also interact with the shock front and the driving current sheet, and thus can substantially modify the flow pattern inside the device.
Such magnetogasdynamic shock
waves have been the subject of extensive theoretical work 9
- 11
and the results are now
well known; however, the relevant experimental results are meager.
Patrick 1 '4 has
extensively studied the case in which initially there is a strong azimuthal and weak axial
magnetic field in the annulus.
From measurements of the radiated light intensity and
the magnetic field inside the annulus, he has shown that under certain conditions a
homogeneous gas sample can be obtained, and that the density of the shock-heated gas
and the change in field across the shock correspond to the predicted values.
and Petschek
6
and Keck
5 '7
Fishman
have studied the current-sheet behavior under a wide range
of experimental conditions with no initial bias fields. These experiments were carried
out in a MAST for which the ratio of the outside to inside radius was large, and thus
radial variations become important.
The shape of the front, and the current distribution
The maximum front speeds (-5 cm/[sec) were
in and behind the front were obtained.
much less than those obtained by Patrick; and their results show no evidence of a shock
Heiser 8 has done some preliminary work on
wave separated from the current sheet.
the effect of an axial bias field and the existence of a switch-on shock.
however, show considerable scatter,
His results,
and a front moving down the tube was observed
only in approximately 20 per cent of his experiments.
His observed front speeds were
approximately 50 per cent of the predicted speed, and the flux speed (see section 3.2a)
was approximately 20 per cent of the front speed. Thus it is not clear what flow pattern
was set up in his experiment.
1.3 EXPERIMENTAL PROGRAM
The experiments described in this report are intended to provide a detailed picture
of the flow pattern inside a MAST when the initial magnetic field is in the axial direction.
The experimental program was set up to provide answers to these two questions which
First, do either of the two existing theoretical
had not been considered in detail before.
models considered predict an accurate over-all momentum balance for the device over
a wide range of experimental conditions with an initial axial magnetic field? Second,
what is the detailed flow pattern inside the device over a range of axial magnetic fields,
and is either of the models considered a reasonable approximation to the observed flow
pattern? It was hoped that evidence would be obtained to indicate that the shock separated from the current sheet, as one of the aims of the project was to develop a device
that would produce a gas sample whose properties could be calculated. Of particular
interest here was the switch-on shock wave, and it was hoped that the existence of such
a shock could be demonstrated. When no evidence of a homogeneous gas sample was
obtained, the current-sheet behavior was studied in an attempt to understand why the
expected separation did not occur.
This report is arranged as follows.
In Section II the two existing theoretical models
In Section III the experimental apparatus,
that are considered are briefly reviewed.
2
measuring techniques, and instrumentation are described in detail.
Section IV contains
a description of the experiments carried out, the results obtained, and an evaluation of
the results. Section V includes the interpretation of some of the flow features that were
observed, and a discussion of the accuracy of the two theoretical models considered
here.
Section VI completes the report with conclusions and suggestions for further
work.
3
II.
THEORETICAL MODELS FOR THE OPERATION OF A MAST
2.1 KEMP AND PETSCHEK SOLUTION
a.
Assumptions
Kemp and Petschek 9 analyzed an idealized model of the flow pattern in a MAST.
They considered the general case for which the initial steady magnetic field has both
axial and azimuthal components;
only the effect of the axial field is of interest here. A
summary of their results follows.
It is assumed that the current sheet acts as a solid piston (high magnetic Reynolds
number) and produces a shock wave in front of and separated from it by a region of
shock-heated gas.
These assumptions are made:
(i) variations in the radial direction are negligible, and the problem can be analyzed
in Cartesian coordinates with variations in the x (or axial) direction only;
(ii)
gas pressure is isotropic;
(iii) gas obeys the perfect gas law with k = 5/3;
(iv) gas has infinite electrical conductivity everywhere; and
(v) drive current is a step function in time and rises instantaneously to a steady
value.
The validity of these assumptions for this experiment is considered in section 2.4.
Assumption (v) results in the region of shock-heated gas having uniform properties;
thus the shock and drive-current phenomena can be treated separately.
b. Effects of Axial Field on the Shock Wave
The effect of a magnetic field normal to the shock wave is well known and has been
summarized by Heiser. 8
The important points and nomenclature to be used throughout
this report will now be discussed.
In shock stationary coordinates,
subscript 1 denotes conditions upstream of the
shock, and subscript 2 conditions downstream of the shock; u denotes the gas velocity;
b x the Alfven speed (Bx/
); uS the shock speed in laboratory coordinates; and cf
11
When
wave
speed.
the fast magnetoacoustic
u s = u 1 >Cf >
f1
I
s
2
>bx,
x2(
(1)
shock conditions are not changed by the axial magnetic field B x perpendicular to the
front. [Note that the theoretical models are expressed in Cartesian coordinates with
B x , the axial field, normal to the front. In our experiments the flow parameters are
expressed in cylindrical coordinates; thus the axial field will be Bz.] The density ratio
across the shock is then given by the usual strong shock limit.
P2
P1
(2)
(2)
(k 2 +
k2 -1
4
As B
is increased, the condition
u
=u
1
is reached.
>Cf
>b
1
=u
(3)
2
2
The shock jump equations then permit a solution for which a tangential
magnetic field exists in region 2 and a current flows in the shock front.
appropriately called a "switch-on shock," since the tangential field is
by this current.
s
This is
"switched-on"
This condition would exist when
bx
k2 -(5)
s 1 k 1'
and the density ratio is now given by
2
P2.
c.
(6)
Effect of Axial Field on the Expansion Wave
The axial field in cylindrical coordinates introduces a jrBz force in the
which produces an azimuthal acceleration of the fluid in the current sheet.
direction
To reduce
this azimuthal acceleration, the current sheet spreads through the gas as a wave.
This
effect causes a slight increase in the shock speed, and a reduction in the length of the
ideal test slug until at a shock speed given by the equality in Eq. 5 the front of the
expansion wave is coincident with the shock.
For values of u
less than this limit, the
front of the expansion wave moves back away from the shock, although part of the
current is left in the shock front, itself.
Extensive numerical calculations on the shock and expansion wave properties have
been done by Kemp and Petschek,9 and when it is appropriate their results will be compared with the experimental data presented in Section IV.
2.2
"SNOWPLOW" MODEL
Another model has been used to describe the performance of this type of device;
is the "snowplow" model.
In this model, it is
radial driving-current sheet is
velocity.
time,
it
assumed that the gas swept up by the
entrained in the sheet and accelerated to the sheet
Thus a surface mass density can be associated with the sheet at any instant in
which is equal to the integrated mass density through which the sheet has moved.
The model assumes that the current is confined to a thin sheet, and thus is not applicable
for large values of the axial field.
It is also assumed that the magnetic Reynolds number
in the sheet is high; thus this model represents the limit of the Kemp and Petschek
model as the density ratio P2/P 1 tends to infinity.
The same momentum balance can be
obtained merely by assuming that all of the gas is swept up by the sheet and accelerated
to the sheet velocity.
5
Thus when the axial field is small a momentum balance can be written:
B
2
du
2° o= PlUs +
f P1 dz,
(7)
where Be is the drive field, and u s the front speed.
2.3 COMPARISON OF THE TWO MODELS
When the front speed is constant (it will be shown that this is a good approximation
to the observed results), Eq. 7 gives the front or current-sheet speed,
Be
u
.
-
(8)
s 2oP 1
This can be compared with the Kemp and Petschek solution for small axial fields
which gives the shock speed
Be
1
(9)
,
-
s]2oP
1
(1-Pl/P2)1/
and the current sheet speed
u
B0( 1-P 1/P 2 )1/2
c
.
L2 op
1
(10)
Notice that the front speed, from Eq. 8, and the shock speed, from Eq. 9, differ only
by the factor (1-P
1 /P 2
)1/2.
For a strong shock this factor will be between 0.87 and 1.0;
the lower limit is obtained when ionization and dissociation are ignored.
Thus the pre-
dicted value of u s does not depend to any marked degree on the choice of model.
2.4 VALIDITY OF THE ASSUMPTIONS
Significant departures from the one-dimensional model, assumption (i), could result
2
from the radial variation of the drive field Be. The ratio of the driving pressure B 0 2pLo
at the inner and outer radii is given by
2
r°2= 1.9.
r i/
(11)
Fishman and Petschek 1 2 have considered the effect of annulus ratio (2(ro-ri)/(ro+ri),
which is 0.32 for this experiment) in the case for which the initial magnetic field is
parallel to the shock front.
Their results suggest that for an annulus ratio of 0.32, the
one-dimensional model should be satisfactory for Alfv6n Mach numbers less than 5 for
an azimuthal bias field.
No calculations, however, have been made for an axial bias
field, and the flow pattern is significantly different, since the expansion wave moves
6
1
_
towards the shock as the axial field is increased.
The validity of a one-dimensional
model will be discussed in Section V.
Assumptions (ii) and (iii) have been adequately discussed by Kemp and Petschek,
and they conclude that the approximations are reasonable for the equilibrium temperatures predicted behind the shock at speeds comparable with those measured in these
experiments.
Assumption (iv) has been considered in detail by Kantrowitz,
Falk and Turcotte.
1 3
1
and more elegantly by
Using these results, we have made calculations of the diffusion of
the current sheet into the shock heated gas (see Appendix A).
The results show that if
the current sheet is preceded by a homogeneous gas sample at the equilibrium shock
temperature calculated from the shock speed, then the diffusion of the current sheet for
front speeds measured in these experiments should be negligible.
But these calculations
provide no evidence that this flow pattern will in fact be set up.
Assumption (v) can be satisfied by suitable design of the drive capacitor bank.
The
bank was set up to provide a square current and voltage pulse, but stray inductance in
the leads and shock tube limited the rise time to 2 Lsec.
All measurements were taken
after the drive current had attained its steady value, which was between 5
10
1
Lsec and
sec after the bank was fired. It was therefore expected that the flow pattern would
not change appreciably over a length of order 50 cm.
7
III. EXPERIMENTAL APPARATUS, MEASURING TECHNIQUES,
AND INSTRUMENTATION
3.1 DESCRIPTION OF THE EXPERIMENTAL APPARATUS
A general view of the experimental arrangement is shown in Fig. 1.
cross section of the shock tube is shown in Fig. 2.
A schematic
A photograph of the electrode end
of the shock tube is shown in Fig. 3, and an accurate cross-section drawing of the
electrodes and current leads in cylinders is shown in Fig. 4. These four figures supplement the following text.
a.
Shock Tube
The tube itself consists of the annular space between two concentric stainless-steel
cylinders sealed at each end with lucite insulators.
The outside and inside radii of the
annular space are 72 mm and 52 mm, respectively.
The tube is mounted inside a 7-inch
diameter, 52-inch long, 3 turn per inch solenoid which provides the steady axial magnetic field.
The electrodes consist of two stainless-steel rings of triangular cross
section projecting 1/8 inch into the annulus from the two steel cylinders.
These rings
are mounted 16.7 cm from the driving end of the tube to ensure that breakdown occurs
in a region of uniform axial magnetic field.
The insulator at the electrode end fills the
annulus for a distance of 15 cm to ensure that breakdown occurs at the electrodes; the
end of the insulator is capped with a 1/4-inch thick Pyrex glass ring to prevent excessive ablation of the lucite by the arc.
spaced around the annulus,
A set of eight identical search coils, uniformly
are mounted inside this insulator to measure the B
mag-
netic field and ensure that the drive-current distribution into and out of the electrodes
Fig. 1.
General view of the experimental arrangement.
8
LOP
STEEL
QUARTZ
AXIAL
TO PRESSURE
L
OR
APERTURE
INLET
LENS
:)
FILTER-PHOTOTUBE
E
Fig. 2. Schematic cross section of the shock tube.
Fig. 3. Detail of electrode end of the shock tube.
9
-
-
-
I)
0
r
E
C
)
0
"U
0o
a)
c
4
0
b4
o
0
r,
4a
C,q
mI
m
U
be
10
is azimuthally uniform.
The insulators at the other end of the tube were also covered
with Pyrex to reduce ablation from the low melting point lucite that was used to seal the
annulus.
Hydrogen, 99.9 per cent pure, was bled continuously through the system to reduce
the impurity level to a tolerable value (in all cases it was less than 0.2 per cent by
A variable leak valve controlled the flow of gas into a manifold outside the
volume).
outer cylinder at the electrode end of the tube. The gas flowed into the annulus through
twelve 1/32-inch diameter holes uniformly spaced around the circumference,
pumped out at the other end of the tube through a molecular sieve.
and was
The flow rate was
adjusted to give the required gas pressure in the system, and this pressure was
measured with an Alphatron pressure gauge which was calibrated against a McLeod
gauge at frequent intervals.
Measurements on the front and expansion wave properties were made through 5/16inch diameter holes cut in the outer steel cylinder. Eighteen of these holes were sealed
with quartz windows to permit measurements to be made with photomultipliers of the
radiated light intensity, and arrival time of the front at various axial and azimuthal
positions.
Eight of these windows were arranged along one side of the tube at 15.3-cm
intervals, the first being 8.6 cm downstream of the electrodes.
The remaining windows
were arranged at opposite ends of horizontal and vertical diameters at 39 cm, 54.2 cm,
and 69.4 cm downstream of the electrodes so that the azimuthal uniformity of the front
could be checked. All windows were mounted flush with the inside wall of the outer
cylinder and were cemented in place with epoxy.
Four of the holes could be used to
insert probes into the annulus at 46.8 cm, 61.8 cm, and 77.2 cm from the electrodes; at
61.8 cm two probe holes and a quartz window were arranged within an arc of 60 ° in the
0 direction so that three simultaneous measurements could be made at this position.
The probes and probe holders were sealed to the tube with "O" rings.
All other seals were made with welded or silver-soldered joints, or with "O" rings.
b. Capacitor Banks
The axial field current, preionization discharge, and drive current were provided by
capacitor banks connected to the shock tube through appropriate switching circuits.
A
schematic circuit diagram is shown in Fig. 5.
(i) Axial field bank
This consisted of five 60-fd, 10-kv capacitors connected in parallel through an
ignitron to the axi-al field coil. The quarter-cycle time of the bank-coil combination
was found to be 560 Isec, and the maximum field attainable inside the annulus was
0.45 wb/m . A field probe in the axial direction over the center 40 centimeters of the
annulus indicated field variations of less than 3 per cent. The accuracy of the calibration was estimated as
(ii)
6 per cent.
Preionization discharge
It was found that a low current (-100 amps) discharge between the electrodes,
11
+3KV
0.25aF
'T
T T
-1
TRANSMISSION LINE DRIVE BANK
Zo= 0.0172, TOTAL OF 288yF
Fig. 5.
Schematic circuit diagram and firing sequence.
1.5 ULsec in advance of the main bank triggering, improved the reliability of breakdown,
but had no subsequent effect on the flow pattern. Two 0.01-FLfd capacitors at -12 kv were
used for this purpose.
(iii) Drive capacitor bank
The drive-current bank was set up with distributed inductance to simulate a
transmission line and thus provide a drive-current waveform that approximated a step
function. To obtain a characteristic impedance low enough to match 'that of the shock
tube, the bank was designed as four parallel transmission lines with eighteen 4-Ifd,
10-kv capacitors in each line. The distributed inductance was provided by parallel
copper plates of appropriate dimensions and separation.
The impedance of the four
lines in parallel was measured to be 0.017 ohm. The high-voltage terminal of the bank
was connected to the electrode end of the inner cylinder through a coaxial spark gap,
and the ground terminal of the bank to the electrode end of the outer cylinder. A
12
combination of parallel-plate and low-inductance cable was used to keep the stray
inductance to a minimum.
Great care was taken to ensure that the azimuthal distri-
bution of the drive current leading into and out of the electrodes was uniform. Figure 3
shows the lead in connections used to achieve this end.
The bank could be operated at
voltages up to 10 kv, and when it was discharged through the shock tube, a current pulse
of the order of 300 kamps with a rise time of 2 uLsec and a pulse length of 10 Lsec was
produced.
A model for calculating the loading placed by the shock tube on the bank is
discussed in Appendix C.
In all of our experiments, the shock tube was run with the center electrode and highvoltage terminal of the bank at a negative potential.
3.2 MEASURING TECHNIQUES AND INSTRUMENTATION
a.
Current and Voltage Measurements
The axial field was measured by monitoring the integrated output of a single loop
wound round the outside of the center of the field coil. This maximum measured voltage
had previously been calibrated against field measurements made inside the annulus.
The error involved in the B z field measurement was estimated as
The drive current was monitored by means of a 15-turn,
6 per cent.
2-mm diameter coil
inserted at the center of the gap between the copper plates leading from the drive bank
to the shock tube. The effective area of this search coil was obtained by the procedure
outlined in Appendix D, and the coil output voltage was integrated with a calibrated RC
circuit whose time constant was 450 pLsec.
The field distribution around the lead-in
plate was measured with a second calibrated coil in terms of the field on the center
line.
The integral of this field around the plate gave the correct conversion factor for
obtaining the drive current from the measured field at the center line.
involved in the drive-current measurement was estimated at
The error
6 per cent.
The voltage between the electrodes was measured by means of two identical(to 1 per
cent) 10 k2, 200 times attenuators connected to a differential preamplifier.
The voltage induced in a loop that surrounds the annulus in a radial plane (see Fig. 2)
was also measured.
This was termed the
voltage, and from it a flux speed UL7 can be
obtained, since it measures the rate of change of flux as the current sheet moves down
the annulus.
It is shown in Appendix B that when the current I is constant, the voltage
$ is given by
= LIuL + ^A,
(12)
where L is the inductance per unit length of the tube, A
is a term allowing for the dif-
fusion of the current through the steel walls, and uL (the flux speed) is the speed with
which the current sheet would move axially if it remained confined to a thin layer.
expression for
(that part of the
An
voltage that is due to axial movement of the current
sheet) with
13
--_
------
_
~
__
_~~
t4=
(13)
- j
$
is given in Appendix B. It is found that the ratio
/$ decreases with time, and is approxi-
mately 0.8 at the time when most of the experimental measurements were made.
b. Measurements with Photomultipliers
The arrival time of the front at various axial and azimuthal positions could be
measured with six photomultiplier systems.
Each of these consisted of an RCA 6655A
0
0
phototube with a 4400 A interference filter of half-bandwidth 100 A in front of the tube
The tube output was fed directly into a cathode follower. The phototube was
collector.
connected to the shock tube with either an optical fibre or a simple optical system, and
two collimated holes were used to restrict the volume of plasma which could be viewed
by the phototube.
The rise time of the system was measured to be less than 0.1 Fsec;
the transit time of the front past the collimator was approximately 0.02
sec.
One of the phototube systems was calibrated with a tungsten-filament lamp of known
horizontal candle power and color temperature,
so that absolute measurements of the
radiated light intensity could be made.
c.
Magnetic and Electric Field Measurements with Probes
Measurements inside the annulus were also made with magnetic and electric field
probes.
Considerable time and effort were spent in developing these probes to give
reproducible and intelligible signals.
Typical probes are shown in Fig. 6, in which the
top probe is a B 0 magnetic field probe,
the second probe an E r radial electric
field probe, and third probe an E z axial
electric field probe.
The probe holder is
also shown; Fig. 2 illustrates how probes
-aka
are inserted into and sealed in the shock
n_
tube.
,,,
·- ,,,,,,·,. ...
The magnetic field, or B
probes,
consisted of a single-turn loop, 2 mm in
: . ....
......
diameter, of #30 Nyclad insulated copper
...L
wire mounted outside the end of a quartz
tube and sealed with epoxy.
Fig. 6.
The coil
was soldered to a short length of 50-ohm
Probes.
Microdot cable and then connected through
a 3:1 voltage divider to an RC integrator of time constant 54 ptsec at the oscilloscope
(see Fig. 7). The voltage divider was included so that when the insulation on the coil
ablated away, the minimum resistance to ground through the probe was 50 ohms, and
the maximum voltage at the oscilloscope terminal was less than 600 v.
14
The insulation
INSULATED
COPPER WIRE
'SCI LLOSCOPE
(IAL CABLE
;CILLOSCOPE
Fig. 7. Schematic drawing of probe construction.
usually lasted between 5 and 20 runs.
The probes were calibrated as described in
The probe-to-probe reproducibility was estimated at ±10 per cent (see
Appendix D.
section 4.4b). When the insulation between the probe and the plasma had broken down,
no useful signal was obtained.
Electric-field probes similar to those used by Burkhardt and Loveberg
developed.
were
Figure 7 illustrates, also, the probe construction and circuit. The voltage
difference between the two coaxial electrodes was measured by using an identical
(0.1 per cent) pair of 1 k2, 20 times attenuators and a differential preamplifier.
Burkhardt and Loveberg have shown under similar conditions that the value of the
resistance of the dividers was not important until it was reduced to 5 ohms.
value was chosen to give a fast rise time (less than 0.05
sec).
The 1-ku
The electrode sepa-
ration was 0.41 cm for the Er probe, and 0.6 cm for the E z probe.
Only the difference
in the floating potential of the probes was measured; this potential may differ from the
plasma potential by approximately kT/e. The value of kT/e corresponding to the equilibrium temperature behind the fastest shock observed was 17 volts.
This is small
compared with the Er signals (- 200v), but not small when compared with the E z signals
(-40v).
Thus the effect of temperature gradients was neglected in the former, and the
E z probes were used only for qualitative considerations, since substantial errors could
be introduced.
d. Firing Sequence
The firing sequence for all experiments and a schematic circuit diagram are shown
in Fig. 5.
At time T = 0 the axial-field ignitron and the oscilloscope monitoring the Bz
field were triggered.
At T= 560 ,isec, at the axial field maximum,
the preionization
circuit was triggered and a pulse sent into a 1.5-ILsec delay line.
This pulse then
15
~-1---
~-
-
-
triggered the main bank spark gap and the oscilloscope monitoring the drive current
and electrode voltage at T = 561.5 psec.
0.5
sec.
Breakdown of the drive bank occurred within
A variable delay was used to trigger oscilloscopes recording phototubes and
probe measurements at the appropriate time during the experiment.
The calibration of all oscilloscopes was checked and adjusted when necessary before
each set of tests.
A typical set of axial-field Bz, electrode voltage VE
phototube traces are shown for B
and initial pressure P
drive current I,
voltage, and
= 0.23 wb/m2, initial drive-bank voltage V
= 250 microns in Fig. 8.
16
= 7.5 kv
IV. EXPERIMENTAL RESULTS
4.1 SUMMARY
Our experimental program can be divided into four separate parts.
(i) A preliminary set of experiments was concerned with verifying the azimuthal
uniformity of the drive field,
and the front position.
It was obviously necessary to
demonstrate that conditions around the annulus were uniform before detailed measurements at any one point could be taken.
(ii) The second set of experiments was aimed at obtaining the operating characteristics of the tube over as wide a range of the parameters P1 initial pressure, B z axial
field, and VO initial drive capacitor bank voltage as possible. Measurements were made
of the front velocity u s along the length of the tube.
(iii) In the third set of experiments, measurements of Bo, E r , and E z in the front
and expansion wave were made with probes at various axial and radial positions for six
selected operating conditions.
These six operating conditions were chosen so that the
effect of the axial field on the flow pattern at two different pressures could be investiThese conditions will be referred to as A, B, C, D, E, and F in the sequel,
gated.
and Table I lists the initial pressure P 1 and axial magnetic field B z corresponding to
each letter. The initial drive capacitor bank voltage VO was 7.5 kv for each case.
Table I. Experimental conditions.
A
B
C
D
E
F
p, microns
250
250
250
100
100
100
Bz wb/m 2
0.1
0.23
0.42
0.1
0.23
0.42
V
7.5
7.5
7.5
7.5
7.5
7.5
O
kv
(iv) In the last set of experiments, absolute measurements of the light intensity
radiated by the front and expansion wave were made with a calibrated phototube. It was
hoped that these measurements would yield information on the electron density in the
gas heated by the front. As we shall see, however, no useful information on the electron
density could be obtained.
Before each set of experiments is considered in more detail, some general comments
on the reproducibility of the data will be made.
About 80 per cent of the runs made at any given set of conditions satisfactorily
reproduced the same flow pattern. Measurements of drive current I and front velocity
u s were reproducible within
Two drive-current and electrode-voltage
5 per cent.
The Bo and Er probe
traces for similar operating conditions are shown in Fig. 8a.
17
-,
_-
-
-
-
-
-
VE
I
(a)
VE
I
(b)
Fig. 8.
I (c)
Types of I and VE oscillograms.
measurements were reproducible within
10 per cent; the problem of probe reliability
is considered in greater detail in section 4.4a.
within
The Ez measurements were reproducible
20 per cent; however, the qualitative behavior was unchanged.
All of these runs
were characterized by smooth level drive-current and electrode-voltage traces as shown
in Fig. 8a.
The remaining 20 per cent of the runs showed drive-current traces in which either
the drive current increased steadily throughout the run (Fig. 8b) or a sharp break in the
trace occurred when the front arrived at the probe position (Fig. 8c).
Data from these
two types of runs were discarded. It was also found that at conditions F, the B e and Er
measurements showed variations outside the limits quoted above.
4.2 MEASUREMENTS ON AZIMUTHAL' UNIFORMITY
The azimuthal magnetic field between the electrodes was measured with eight identical search coils uniformly spaced around the annulus and built into the lucite insulator
(see Fig. 4).
The output of each coil was integrated with a calibrated RC integrator
(time constants between 320
1 Lsec
and 420
18
sec).
These signals were compared for
various values of the drive current and axial field, and the shape and magnitude were
found to agree within
ment.
4 per cent, which is within the estimated error for the measure-
It was concluded that the drive-current distribution entering and leaving the
electrodes was azimuthally uniform.
Measurements were also made to check the fact that the arrival time of the front at
any axial position did not depend on azimuthal position.
The maximum time difference
measured between arrival times at opposite ends of a horizontal or vertical diameter
This corresponds to a tilt in the
39 cm downstream of the electrodes was 0.05 ILsec.
shock front of approximately 3 across the mean diameter of the annulus; thus it was
considered negligible.
It was therefore assumed in all subsequent measurements
that the front and
expansion wave properties did not vary significantly with azimuthal position. The similarity in shape and magnitude of B o probe traces from the same axial and radial position,
but separated by an angle of 60 ° , also supported this assumption (see Fig. 16).
4.3 MEASUREMENT OF THE FRONT SPEED
a.
z-t Diagrams and Flux Speed
Measurements of the front velocity u s along the length of the tube were made by
measuring the arrival time of the front at positions z = 23.8, 39, 54.2, and 69.4 cm from
A typical oscillogram is shown in Fig. 9.
the electrodes, with four phototubes.
It was
found that the front speed was essentially constant from 20 cm to 70 cm downstream of
the electrodes; the drive-current pulse was constant (10
per cent) over the corre-
Typical z-t diagrams for conditions A through F are shown in
sponding time interval.
Fig. 10.
The flux speed uL, calculated from Eq. 12 and the appropriate
trace, and the front
speed u s are compared in Fig. 11 for conditions B and D. It was found that the
2
changed little between B z = 0.1 wb/m
were much smoother.
and 0.42 wb/m , although the traces at higher B z
The ratio of the flux speed to the front speed will depend on the
flow pattern (the Kemp and Petschek model gives uL/us ~ Uc/u
model gives uL/us
traces
2
~ 1).
Figure 11 indicates that UL/Us
s
= 0.75; the snowplow
is between these two values,
and that the current sheet spreads axially as the front moves down the tube. For times
less than 5.5
1 Lsec,
uL > u s .
This is because the drive current has not reached its
steady value, and thus Eq. 12 is incorrect, since it neglects the dI/dt term. Note also
that for T > 8.5 when I declines in value, the calculated uL will be too low for the same
reason. Appropriate drive-current traces are included in Fig. 11 to demonstrate when
the current is constant.
b. Variation of Front.Speed with Initial Pressure
The variation of the front velocity with initial pressure was then obtained and is
shown in Fig. 12 for B z = 0.1 wb/m 2 and V
= 7.5 kv.
Front velocities were obtained
19
_______1__111____11I
1
-- _-
---
,- 200
s
0.098 wb/m
Bz
2
-I
'
-' 1
2,s
I, Rr tv pv
...
2Kv
VE
T-
I
125 ka
-I
J-Z2/I
I Kv
r
-H
4LS
4_a
0.5 s
PHOTOTUBES
Fig. 9. Typical B z,
I, VE ' ,
20
u s oscillograms.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
I
·
I
I
r-
8
n
0L
w
LL
n4
cr 3
w
2
I
10
0
Fig. 10.
I
I
I
I
-
I
20
30
40
50
60
70
DISTANCE FROM ELECTRODES z (cm)
80
z-t diagrams for conditions A through F.
18
16
14
E
J
o
(L
8
z
'
6
300
200 zX
Z
4
n-
2
100
i:
0
1+
b
r
f
Y
IV
TIME AFTER BREAKDOWN (sec)
Fig. 11.
Flux speed and front speed
for conditions B and D.
21
___I
I
I
I
I
I
l
I
I l
I
I
25
20
CHEK
G)
E
10
0)
SNOWPLOW
5
0
30
Fig. 12.
Bz = O. I wb/m
Vo= 7 . 5 kv
I
40
2
I I I
60 80 100
MODEL
I
200
pl (microns)
I
400
I
600
Front speed as a function of initial pressure.
by averaging the measured velocity over two adjacent 15.3-cm intervals placed so that
the drive current had just reached its steady value at the start of the measurement.
The scatter in the observed values of u is approximately 5 per cent. Two theoretical
curves are shown; one is obtained from the Kemp and Petschek 9 calculations, where
their parameter, B/Bo = Bz /(B+B)1/2 is computed from the measured B z , and Be
is calculated at the mean radius (6.2 cm) from the average of the steady values of the
drive current measured at a given pressure. The other curve shows the value of u
obtained from the snowplow model (Eq. 8) with B calculated as above. Note that the
accuracy of the theoretical curve will depend on the accuracy of the drive-current
measurement. In addition to errors involved in measuring the voltage output of the
search coil-integrator combination (see section 3.2a) a constant error from the calibration of the search coil, calibration of the integrator, and integration of the field
around the current lead in plate will be present. This constant error was estimated to
be within ± 6 per cent.
c. Variation of Front Speed with Initial Drive Bank Voltage
The variation of front velocity with Vo, the initial voltage on the drive bank, is
2
.
shown in Fig. 13 with P = 250 microns, and B z = 0.2 wb/m
This variation was only
attempted at this one pressure, since it was not possible to obtain reliable triggering of
the experiment over any appreciable range of drive voltages when the initial pressure
was approximately 100 microns.
The flux speed uL was obtained from the
traces for
these runs at the time the current reached its steady value, and the ratio uL/us is also
22
I
I
I
I
I
16
KEMP
PETSCI
14
12
PLOW
"'L
a)
E
U
Fig. 13.
8
pi
=
250 microns
Bz = 0.2 wb/m2
6
Front speed and flux speed
as a function of initial drive
bank voltage.
1.0
4
o
2-
us
0.5-- .J
A UL/Us
I
I
I
2
4
I
I
I
I
I
I
6
8
V
o ( kv)
included in Fig. 13.
10
Theoretical curves for the Kemp and Petschek and snowplow
models are shown; the experimental points lie between the two curves.
d. Variation of Front Speed with Axial Magnetic Field
The effect of the axial field was considered at two initial pressures (250 and 100
microns) and V
= 7.5 kv.
The measured front speeds, and Kemp and Petschek and
snowplow model theoretical curves are shown in Figs. 14 and 15.
I
I
I
KEMP AND PETSCHEK
I
Note that the
I
MODEL
14
0S
°
12
0-NOWPLW
10
SNOWPLOW
0---MODEL
u
Fig. 14.
E 8
u
m
6
p1
=
Front speed as a function
of axial magnetic field with
P 1 = 250 microns.
250 microns
VO:7.5 kv
2
2
I
0
0.1
I
I
0.2
0.3
2
Bz (Wb/m )
I
0.4
I
0.5
23
N___
_
I
I
I
KEMP AND
IMODEL
PETSCHEK
MODEL
20
SNOWPLOW
15 _8
as
I
?
MODEL
I
o
0
88
Fig. 15.
E
pl
=
Front speed as a function
of axial magnetic field with
P
100 microns
= 100 microns.
Vo= 7.5 kv
5
I
0.1
0
I
0.2
Bz
I
0.3
(Wb/m
2
I
0.4
I
0.5
)
measured front speeds decrease slightly as B
observed by Heiser.
is increased; a trend that was also
The drive current (which is obviously proportional to the value
of u s predicted by the snowplow model) remains almost constant over the whole range
of B
z
considered in both cases.
4.4 INTERNAL MEASUREMENTS WITH B,
a.
E z , and E r PROBES
Summary
To obtain more detailed information about the flow pattern inside the annulus, sets
of probe measurements were made with the B,
section 3.2c.
Ez, and Er probes described in
These measurements were designed to answer the following questions.
(i) Does all of the drive current move down the tube with the front, or is part of it
left at the insulator face to cause ablation of material from the insulator (see Keck 7 )?
Obviously the momentum balance will be incorrect if appreciable ablation occurs.
(ii)
Does the shock front (as identified by the phototube output) separate from the
current sheet (Be trace rise) for values of axial field when a homogeneous gas sample
should exist? If no such separation is observed, then the Kemp and Petschek model
will not be applicable.
(iii) Can any change in the flow pattern be observed at the point where the switchon shock could exist?
(iv) What is the shape of the front?
Previous experiments by Keck 5 and by
Burkhardt and Loveberg 3 have shown that the front is approximately planar when the
center electrode is negative, and bullet-shaped when the center electrode is positive.
(v) What is the variation of B with radius?
(vi) Can an axial electric field caused by charge separation be observed in the
front? This would provide a way of identifying the shock front by using the theoretical
work of Jaffrin.14
24
_
_
(vii) What information can be obtained about the gas velocity from radial electric
field measurements?
The results will be discussed in the order in which they provide answers to these
Some remarks on the validity of the probe measurements will be given first.
questions.
It is important to show that probes inserted into the annulus do not affect the flow
pattern in any significant way. Obviously, the probe will cause changes in the velocity,
temperature, and pressure in the region close to and downstream of the probe.
But if
it can be shown that the current distribution remains essentially unchanged, then such
features as the front speed, and the Be and E
distribution should not be affected.
When
the local axial velocity of the gas is important, as in the E r measurements where a
large part of the signal is the inductive uzB o voltage, then the probe output must be
interpreted with more caution.
While it could not be demonstrated conclusively that the over-all flow pattern was
not changed in any significant way, the following evidence suggests that this assumption
is justified.
We found that some of the drive-current and electrode-voltage traces showed abrupt
changes in slope (see Fig. 8c) when the front reached the probe position.
times occurred when the insulation of the probes broke down.
This some-
These data were dis-
carded; it was concluded that the probe had appreciably changed the flow pattern, and
thus the load on the drive capacitor bank.
Second, it was found that when the drive-
current and electrode-voltage traces were smooth (80 per cent of the runs) neither the
number nor the position of probes inserted into the annulus appreciably affected the
value of the front velocity or the signals recorded at each probe. Against this, however,
must be set the fact that on dismantling the tube, black marks downstream of the probe
positions were observed on the steel cylinders,
thereby indicating that a wake had
formed behind the probe and that material (from the epoxy seal, for example) was being
transferred from the probe to the flow.
In the experiments on the axial and radial variation of B e that will be reported next,
measurements at any given Pl, Bz, Vo, z, and r were made with at least two different
probes.
This was done to ensure that any individual probe peculiarities would be
immediately apparent.
b. B
Measurements as a Function of Axial Position
Figure 16 demonstrates the reproducibility of B 8 probe measurements.
Figure 16a
shows the probe-to-probe reproducibility for the same run at the same axial and radial
position; Fig. 16b shows the shot-to-shot reproducibility of the same probe for three
runs. For conditions F, however, the reproducibility was greatly inferior.
The azimuthal magnetic field is given by
B where
V=is 3RC
the VI
A
voltage read from the oscillogram (as described in
where V is the voltage read from the oscillogram (as described in Appendix D).
25
(14)
The
l1 s
Be MAX.
0.8 wb/m
2
B e MAX.
2
0. 81 wb/m
Fig. 16. Oscillograms showing
reproducibility of B o
probes.
(a)
0.33 wb/m 2
-T
(b)
error in calibrating and positioning the probe, and in calibrating the integrator, is estimated as
8 per cent.
The important features of the signal are the sharp rise in B
as
the front passes the probe (the rise time is approximately 0.1 psec, corresponding to a
and then a more gradual rise to a maximum B
distance of 1.5 cm),
later.
from 1 to 2 sec
It will be seen, however, that under some conditions the front and the rise to
maximum B o cannot be separated.
To investigate how much of the drive current moves down the tube with the front,
measurements of B
were taken at distances z = 46.8, 61.8, and 77.2 cm from the
electrodes at the mean radius (6.2 cm) for conditions A through F.
The change in B 0
across the clearly defined front and the maximum value of Be were measured from
each oscillogram.
These measurements were nondimensionalized with the value of the
field (B I ) calculated at the appropriate radius, from the drive-current value at the time
the Be measurement was made. The ratio
Be
B.
I
2
rrBe(t)
(15)
LoI(t)
26
__~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~-
I
I
I
I
I
1.0
1.0
Be
BI
Be
BI
0.5
I
I
0.5
Im
50
40
I
60
A
I
70
I
80
z(cm)
0
40
50
60
70
D
1.0
80
z(cm)
1.0
Be
I
B1
I
I
I
BI
0.5
fi
0.5
0
40
60
B
50
70
0
80
z(cm)
fI
40
50
I
1.0
60
E
70
I
II
Be
BI
0.5
0.5
A
I
I
v40
I
8
A
A
0
80
z (cm)
1.0
0
Be
B
i
A
I
50
I
60
C
0
I
70
A
80
z(cm)
40
50
60
F
70
80
z(cm)
A MEASURED AFTER
FRONT
o MEASURED AT MAXIMUM
o MAXIMUM AT FRONT
Fig. 17.
B/B
I
as a function of axial position for conditions A through F.
is plotted against z in Fig. 17 for conditions A through F.
The ratio of maximum Be
to B I should be unity if all of the drive current passes the probe and measurements are
made during the time the drive current is constant.
The interpretation of the results is complicated by evidence presented in section 4.4d
that current loops flow in the gas behind the front. The measurements of maximum field
indicate, however, that with the exception of condition F, 90-100 per cent of the total
drive current flows past the probe at the mean radius at each axial position. In Fig. 18
two sets of Be traces are shown to illustrate that the shape of the profile (substantially
different for each case) changes little along the length of the tube, although the position
of the Be maximum moves away from the front with increasing time. This agrees in a
qualitative way with the plots of flux speed uL shown in Fig. 11 where uL decreased with
time and uS was constant.
27
i
_L
rr IA
rr
0.33
0.33
U.01i
z =46.8cm
z = 61.8cm
.
u
i
T
z = 77.2 cm
T)h
0.35
0.35
t1~
B
T
D
Fig. 18. Oscillograms of B e profiles at z = 46.8, 61.8, and 77.2 cm,
and the mean radius for conditions B and D.
c. Comparison of Light Intensity Front with Be Front
In this set of experiments, simultaneous measurements were made at z = 61.8 cm
with a B. probe at the mean radius, and with a phototube arranged so that the collimated
holes of the phototube collecting system and the probe were separated by an angle of 300
in the azimuthal direction. The two signals were displayed on the same oscilloscope,
and the arrival times of the two clearly defined fronts were compared over the range of
conditions A through F.
With the exception of condition F (where a clearly defined light-intensity front was
not always observed), the light-intensity front was always slightly behind (-0.05 sec)
the B front. This time difference was not considered significant, since it was of
the order of the difference in transit times for the signals through the two measuring
circuits. Thus within times of less than 0.05 pFsec, the two fronts were coincident;
therefore, one must conclude that the drive current flows at the shock front and no
homogeneous gas sample collects between the shock and the current front. Precise
agreement with the Kemp and Petschek model would not therefore be expected.
28
I
_
d. B
Measurements as a Function of Radius
The B 8 probes were then used to measure:
(i) the tilt of the front,
(ii)
the variation of Be with radius over the range of conditions A through F.
The tilt of the front was obtained by measuring the arrival time of the front at two
B( probes, one close to the inside wall, the other close to the outside wall at z= 61.8 cm.
The probes were separated in the
direction by an angle of 60°; therefore, the azimuthal
symmetry of the front as it approached the probe positions was important.
checked with phototubes at two windows 90
positions.
°
This was
apart, 7.6 cm upstream of the probe
After correcting the arrival times for any slight difference in arrival time
from the phototube traces, the maximum differences in arrival times at the probes
corresponded to a tilt across the 2-cm annular space of
shock-tube axis.
25
°
from the normal to the
These data are in agreement with the measurements 3 '5 mentioned in
section 4.4a (the center electrode was run at a negative potential, and it was found that
the front was approximately perpendicular to the tube axis).
Measurements of Be were then made at r = 5.5 or 5.6 cm and r = 7 cm; at z
61.8 cm; for conditions A through F to obtain the radial variation of Be.
Typical
oscillograms for conditions A through F for r = 5.5 or 5.6 cm and r = 7 cm are shown
in Fig. 19.
(B o profiles at the mean radius (6.2 cm) and this axial position are shown
in Fig. 26.)
As before, the value of B
after the clearly defined front and the maximum B8 were
measured and nondimensionalized with B calculated at the appropriate radius from the
measured drive current. Plots of Be/BI as a function of radius r are shown in Fig. 20.
The values of B(/B
also included.
I
from the previous experiments at z = 61.8 and the mean radius are
It is immediately apparent that the simple model of the drive current moving down
the tube as a confined sheet is inadequate for all of the conditions considered.
Probes
close to the inside wall record values of B 8 -50 per cent greater than the field resulting
from the drive current alone; although it is found that with the exception of conditions
F the current in the sharply defined front corresponds to the field caused by the drive
current within ±15 per cent.
Close to the outside wall, the maximum field measured
was always less than the calculated B I , and the rise time of the front increased substantially.
It was felt that the 5/16-inch diameter hole in the outer steel cylinder
through which the probe and probe holder were inserted would disturb the distribution
of current flowing in the wall.
Thus the field measured close to this probe hole may
not be the same as the field existing close to the outside wall away from any probe
holes.
To investigate the current distribution both in and behind the front in greater detail,
a radial traverse was made with a single B
probe at conditions B and z = 61.8 cm.
This particular set of operating conditions was chosen because the flow pattern appeared
29
____II
_I
r (cm)
0.33
0.33
*-7. 0-
T
T
I
'5.
0.61
i
6
0.73
T
5.5-
T
D
A
l
0.33
0.33
-7. 0-
T
-T1
I
4-5.6
0.61
0.73
T
5. 5-
T
E
B
I
0.33
-7. 0--
T
0.33
T
- D.
I
b
0.61
0.73
T
5.5-
F
C
Fig. 19.
T
Oscillograms of B 0 profiles at z = 61.8 cm, r = 5.5 or
5.6 cm, and r = 7.0 cm, for conditions A through F.
30
,
I,
9
1.5 _
1.5 _
1.0
1.0
B8
f
-aA
A
B8
BI
BI
0.5
0.5
A nl
0
0
v ,-
D
A
7
6
r (cm)
I
I
-
a
B8
98
BI
BI
0.5
0.5
0
nfl
A
I
-5
B
I
80
1.0
9~~~
9~
a
B8
I
1.5
8
1.0
7
0
o
1.5
6
r (cm)
D
I
,
5
0
I
6
r(cm)
7
j _
5
8
b
6
r (cm)
7
E
1.5
I..5
1.0
[,
.0
B8
8
B8
BI
BI
0.5
O..5
oL i I
v5
C
0
1
6
r (cm)
7
F
A
MAXIMUM B8
B AT FRONT
D
MAXIMUM AT FRONT
O
6
r(cm)
v5
Fig. 20. Be/BI as a function of radius at z = 61.8 cm for conditions A through F.
31
---
I
r = 7.0 cm
0.39
t
I
-00.39
r = 6.5 cm
T
0.39
r = 6.0 cm
7-
0.78
r =5.5 cm
T
Fig. 21. Four oscillograms from Be radial traverse
at z = 61.8 cm, and condition B.
to be particularly reproducible.
Four of the oscillograms are shown in Fig. 21.
that the shape of the profile changes substantially with radius.
Note
The values of Be/BI
after the front, and the maximum values were obtained and are shown in Fig. 22 as a
function of radius.
The rapid fall off in B 0 /B I at radii close to the outside wall supports
the supposition that the decrease is due to the probe hole in the wall. If this were not
the case and the measured field does correspond to that existing close to the wall away
from any probe holes, then axial currents of the order of the drive current must flow in
the 0.5 cm close to the wall.
With this explanation in mind, Fig. 22 shows that the current flowing in the front
over most of the annulus is 10-20 per cent greater than the drive current. While this
32
o
Be MAX IMUM
67
o
A
/aL
-Be AT FRONT
1.0
-
Fig. 22. Plot of B 0/B
p = 250 microns
2
Bz = 0.23 wb/m
cn
Vo = 7.5kv
0.5
as a function of
rio
r
-A,
V
-
0
I
radius for radial traverse at
z = 61.8 cm, and condition B.
I
I;-r
I
6
5
7
r (cm)
difference is only just outside the experimental error involved in the measurement,
it
does agree with the values obtained from two different probes (see Fig. 20b).
A current map showing the approximate current distribution in the front and the
The
expansion wave behind it, can be obtained from the four traces shown in Fig. 21.
current density at any point in the annulus is given by
1 aBe
ir
Jr
=
~F
az
(16)
1
jz
Lr
a(rB 0 )
ar
since a/a80 = 0, B z is constant and it is assumed that any B r that is due to currents in
the 0 direction can be neglected.
If it is further assumed that the gas velocity behind
the front is approximately constant (see section 4.4f), and the current distribution does
not change significantly with z (see section 4.4b), then Eq. 16 can be replaced by the
approximate expressions
1 AB 0
Jr
4o uAt
(17)
Jz
1 A(rB 0 )
0r
Ar
These current densities can be evaluated from the oscillograms at a series of points in
Then, by integrating between pairs of points, the actual current distribution
can be obtained. It is shown in Fig. 23a, where u was assumed to be 10 cm/psec, and
the front was arbitrarily taken to be perpendicular to the tube axis. Any variation in u
the annulus.
33
__1^11_____11_111·--·1--·-
--
I
I_-
o
4
o
0
E
c"
C
CU
.L
z
u
2
1r
o
L
Li
\
Z
:I
7
n
\
o
'
N
v
o
\
en
Ac
e0
<W
N
.wJ
-4
\
2
0
-
LiL
>
34
_
__
will merely alter the z-length scale.
of the walls,
Since no measurements were made within 3 mm
r and jz were not computed in these regions,
lines (shown dashed) are only estimated.
and the constant-current
The map shows that a closed-current loop of
105 amps flows in the gas behind the front spread out over a distance of -18 cm axially.
Part of this loop flows at the front; thus B
BI.
after the front is 15 per cent greater than
The center of the loop lies between the mean and inside radii, where B
is 50 per cent greater than B I .
The loop is shaped so that B
maximum
near the outside radius
falls off more rapidly than Be near the inside radius.
Since the field changes with radius and time were often small, this map is only an
approximate solution to Eq. 16.
therefore desirable.
Additional evidence to support this flow pattern is
Accordingly, axial electric field measurements were made with
the E z probe described in section 3.2c in the regions where the current flow was predominantly axial. A radial traverse was made at conditions B and z = 61.8 cm, and four
oscillograms are shown in Fig. 24. A deflection upwards from the zero line corresponds
to an electric field pointing toward the shock front.
The sharp rise in the E
was found to correspond to the arrival of the sheet at the B
probe.
signal
The important
characteristics of the traces are listed
below.
(i) An initial sharp spike occuring in
r = 7.0 cm
the front.
It was concluded that this is
caused by charge separation, and its magnitude will be considered.
(ii) A region of Ez directed toward the
r
=
shock of approximate magnitude 60 v/cm
6.6cm
almost independently of radius and lasting
0.8 Utsec (-8 cm).
(iii) Close to the inside wall an abrupt
change in the direction of E
at 0.8
sec
from the front; close to the outer wall, a
r = 6.3 cm
gradual reduction in E z but no change in
direction.
negtiv
__o-____rot
f_._ an
theregions
tnese
positive
toar traces,
__rete
E From
Ez (directed toward the front) and negative
E z (away from the front) can be obtained;
these are shown in Fig. 23b. A compari-
r = 5.8 cm
son with the current map shows in a qualitative way that axial electric fields do
exist to drive
Fig. 24.
Four oscillograms
from E
the current lnnn.
the line of zero E
radial traverse at z= 61.8 cm,
and condition B.
lthnih
falls above the line
joining points where jz = 0. Exact agreement should not be expected, however, as
35
Hall effects have not been considered, and the axial component of the V X B field (vrB0
from the radial motion of the gas) which should be included in the transformation from
probe coordinates to gas stationary coordinates, has been ignored.
Point (ii) suggests that since no substantial change in the positive E
field occurs
with radius close to the outside wall, in the first microsecond after the front, the low
Be values measured are due to the influence of the probe hole on the current distribution
in the wall as outlined previously.
c. Axial Electric Field in the Front
Work by Jaffrin 1
4
on shock structure in an ionized gas has shown that an electric
field caused by charge separation occurs inside the shock.
In shock stationary coordi-
nates the electrons are decelerated before the ions and an electric field directed toward
the front is set up in the shock layer.
A measurement of this field would be one way of
identifying the shock layer. An obvious difference between the model analyzed by
Jaffrin and the observed flow pattern in the MAST is that he treated the case of no magnetic fields or currents. It has been shown that in the MAST a current of the order of
the drive current flows in the shock layer. The momentum equation for the electrons 2 0
for the appropriate analytical model should therefore include a (j X B) force, which in
shock stationary coordinates will act with the gradient of the electron pressure to
decelerate the electrons entering the shock layer.
will be unchanged.
The momentum equation for the ions
Thus though the magnitude of the calculations done by Jaffrin may
not be correct for the observed flow pattern, the phenomenon that his analysis predicts
(the charge separation field inside the shock layer) should be observed in the MAST.
Jaffrin computed this electric field in the shock layer in Hydrogen with no currents or
magnetic fields for initial conditions corresponding to condition B (shock speed of
12.5 cm/,psec, initial density 8.75 H 22 molecules cm- 3 , initial temperature 300°K) under
the assumption that the fraction ionization (a) was 0.05. He found that the shock thickness was 0.3 cm and the integrated electric field across the shock layer was 35 volts
(these results changed little for calculations with a = 0.01 and a = 0.1).
0.5u.s
HFl67v/cm
Ezt
T
36
Fig. 25. Enlarged Ez oscillogram for condition B.
An enlarged E z oscillogram is shown in Fig. 25, in which the spike in the front is
apparent. Since the thickness of the front is of the order of the electrode separation of
the probe, the calculation of the change in potential across the shock layer will only be
approximate.
This change in potential A% is given by
A = f E z dz
Us
E z dt = 33 volts.
This is also the peak voltage measured between the electrodes.
Thus the thickness of
the shock layer is approximately equal to the electrode separation of the probe, which
is 0.6 cm.
These numbers must be interpreted with caution, since the sheath potential
is not necessarily small compared with the measured signal (see section 3.2c).
The
magnitude and direction of this measured field suggest that it is the charge separation
field predicted by Jaffrin, which accelerates the ions.
f.
E
r
Measurements at the Mean Radius
Radial electric field measurements were made at the mean radius (6.2 cm) and z =
61.8 cm for conditions A through F with the Er probe described in section 3.2c.
The
oscillograms are compared with B 0 oscillograms made at the same conditions and
position in Fig. 26.
The electric field deflection downward from zero corresponds to a
radially inward direction in the shock tube. It was found when both Er and Be measurements were made for the same run at the same axial position, that the abrupt change in
the signals when the front reached the probe positions was within less than 0.05 ~sec.
From the traces in Fig. 26, the following points can be made.
(i) The voltage difference between the two electrodes of the E r probe ahead of the
front is negligibly small for B z = 0.1 wb/m 2 , but increases rapidly at higher axial fields
until at condition F (B
(ii)
= 0.42 wb/m
2
) the front is barely discernible.
The shape of the Er trace is similar to that of the Be trace (with the exception
of condition F); the peak Er and Be signals coincide.
(iii) The ratio Er/usB8 can be obtained as a function of time behind the front.
It
will be shown that information on the velocity can be obtained from this ratio.
We shall consider each of these points.
The probe will only measure an electric field if the gas surrounding the probe is
electrically conducting and has currents flowing in it.
Thus any electric field measured
ahead of the front must be due to a precursor effect.
Such precursors in shock tubes
driven by an arc have been studied for some time, and a model suggested by Paxton and
Fowler, 1
5
in which the wave front of the precursor or breakdown wave is assumed to be
an electron shock wave predicts propagation velocities of the correct, order of magnitude.
An axial magnetic field would be expected to interact with such an electron pre-
cursor effect, but since propagation speed of the wave is of the order of 5 X 107 m/sec,
the effect of the field on the electrons behind the wave is of greater interest here.
It
would be expected that the containment provided by the applied axial field would increase
the conductivity in this region.
37
B8
0.41
0.43
240
Er
2 40
I
A
D
0.33
0.33
240
Er
240
E
B
i
0.33
0.33
BE
T
I
Er
480
480
T-
T-
C
Fig. 26.
F
Oscillograms of Be and Er at z = 61.8 cm,
and mean radius for conditions A through F.
38
Points (ii) and (iii) yield information on the velocity of the gas behind the front. The
radial electric field in probe coordinates is given approximately by
E
r
Jr
l-+u B
C
z
+vB
z
Here, effects that are due to tensor conductivity have been neglected.
The order of magnitude of the resistive drop can be estimated as follows.
For runs
2
where the axial field is small (-0.05 wb/m ) the difference between the voltage measured
between the electrodes and the
electrodes.
voltage will be the resistive voltage drop across the
This difference is -400 V.
The computed resistive drop in the steel walls
accounts for half this voltage, and thus the resistive voltage drop across the 2-cm
annulus will be 200 V.
This drop includes the contact resistance and the resistance of
the gas; thus jr/a should be less than 100 V/cm.
The values of Er measured were
-500 V/cm, and the resistive part of this voltage can therefore be neglected in any
qualitative discussion.
Er
usBo
uz
uB
.
us
The ratio Er/usB0 is therefore given approximately by
v
Bz
us
Bo
B'
(18)
and is a measure of the gas velocity.
Er/usBe was computed from the data in Fig. 26
and is shown as a function of time behind the front in Fig. 27. The curve for condition F
is shown dashed, since the shot-to-shot variation of B 0 and E r traces was considerable,
and it is not clear how the shape of this Er trace can be interpreted with Eq. 18.
It would be expected from Eq. 18 that Er/usBe would be of order one for low values
of B, and greater than one for high values of B; the measured data give values
approximately one-half those expected.
This discrepancy was attributed to the dis-
turbance that the probe introduces into the flow, since the gas velocities adjacent to
the probe will be less than the undisturbed gas velocity.
Er/UsB o increases by a factor of 2 from Bz = 0.1 wb/m
It is apparent, however, that
2
and B remain essentially constant (see Figs. 14 and 15).
to B
= 0.42 wb/m
2
, while uS
This increase will be due to
the azimuthal acceleration of the gas in the current sheet by the jrBz force; at high B z
values the azimuthal velocity v
can be of the order of Er/Bz (-25 cm/pLsec).
A qualitative interpretation of Figs. 26 and 27 indicates that the peak gas velocity
occurs approximately at the peak B
field; thus the gas is accelerated over a distance
that is longer than the thickness of the clearly defined front (distances of 5-10 cm,
while the front thickness is -1 cm).
From 0.5
sec to 2.0 pLsec behind the front, the
gas velocity is approximately constant.
4.5 ABSOLUTE LIGHT-INTENSITY MEASUREMENTS
In the final set of experiments measurements were made with a magnetically shielded
calibrated phototube system of the absolute magnitude of the radiated light intensity
from the front and region behind it.
Measurements were made at two pressures (100
39
1.0
0.8
0.6
L
0.4
0.2
0
T-1 -1-
r
*~
I .U
0 "
.
'r,
/- -
T-1
.0---
.
r/ USD 0 Iour conulllons i-k
I- + ~ ~~ ~~~ ~ ~ ~ ~ ~ ~ ~~~~~~~~~~~~6LtIUUgIu
\K
~
ig.
h
-I
-
rui a
ma,.-':a
uncrLLon I
time after passage of the
I-
- --
F
front.
0.8
0.6
LU
0.4
I/
I
D
I
0.2
A
I
I
I
1.0
I
I
2.0
TIME ( sec)
and 250 microns), V
= 7.5 kv, and a wide range of axial magnetic fields.
The phototube
system consisted of a collimator (two 1/32-inch diameter holes separated by a distance
of 10.6 cm); simple lens system (two double convex lenses to focus the light from the
collimator onto the phototube collector); a second-order interference filter of half0
0
bandwidth 100 A centered about 4400 A; an RCA 6655A phototube; phototube circuit; and
fast rise-time cathode follower across the anode resistor of the photdtube. This system
was calibrated by using a tungsten-filament lamp of known horizontal candlepower (80.7)
and color temperature (27000K).
It was hoped that from these measurements estimates
of the electron density in the front could be made, by using calculations carried out by
Janes and Koritzl 6 of absolute Bremsstrahlung intensity for a fully ionized Hydrogen gas.
Typical oscillograms for conditions A through F are shown in Fig. 28 (oscillograms
for condition F showed large variations in shape and magnitude). The light intensity
40
A
4.33
B
3.89
i
1.67
C
D
2.52
t-
E
0.81
F
0.17
1F
Fig. 28. Oscillograms of phototube output for conditions A through F.
41
corresponding to the peak phototube output voltage just after the front is plotted against
axial magnetic field in Fig. 29.
If the results of Janes and Kortiz16 are used to calculate electron densities from
the measured light intensity, the intensities are too high by at least an order of magnitude because the total number of electrons in the front exceeds the maximum possible
Thus all of the radiated light output cannot be due to Bremsstrahlung
by a factor of 3.
alone, and an alternative explanation must therefore be considered.
,,15
I(J
I
I
I
I
I
I
U
o
0
-
0,
Fig. 29. Peak value of light-intensity
measurements as a function
of axial magnetic field.
O
E
1014
o
E
7<
o pl = 10 0 microns
-
A
0
P = 250 microns
II I I
lr)13
I
0.01
l
l
l I
1 22
(wb/m
B, (wb/m
I I
I
I
1.0
)
Keck 7 used tungsten detectors operating in the ultra violet to measure the position
of the front, and showed that most of the light observed came from the arc spot on the
inside electrode.
The voltage output from his UV detectors was similar in shape to the
traces shown in Fig. 28. It will also be seen from a comparison of Figs. 26 (Be traces
at mean radius) and 28 that the change in shape of the light-intensity profile with axial
field somewhat resembles that of the B trace.
We have tentatively concluded,
there-
fore, that the photomultiplier was measuring light from the arc spot on the inner cylinder.
A further point needs to be considered; that is,
axial magnetic field, as shown in Fig. 29.
the decrease in intensity with
The results appear to be asymptotic to a
line of slope -2 at high B z fields, and to a horizontal line as B z
l/(l+e7e) dependence, but we have not investigated this.
42
-
0.
This suggests a
V. INTERPRETATION OF THE RESULTS
5.1 SUMMARY OF FRONT PROPERTIES
The following features of the front have now been established. First, the start of the
sharply defined front on the B,
less than 0.05
1
sec (-0.5 cm).
E z , Er and light-intensity profiles takes place within
Thus no shock wave precedes the current sheet, and it
would appear that the Kemp and Petschek flow pattern is never established.
We found
that between 50 and 100 per cent of the drive current flowed in a clearly defined front,
1.5 cm thick, and that the maximum Be field was of the order of the drive-current field
at the mean radius, and approximately 1.5 times the drive-current field close to the
inside cylinder.
Thus current loops flow behind the front over a distance of 20 cm in
all of the cases considered.
front and the B
Measurements with the E z probe indicate that the shock
front coincide,
but the E r traces suggest that the gas is accelerated
until the maximum Be field is reached, 10 cm behind the front. Hence it is not expected
that gas conditions behind the front are uniform or that either of the simple onedimensional models considered could accurately predict the flow pattern.
Since we have
shown that the Kemp and Petschek flow pattern does not exist, the experimental results
will be discussed with reference to the snowplow model only.
5.2 MOMENTUM BALANCE
It has been shown that a momentum balance (which predicts the front speed) is not
sensitive to the model that was used to describe the flow pattern.
Hence in the absence
of losses (which have been ignored) reasonable agreement between the measured and
predicted u s would be expected.
Figures 12-15 show that such agreement is achieved,
and it will now be shown that the departure from the predicted behavior can be explained
qualitatively by considering three phenomena affecting the momentum balance.
are losses caused by wall friction,
These
ablation, and diffusion through the current sheet.
It will be shown that ablation causes losses that increase as the initial pressure is
decreased, and diffusion, which results in an increase in u s , will increase as the
initial pressure is increased.
Thus it is not possible to separate the effects of these
phenomena.
a.
Wall Friction
To the author's knowledge no theoretical solution exists for the type of magneto-
hydrodynamic boundary layer found in the MAST.
Thus a quantitative estimate of the
loss resulting from friction is not possible. It is well known, however, that in conventional shock tubes, as the shock speed is increased and the initial pressure decreased,
losses caused by boundary-layer leakage of test gas become increasingly important
(Roshko 7 ), and the shock speed attenuates along the length of the tube.
But in this
experiment, most of the drive current flows in the shock front; thus the diffusion of the
43
shock-heated gas to the walls is restricted by a magnetic field of the order of 1 wb/m
2
parallel to the tube walls. The solution obtained by Roshko, therefore, is not applicable
to this case; nor is it obvious that increasing shock speeds and decreasing initial
pressure, which in the conventional shock tube cause increased losses, will have the
same effect here because the containment should be more effective at the higher temperatures behind the shock, which such trends should produce.
No useful estimate of the
effect of wall friction can be made.
b. Ablation
Keck7 has shown that ablation of material from the insulator end wall by a fraction
of the drive current flowing across the insulator face could explain the large velocity
defects observed in his experiments.
He considered a lucite insulator.
The insulator
used in his experiments was capped with a Pyrex ring to reduce any ablation to minimum, but on dismantling the tube it was found that the surface of the glass (initially
polished) was etched with fine lines indicating that the surface had been heated by the
It was shown, however, that from 90 to 100 per cent of the drive current moves
arc.
down the tube with, or closely behind (-15 cm), the front, which limits this ablation
from the end wall.
One other source of extraneous material must be considered, namely the cylindrical steel walls of the tube.
Kantrowitzl presents calculations based on simple heat-
conduction theory of the time required to raise the surface temperature of various
materials to the melting point for a given heat flux per unit area per unit time to the
wall.
This heat flux is calculated from the plasma energy reaching the wall with no
containment,
and thus represents a limiting case.
For a plasma with n = 1022 m
3
,
T = 106°K, and mean thermal speed 2.4 X 107 cm/sec he computes the time for stainless steel to reach its melting point at the surface as 1
sec.
Note that the plasma
temperature is an order of magnitude higher than the equilibrium temperature behind a
shock at the front speeds measured here, and also that containment is ignored.
This
estimated time is therefore too small by two orders of magnitude; and the temperature
rise at the surface in 1
sec will be one order of magnitude less than the melting point
of steel, that is, approximately 150 ° . Thus gas evolved from the walls could contribute
to the observed momentum defect. Note that the momentum defect is greatest (Fig. 12)
when the highest temperatures behind the shock would be expected, and when the mass
of gas swept up by the sheet is least.
c. Diffusion through the Sheet
The value of the magnetic Reynolds number (RM =
or v L) in the current sheet will
determine whether appreciable diffusion of gas through the sheet takes place.
The
inequality Rm >>1 must be satisfied for the solid piston model discussed in Section II
to be valid.
If v is taken as the measured front velocity,
librium temperaturel
8
calculated from the equi-
behind a shock of Mach number corresponding to u s , and L
44
taken as the distance between the front and the B 0 maximum (-5 cm), at P1 = 60 microns
3
2
RM is of the order of 10, and at P = 500 microns RM is of the order of 10 . These
figures are order-of-magnitude estimates only and could be substantially in error on
the high side because the equilibrium shock temperature represents an upper limit for
the conductivity.
The fact that the Kemp and Petschek flow pattern was never set up,
indicates that the magnetic Reynolds number in the front must be much less than these
estimates, since the calculations in Appendix B indicate that if it were of the order indicated, a shock wave would precede the current sheet.
Diffusion through the current
sheet results in an increase in the observed front speed, since momentum leaks out of
the back of the sheet.
This increase in front speed would be most apparent at the
highest initial pressures considered,
since this corresponds to the lowest magnetic
Reynolds number in the sheet.
5.3 INTERNAL FLOW PATTERN
The important features of the front and region behind it have been summarized.
In
this section possible mechanisms for creating the observed flow pattern will be discussed, but first let us consider the limitations of the experimental data.
The B. probe
measurements provide a quantitative picture of the current distribution inside the
annulus; the Er measurements give qualitative information on the axial velocity distribution; but nothing is known about the temperature, density, and radial and azimuthal
velocity distributions in and behind the front. A detailed discussion will not be attempted,
but some comments will be made on (i) the shape of the front; (ii) the existence of the
current loops; and (iii) the effect of the axial field particularly at conditions F.
The shape of the front will be related to the model used for the momentum balance
in the following manner.
In the snowplow model it is assumed that the gas swept up by
the current sheet remains close to the front.
Since the driving pressure varies by a
factor of 2 from the inside to the outside radius, the resulting front should be bulletshaped.
Keck 5 showed that with the center electrode positive a bullet-shaped front is
observed and the front is inclined to the tube axis at an angle of approximately 30 ° .
He
found that with the center electrode negative, the front was perpendicular to the tube
axis; a result that is in agreement with our measurements (section 4.4d).
suggests an explanation for this change in shape:
Bostick 19
The vector sum of the Hall current (in
the -j X B direction) in the front and the bullet-shaped drive current produce a planar
front when the center electrode is negative.
An estimate of the Hall parameter (We
e
)
will tell us whether the magnitude of the Hall current is large enough to appreciably
change the shape of the front. When based on equilibrium temperature and density behind
a shock at the measured front speed (at
=
100 microns) it is approximately 5, which
would indicate a Hall current of the order of the drive current. Again, this represents an
upper limit, since we have shown (section 4.4f) that the gas velocities just behind the
front are much less than the front speed itself, and that the peak gas velocities comparable to those expected behind a normal shock are only attained 10 cm behind the front.
45
-
-
-
The next point to consider is the closed-current loop behind the front, which was
observed for all conditions A through F.
Burkhardt and Loveberg3 also measured a
similar anomalously high B o field close to the cathode (center electrode) in their plasma
gun; in their experiment there was no axial magnetic field.
It has been shown that
electric fields exist to drive this loop, but mechanisms for creating these fields have
not been discussed.
The Hall parameter has been estimated to be of the order of 5;
therefore Hall effects both in and behind the front could be significant. Gradients in the
Hall field will also exist, since the B o field varies by a factor of 1.4 across the annulus,
and it has been shown that profiles through the front change significantly with radius.
Axial currents, as well as Hall effects,
ponent of the V X B induced field.
could also be generated from the v rB
com-
Note that the direction of the current loop in Fig. 23
is such that the j X B force opposes radial motion toward the mean radius. Finally, the
Er traces (Fig. 26) show that axial velocity gradients (uz/az)
exist in the gas behind
the front. These velocity gradients will cause axial variations in radial electric field in
front stationary coordinates, and current loops may be forced to flow to balance out
these gradients.
All of these mechanisms could exist and drive the observed current
loop, but in the absence of more detailed information on the gas temperature and
velocity a quantitative explanation will not be attempted.
The effect of the axial field on the flow at the two pressures considered can be
summarized as follows.
In the P
= 250 microns runs (A, B, and C) the effect of
increasing the axial field moves the position of the B 0 maximum behind the front closer
to the front. In the P = 100 microns runs (D, E, and F) this effect is not apparent; but
at condition F the B
front is less clearly defined,
a smaller fraction of the drive
current flows in the front, the current sheet is spread over a greater axial distance,
the E r front is barely discernible and the light-intensity front is not always distinct.
Figures 19, 20, 26 and 28 illustrate these points.
Note that the front speed and drive
current are almost independent of the axial field (Figs. 14 and 15).
In condition F there
is the greatest Alfven speed ahead of the shock (b z = Bz/oP).
If this is computed
from the initial density (under the assumption that the gas ahead of the front is completely ionized), bz = 10 cm/ILsec; the measured u s is
14 cm/psec.
This computed
Alfvdn speed will be less than the actual Alfvdn speed, as the maximum possible density
was taken.
In the Kemp and Petschek calculations, as B z is increased and the Alfv6n
Mach number (Us/b
z)
tends to unity, the shock and current sheet approach an infinitesi-
mal magnetohydrodynamic disturbance, although, as the authors explain, some of their
assumptions would then be invalid.
being observed here.
The measured profiles indicate that this trend is
Note that the Alfvdn Mach number of 1.4 is less than the value
(2.0) at which the switch-on shock could occur.
No significant changes in flow pattern
were observed at the axial field strength corresponding to this Alfv6n Mach number
of 2.0.
46
VI. CONCLUSIONS
6.1 SUMMARY
The results presented in Section IV show that neither the snowplow nor the Kemp
and Petschek model is a satisfactory approximation to the observed flow pattern.
In
Section V, however, it was shown that the momentum balance predicted by the snowplow
model is in reasonable agreement with the measurements of front speed over a wide
range of experimental conditions.
Loss mechanisms and diffusion were discussed in a
qualitative way to show that exact agreement should not be expected.
The behavior pre-
dicted from the Kemp and Petschek theory at high axial fields was not observed as the
essential feature of their model; a shock wave separated from the driving-current sheet
was never set up.
Our internal measurements show that a one-dimensional model will not adequately
predict the finer features of the flow, since a substantial variation with radius of
profiles measured through the sheet was found to occur.
No homogeneous gas sample
was observed, and the gas is continuously accelerated from the front to the position of
the peak B
field over a distance of approximately 5 cm.
Thus no region of uniform
properties exists behind the front, and it is therefore difficult to evaluate the change in
gas properties across the front. It has been demonstrated that the clearly defined front
(1 cm thick) shows axial electric field characteristics similar to those predicted in a
shock wave in partially ionized Hydrogen at the experimental conditions.
The measure-
ment of shock properties in the regime where a switch-on shock could exist was
obscured by the presence in the front of a substantial fraction of the drive current.
Thus no conclusions on the existence of the switch-on shock can be made, and it was
found that the axial magnetic field produced significant changes in the front profiles only
when the Alfven Mach number of the front was reduced to 1.4.
6.2 SUGGESTIONS FOR FURTHER WORK
In one sense the experiments reported here were unsuccessful, in that no homogeneous gas sample was obtained under any of the conditions considered.
Thus, although
the MAST operated as a plasma accelerator, it did not really operate as a shock tube.
It has been shown that the cause of this observed behavior probably is the low magnetic
Reynolds number in the front, because of the low electrical conductivity of the gas
ahead of the front.
This suggests that the next stage in the development of the shock
tube should be to raise the conductivity of the gas ahead of the front until the Kemp and
Petschek flow pattern (that is, a shock in front of and separated from the current sheet)
is set up.
It has been shown that if this flow pattern is set up, it should persist.
One
possible way of achieving this flow pattern would be to have the main drive-current discharge preceded by a substantial ionization discharge, timed so that the drive current
reaches the back of the ionization discharge before the front enters the test region of
47
---I
the shock tube.
Thus the drive current would be flowing at the back of a region of high
electrical conductivity.
A more detailed investigation of this type of approach seems to
be in order.
Several instrumentation problems still exist; these will be summarized as suitable
areas for further development.
The effect of the electric field probes on the flow should be considered in more
detail, and the interpretation of the Er probe signals made more quantitative.
A radial
traverse with the Er probe would provide more information on the gas velocity behind
the front.
Provision for inserting probes axially into the annulus should be considered
so that the effect of probe holes can be eliminated.
The relation between arc spots on
the inside cylinder and the phototube output should be investigated in greater depth, and
experiments following those done by Keck 7 should be considered.
Since no knowledge of
the plasma density behind the front was obtained, the development of Langmuir probes
suitable for inserting into the annulus seems worth while.
48
APPENDIX A
Diffusion of the Current Sheet into the Shock-Heated Gas
Falk and Turcotte 13 analyze the problem of the diffusion of a current layer in a onedimensional pinch. Their results can be used here to estimate the distance over which
the driving-current sheet in the MAST would diffuse into the homogeneous gas sample
between the sheet and the shock, if the Kemp and Petschek flow pattern is set up. Falk
and Turcotte show that the field penetrates the plasma a distance of -2`t/hNo
(approximately the skin depth of the plasma). Kantrowitz1 shows that for the Kemp and Petschek
flow pattern to persist, the rate of increase of the length of the homogeneous gas sample
must exceed this diffusion of the current sheet into the plasma.
u t
Pl
Thus it is required that
> 2/7t ,O .
(A-l)
The time TD at which these two lengths are equal, and the depth of penetration d at
t = 5 sec (the time after breakdown at which measurements were usually made) were
calculated from the predicted shock speed and equilibrium valves of temperature and
density behind the shockl
8
(see Table 2).
Table 2.
Results of calculations.
P1
Predicted u s
TD
d
(microns)
(cm/pusec)
(seconds)
(cm)
100
19
3 X 10 - 9
0.6
500
10
3 X 10 - 7
1.8
The calculations show that the high magnetic Reynolds number assumption ought
to be valid at pressures of approximately 100 microns, provided that the Kemp and
Petschek flow pattern is set up initially, but may be less valid at the highest pressures
considered.
49
.~~-1---_11·I
.
APPENDIX B
Equation for the Flux Speed
loop (see Fig. 2) measured the time rate of change of
The voltage measured in the
flux through the loop. As the current sheet moves down the annulus, the voltage induced
in this loop will be due to three different effects.
These are the change in flux behind
the sheet caused by the change in magnitude of the current, the axial movement of the
sheet, and the diffusion of the current into the steel walls of the tube. Thus we can write
(B-l)
= Ll d + LIuL + A(L),
where L is the inductance per unit length of the annular region, I is the axial distance
through which the sheet has moved, uL is the flux speed (a speed that can be regarded
as the axial speed of the center of gravity of the current sheet), and A
the
is that part of
signal resulting from the diffusion of the current outward through the steel walls.
The term that is due to dI/dt will be neglected, since the flux speed will be computed
The A
voltage only while the drive current is constant.
from the
included because it is approximately 20 per cent of the total
dA will now be made so that uL can be evaluated from the
sidered is shown in Fig. 30.
term must be
signal.
An estimate of
4 voltage.
The model con-
Since the skin depth in the steel is small compared with
(2
o
RRENT SHEET
rEEL
Fig. 30.
the steel thickness,
Model for diffusion calculation.
the effect of finite wall thickness will be ignored.
Note that two
time scales are important: t, the time after breakdown; T = t - x/uL, the time at any
position x after the sheet has passed.
B =erfc(y
B =
4or/2
The magnetic field in the steel is given by
1),
(B-2)
o
and the rate of change of flux caused by diffusion into one wall will be given by a voltage
V, where
V
dt {
f
(B-3)
B dydx}
50
___
-
The J0 B dy can be evaluated numerically to the degree of precision required here
from (B-2); and from the definition of
V = 1.2BoU
L
, and by noting that t =
uL it follows that
/
(B-4)
A; is the sum of V evaluated at the inside and outside radius; thus
AS = 1
2u L
/X
(B-5)
[Bo(ri)+B(ro)]
If it is assumed that only the drive current flows in the steel; and that AQ is small
compared with $ so that second-order terms can be neglected, then
1-2 J
t
r
o riroi
+ ro
n
.
(B-6)
ro/ri
Substituting r i = 5.2 cm, r
= 7.2 cm,
can evaluate the ratio A/
as
= 1.7 X 106 mho/m with t in microseconds, we
00.8 T.
Thus for t of approximately 5
(B-7)
sec, A+/4 is approximately 0.2.
Equation B-7 is used
in the evaluation of the flux speed uL.
51
-
~ ~
--
--
APPENDIX C
Drive-Bank Performance with the Shock Tube as Load
The load which the idealized lossless shock tube presents to the drive capacitor
bank can be estimated by using the snowplow model described in section 2.2. The idealized case, in which the flux speed uL and the front speed u s are equal and constant, and
the drive current I has reached its steady value, will be treated,
since it has been
shown that the existing flow pattern is an approximation to this model. In general when
the shock tube is regarded as a time-variant inductance L T in series with a resistance
R, by representing the resistance in the leads, gas, and contact resistances, the equation
governing the current can be written,
Vo = I(Zo+R) +
where Z
I dLT
d
+
d'
LTdt'
(C-l)
is the characteristic impedance of the drive bank (which was set up to simu-
late a transmission line). For the idealized model described above, (C-1) reduces to
(C-2)
Vo = I(Zo+R+Lus),
where L is the inductance per unit length of the shock tube.
When we wish to compare
(C-2) with the actual performance of the bank, an additional component in the dLT/dt
U.
Fig. 31.
2
3
4
5
106
1megamps
I
( megamps
52
Plot of u s against I.
term must be included.
This is the LA
term derived in Appendix B, which represents
the change in inductance because of the diffusion of the drive current into the steel
walls. Since LIu s is now the ideal $ voltage, Eq. C-1 for dI/dt = 0 will now reduce to
VoR + Zo + Luz o
(C-3)
V 0 =I
or
V
o_
o
1
1
R+Z
R+ZQo
(C-4)
A plot of the measured u s against the measured 1/I is shown in Fig. 31 for the data presented in section 4.3b. The line of slope Vo/L(+
points is also shown (V
of 1.15).
= 7.5 kv, L = 6.5 X 10
- 8
AS/S) which best fits the experimental
h, 1 + A+/+) evaluated at a mean value
Note that the calculated intercept at zero u s (which equals (R+Zo)/V
evaluated from the measured Z
the line that best fits the data.
0
and is
and estimated R) lies close to the actual intercept of
Equation C-3, therefore, accurately predicts the per-
formance of the shock-tube, drive-bank combination.
53
--11IIII(---L_
_II1I---
---
-
APPENDIX D
Calibration of B o Probes and Magnetic Search Coils
The effective areas of all B
probes and magnetic search coils used to measure the
magnitude of local magnetic fields were found by measuring the output of each coil when
it was placed in a known sinusoidal field.
A Helmholtz coil was used for this purpose,
since at its center the field is uniform over a distance comparable to the radius.
The
field at the center of the Helmholtz coil (BH) is given by
8Lo0 iN
BH -
(D-l)
53/2R
where i is the value of the current in amps, N is the number of turns in each coil, and
R is the radius in meters.
A coil of 0.367-inch radius with three turns per coil was constructed,
and the
validity of Eq. D-1 was checked with a DC gaussmeter and a constant current.
The
measured B field agreed with the predicted B field within ±1 per cent. The sinusoidal
current through the coil was obtained from a bridge oscillator that produced currents
of -1 amp with the coil as load, at frequencies from 5 kc to 50 mc.
The value of the
current was measured with a Tektronix current probe and passive termination, and the
current and probe output waveforms were displayed on a dual-beam oscilloscope having
two similar preamplifiers.
If i
A photograph of the calibration rig is shown in Fig. 32.
is the peak value of the current in amps, V
probe in volts,
the peak output voltage of the
Tc the period of the current and voltage waveforms in microseconds,
-1
Fig. 32. Rig for calibration of magnetic probes.
54
--
----
and A the coil area in m 2 , then from Eq. D-1, Faraday's law of induction, and the coil
dimensions it can be shown that
A = 5 52 X 10
4
pc
i
(D-2)
o
The drive current,
and axial field calibrating coils were calibrated by means of
(D-2) over an order-of-magnitude range of frequencies that spanned the basic frequency
of the measurement.
The effective area was constant (2
per cent) over these ranges.
The Be probes were calibrated from 1 mc to 10 mc before insertion into the annulus
and after the probe, had been removed. The two calibrations always agreed within ±5 per
cent.
The effect of the voltage divider (three 50-ohm, 1 per cent, low-inductance resis-
tances (see Fig. 6) was also investigated over this range of frequency and the effective
area was reduced by the expected factor of 1/3.
No frequency dependence over the
range of frequencies used in calibration was observed. With the probe connected to the
oscilloscope through an RC integrator whose time constant is long compared with the
signal length (at least a factor of 30 in all measurements), the magnetic field measured
by the probe is given by
B
3
RCV,
where V is the integrator output in volts,
(D-3)
and the factor 3 is introduced by the voltage
divider.
55
__
I_-··I-·I)I
Il-·llll----·I___L(IC-
^-
I
I_
ACKNOWLEDGMENT
The author wishes to express his thanks to many people who contributed substantially to this project.
He is particularly grateful for the assistance and support provided by his thesis
supervisor, Professor A. H. Shapiro, and by his thesis committee Professors J. A. Fay,
H. H. Woodson, and W. H. Heiser, not only in committee meetings but also in the many
fruitful hours of individual discussion spent with each of them. He is especially indebted
to Professor Heiser for his patient encouragement.
His fellow students Mr. William F. Ulvang and Mr. Ashok S. Kalelkar spent much
time and effort developing and calibrating probes, and assisting in the experiments.
The staffs of the Fluid Mechanics Laboratory of the Department of Mechanical
Engineering, M. I. T., and the Research Laboratory of Electronics, M. I. T., also contributed to the project, and the author wishes to thank Mr. Erland R. Babcock and
Mr. David A. Carlson in particular for their efforts in apparatus construction, instrument calibration, and many mechanical design problems.
56
REFERENCES
1. A. Kantrowitz, "Shock Tubes for High Temperature Gas Kinetics,"
Report 141, Avco Everett Research Laboratory, 1962.
Research
2. J. Marshall, "Performance of a Hydromagnetic Plasma Gun," Phys. Fluids 3,
134 (1960).
3. L. C. Burkhardt and R. H. Loveberg, "Current Sheet in a Coaxial Plasma Gun,"
Phys. Fluids 5, 341 (1962).
4. R. M. Patrick, "The Production and Study of High Speed Shock Waves in a Magnetic
Annular Shock Tube," Phys. Fluids 2, 589 (1959).
5. J. C. Keck, "Current Distribution in a Magnetic Annular Shock Tube,"
Fluids 5, 630 (1962).
Phys.
6. F. J. Fishman and H. Petschek, "Flow Model for Large Radius-Ratio Magnetic
Annular Shock-Tube Operation," Phys. Fluids 5, 632 (1962).
7. J. C. Keck, "Current Speed in a Magnetic Annular Shock Tube," Research Report 152,
Avco Everett Research Laboratory, 1963.
8. W. H. Heiser, "Axial Field Effects in a Magnetically Driven Shock Tube," Technical
Report 408, Research Laboratory of Electronics, M.I.T., Cambridge, Mass.,
March 29, 1963.
9. N. H. Kemp and H. E. Petschek, "Theory of the Flow in the Magnetic Annular Shock
Tube," Phys. Fluids 2, 599 (1959).
10. J. A. Shercliff, "One-Dimensional Magnetogasdynamics in Oblique Fields," J. Fluid
Mech. 9, 481 (1960).
11. J. E. Anderson, Magnetohydrodynamic Shock Waves,(The M. I. T. Press, Cambridge,
Mass., 1963).
12. F. J. Fishman and H. E. Petschek, "Deviation of Mast Operation from OneDimensional Model," Phys. Fluids 5, 1188 (1962).
13. T. J. Falk and D. L. Turcotte, "Current-Layer Diffusion in a One-Dimensional
Pinch," Phys. Fluids 5, 1288 (1962).
14. M. Y. Jaffrin, "Shock Structure in a Partially Ionized Gas," Publication No. 64-9,
Fluid Mechanics Laboratory, M.I.T., October 1964.
15. G. W. Paxton and R. G. Fowler, "Theory of Breakdown Wave Propagation," Phys.
Rev. 128, 993 (1962).
16. G. S. Janes and H. E. Koritz, "Numerical Calculation of Absolute Bremsstrahlung
Intensity for a Fully Ionized Fully Dissociated Hydrogenic Gas," J. Appl. Phys. 31,
525 (1960).
17. A. Roshko, "On Flow Duration in Low Pressure Shock Tubes," Phys. Fluids 3, 835
(1960).
18. E. B. Turner; "Equilibrium Hydrodynamic Variables Behind a Normal Shock Wave
in Hydrogen, Report GM-TR-0165-00460, Space Technology Laboratories, Inc.,
Rodondo Beach, Calif., 1958.
19. W. H. Bostick, "Hall Currents and Vortices in a Coaxial Plasrra Accelerator,"
Phys. Fluids 6, 1598 (1963).
20. L. Spitzer, Jr., Physics of Fully Ionized Gases (John Wiley and Sons, Inc., New York
and London, second revised edition, 1962), p. 23.
57
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Office of Deputy Director (Research
and Info)
Department of Defense
Washington 25, D.C.
Dr. H. Hattison
National Aeronautics & Space Administration
Code RRE
Washington, D.C. 20546
AEC
Civ of Tech Info Ext
P.O. Box 62
Oak Ridge, Tenn.
AFRST (SC/EN)
Lt Col L. Stone
Rm 4C 341
The Pentagon
Washington, D.C. 20301
U. S. Atomic Energy Commission
Lib rary
Gaithersburg, Md. 20760
Frank J. Seiler Rsch Lab
Library
USAF Academy, Colo 80840
ARL (AROL)
Wright-Patterson AFB,
Ohio 45433
Office of Research Analyses
Library
Holloman AFB, NMex 88330
LOOAR (Library)
AF Unit Post Office
Los Angeles, Calif 90045
Churchill Research Range
Library
Fort Churchill
Manitoba, Canada
Los Alamos Scientific Lab
Attn: Technical Library
Los Alamos, NMex 87544
Battelle Memorial Institute
Technical Library
505 King Avenue
Columbus, Ohio 43201
John Crerar Library
35 West 33rd St.
Chicago, Ill.
Linda Hall Library
5109 Cherry St.
Kansas City, Mo.
National Science Foundation
Library
1951 Constitution Ave., N.W.
Washington, D.C. 20550
JOINT SERVICES DISTRIBUTION LIST (continued)
RTD (Tech Library)
Bolling AFC, D.C. 20332
Johns Hopkins University
Applied Physics Lab Library
White Oak
Silver Spring, Md. 20910
AFFTC (Tech Library)
Edwards AFB, Calif 93523
Stanford Research Institute
Library
820 Mission St.
South Pasadena, Calif. 91030
AFMDC (Tech Library)
Holloman AFB, NMex 88330
AFMTC (Tech Library)
Patrick AFB, Fla 32925
Southwest Research Institute
Library
8500 Culebra Road
San Antonio, Texas
AFWL (WLIL, Tech Library)
Kirtland AFB, NMex 87117
APGC (Tech Library)
EglinAFB, Fla 32542
DDC (TISIA- 1)
Cameron Station
Alexandria Va. 22314
AEDC (Tech Library)
Arnold AFS, Tenn 37389
ARPA, Tech Info Office
The Pentagon
Washington, D.C. 20301
RADC (Tech Library)
Griffiss AFB, N.Y. 13442
DDR&E (Tech Library)
Rm 3C 128
The Pentagon
Washington, D.C. 20301
Director
National Aeronautical Establishment
Ottawa, Ontario, Canada
CIA
Industrial College of the
Armed Forces
Attn: Library
Washington, D.C.
OCR/LY/IAS
IH 129 Hq
Washington, D.C. 20505
National Defense Library
Headquarters
Ottawa, Ontario, Canada
AFIT (MC LI)
Tech Library
Wright- Patterson AFB
Ohio 45433
Technical Library
White Sands Missile Range
NMex 88002
AUL 3T-9663
Maxwell AFB, Ala 36112
NASA/AFSS/1 FOB6
USAFA (DLIB)
USAF Academy, Colorado 80840
Tech Library, Rm 60084
Washington, D.C. 20546
AFSC (Tech Library)
Andrews AFB
Washington, D.C. 20331
Space Systems Division
Los Angeles Air Force Station
Air Force Unit Post Office
Los Angeles, California 90045
Attn: SSSD
ASD (Tech Library)
Wright-Patterson, AFB
Ohio 45433
Regional Science Office/LAOAR
Embassy
676
York, N.Y.
BSD (Tech Library)
Norton AFB, Calif 92409
U.S.
U.S.
APO
New
ESD (Tech Library)
L. G. Hanscom Fld
Bedford, Mass 01731
Ames Rsch Center (NASA)
Technical Library
Moffett Field, Calif 94035
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JOINT SERVICES DISTRIBUTION LIST (continued)
Commander
Air Force Cambridge Research Laboratories
Office of the Scientific Director
L. G. Hanscom Field
Bedford, Massachusetts
High Speed Flight Center (NASA)
Technical Library
Edwards AFB, Calif 93523
Goddard Space Flight Center (NASA)
Greenbelt, Md. 20771
Commander
Air Force Systems Command
Office of the Chief Scientist
Andrews AFB, Maryland
Geo. C. Marshall Space Flight
Center (NASA)
Redstone Arsenal, Ala 35808
Lewis Research Center (NASA)
Technical Library
21000 Brookpark Road
Cleveland, Ohio
Commander
Research & Technology Division
AFSC
Office of the Scientific Director
Bolling AFB 25, D.C.
Aerospace Corp (Tech Library)
P.O. Box 95085
Los Angeles, Calif 90045
Commander
Rome Air Development Center
AFSC
Office of the Scientific Director
Griffiss AFB, Rome, New York
Rand Corporation
17 Main St.
Santa Monica, Calif 90401
Commander
Electronics Systems Division (AFSC)
Office of the Scientific Director
L. G. Hanscom Field
Bedford, Massachusetts
Carnegie Institute of Technology
Science & Engineering Hunt Library
Schenley Park
Pittsburgh, Pa. 15213
California Institute of Technology
Aeronautics Library
1201 East Calif St.
Pasadena 4, Calif
Department of the Navy
Dr. Arnold Shostak, Code 427
Head, Electronics Branch
Physical Sciences Division
Department of the Navy
Office of Naval Research
Washington, D.C. 20360
AVCO Research Lab
Lib rary
2385 Revere Beach Parkway
Everett, Mass 02149
Dr. G. E. Knausenberger
SACOM Mail Room
APO 407
New York, N.Y.
Chief of Naval Research, Code 427
Department of the Navy
Washington, D.C. 20360
Commander
Space Systems Division (AFSC)
Office of the Scientific Director
Inglewood, California
Commander
Aerospace Systems Division
AFSC
Office of the Scientific Director
Wright-Patterson AFB, Ohio
Chief, Bureau of Weapons
Department of the Navy
Washington, D.C. 20360
Chief, Bureau of Ships
Department of the Navy
Washington, D.C. 20360
Attn: Code 680
Commander
Aerospace Research Laboratories (OAR)
Office of the Scientific Director
Wright-Patterson AFB, Ohio
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Commander
U. S. Naval Air Development Center
Johnsville, Pennsylvania
Attn: NADC Library
JOINT SERVICES DISTRIBUTION LIST (continued)
Library
U. S. Navy Electronics Laboratory
San Diego, California 92152
Commanding Officer
U. S. Navy Underwater Sound Laboratory
Ft Trumbull
New London, Connecticut
Director
Naval Research Laboratory
Washington, D.C. 20390
Commanding Officer
Office of Naval Research Branch Office
Navy 100, Fleet P.O. Box 39
New York, New York
Chief of Naval Operations
Pentagon OP 07T
Washington, D. C.
Commanding Officer
Officer of Naval Research Branch Office
495 Summer Street
Boston, Massachusetts 02110
Commander
Naval Ordnance Laboratory
White Oak, Meryland
Attn: Technical Library
U. S. Navy Post Graduate School
Monterrey, California
Attn: Electrical Engineering Department
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