A
OF
STUDY
VERSATOR II
LOWER
HYBRID
TOKAMAK
WAVE
MICROWAVE
USING
ON
PROPAGATION
THE
SCATTERING
by
Rajeev
Rajan
'ohatgi
M.Sc., Indian Institute of Technology, Bombay (1980)
Submitted to the Department of Physics in Partial Fulfillment
of the Requirements for the Degree of
DOCTOR
OF
PHILOSOPHY
at the
MASSACHUSETTS
INSTITUTE
OF
TECHNOLOGY
May 1986
Massachusetts Institute of Technology
Signature of Author
1986
Department of Physics
'Qecember 1985
Certified by
Bekefi
Prof Geor
ervisor
Su
Thesis
Accepted by
MASSACHUSETTS INSTITUTE
OF TECHNOLOGY
Archives MAY 2 9 1986
- 1 -
Prof George Koster
Chairman, Departmental
Graduate Committee
Section
[2]
Prefatory:
TABLE OF CONTENTS
1
Title and Certification
1
2
Table of Contents
2
3
Abstract
-
3
4
Acknowledgment .
4
5
List of Figures
6
6
List of Tables .
9
7
Notation
.
8
Introduction
10
15
8A
Lower Hybrid Waves
24
9
Experimental Setup
28
10
Experimental Procedure
.
48
11
Analysis
.
58
12
Experimental Results
63
13
Theoretical Modelling
83
14
Comparison Between Theory and Experiment
15
Conclusion
.
110
16
References
.
114
Appendices:
.
101
17
Scattering Calculation
. 116
18
Lower Hybrid Wave Calculation
. 125
19
Microwave Measurements
. 130
20
High Voltage Filter Feedthroughs
* 138
21
Computer Programs
0 142
-
2 -
.
Section
A
[3]
STUDY
ABSTRACT
OF
VERSATOR II
LOWER
HYBRID
TOKAMAK
WAVE
USING
PROPAGATION
MICROWAVE
ON
THE
SCATTERING
by
Rajeev
Rohatgi
Submitted
to
the Department of
Physics
on
May 2, 1986
in
partial
fulfillment
of
the
requirements for the Degree of Doctor of Philosophy
in Physics.
Abstract
A 139 GHz microwave scattering diagnostic is used to study
the penetration of externally launched 0.8 GHz lower hybrid
waves in current drive (n
< 6 x101 2 cm- 3 ) experiments on
A 7 W Extended Interaction
II tokamaR.
MIT's Versator
Oscillator is used to provide the incident 139 GHz beam.
Waveguide optics are used. The scattered signal is measured
by means of a homodyne detection technique using a balanced
The
mixer, with a spectrum analyzer as the IF detector.
receiver noise is under 10- 1 3 W in a 300 kHz bandwidth;
however, the experimental sensitivity is usually limited by
Various scattering geometries
background plasma emission.
The 0.8 GHz lower hybrid waves are launched
are available.
using a 150 kW klystron and a phased 4 waveguide grill.
Our results
A variety of experiments has been performed.
indicate a spatially defined resonance cone near the edge of
the plasma, with very directional power flow that is in
excellent agreement with theoretical modelling.
Power does
some evidence of wave absorption
reach the plasma center;
during current drive is seen.
Wavenumber
spectra and
Some data has
frequency spectra have also been measured.
been taken at densities outside the current drive regime. A
major discrepancy between theory and experiment is the
measured power
levels, which are low by 2-3 orders of
magnitude.
Experimental setup, procedure, analysis, results, and the
theoretical modelling are all described in some detail.
Thesis Supervisor: George Bekefi
Title: Professor of Physics
- 3 -
Section [4]
ACKNOWLEDGMENT
The Versator lab has been an excellent place to work. I do
not think I could have asked for better, either in terms of
enthusiastic, able, and easy-to-get-along-with people or in
terms of facilities.
My foremost debt of gratitude is to Kuo-In Chen, who was my
partner during almost all of my experimental runs.
I really
do not know what shape my experiment and myself would have
been in, were it not for his selfless generosity and
willingness
to help me.
Second,
I must thank Ed Fitzgerald,
our senior technical staff member, from whom I have probably
learnt more than from any other individual (well, except my
parents, I guess).
He has also been an invaluable ally,
willing to tackle any problem with resourcefulness and good
humor.
Prof George Bekefi has supported me and trusted me through
thick and thin; I would especially like to thank him for the
opportunity I have had to work with this group. I would also
like to thank Prof Miklos Porkolab and Stan Luckhardt for
their encouragement and guidance.
The students and staff of
Versator have over the years been both good friends and
colleagues;
I would like to acknowledge with gratitude the
willing help and support I have received from
- 4 -
Tom Evans
Steve Knowlton
Alan Palevsky
Alan Fisher
Jerry Lorden
Burton Richards
Kirk Hackett
Ivan Mastovsky
Adam Sapirstein
Bob Kaplan
Scott McDermott
Joel Villasenor
with special mention for Matt Mayberry, who has been my
fellow graduate student, neighbor, and close friend for the
last
five years,
as we have gone through the ups and downs
of graduate life.
There have
been occasions
when
I have
had
to
seek the
assistance of others to help me with some specific problem.
Without exception, they have helped me generously.
Paul
Bonoli provided me with his ray tracing code and helped me a
lot with difficulties I ran into while doing the theoretical
modelling.
Others
I would
Barrett, Mike Doucette,
Cliff
like
to
Surko,
thank
include
Jack
Dave Taylor and Paul
Woskoboinikow. I would also like to take this opportunity to
thank two faculty members who, although not associated with
my experiment, have taught me a lot:
Prof Jeff Freidberg and
Prof Robert Kyhl.
And
lastly
my gratitude
to
my parents
and my numerous
friends over the years for just being there.
this includes you !)
-
5 -
(Ken and Joel*,
Section [5]
LIST
OF
FIGURES
.
.
20
.
.
.
29
.
.
.
30
8.1
Scattering Wavevectors
9.1.1
Versator Port Allocation
9.2.1
Experimental Schematic
9.3.1
EIO Power Circuit
.
9.3.2
EIO Cooling System
.
9.4.1
Mirror Assembly
9.4.2
Sample Scattering Volumes
.
.
.
35
9.4.3
Sliding Dovetail Bracket
.
.
.
37
9.5.1
Wedge Reflector
.
.
38
9.6.1
Microwave Receiver
.
40
9.8.1
Signal Amplifier and Transmission Line
.
42
9.9.1
Launching Lower Hybrid Waves
.
44
9.9.2
Launched
.
for
33
.
35
.
.
Spectrum
33
+90* Phasing
.
9.10.1 Plasma Current and Loop Voltage Windings
10.4.1
Typical Low Density Shot
10.4.2
Use of Aluminum Foil to Deflect Incident Beam
.
.
44
.
.
.
46
.
54
.
55
Radial Scans
12.2.1
N%%=3
Low
Density
+900 Phasing
.
.
66
12.2.2
N,, =5
Low
Density
+90
Phasing
.
.
66
12.2.3
N,, =3
High
Density
+900 Phasing
.
.
67
12.2.4
N4 =5
High
Density
+90* Phasing
.
.
67
NEl
Spectra
12.3.1
r/a=0.85 Low Density +90a Phasing
.
.
71
12.3.2
r/a=0.0
Low Density +90' Phasing
.
.
71
12.3.3
r/a=0.85 High Density +90* Phasing
.
.
72
-
6 -
(N, Spectra)
High Density +90* Phasing
12.3.4
r/a=0.0
12.3.5
r/a=0.85 Low Density
180* Phasing
73
12.3.6
r/a=0.0
Low Density
180* Phasing
73
12.4.1
Orientation Spectrum
.
.
.
76
12.6.1
Frequency Spectrum
.
.
.
79
12.6.2
Power Scan
.
.
.
-
80
12.6.3
Poloidal Scan
.
.
.
.
81
13.2.1
Geometry for Brambilla Spectrum Computation
.
84
13.3.1
Geometry for Ray Tracing
.
.
85
13.4.1
Power Map in Scattering Plane
.
.
89
13.4.2
Puncture Plots for +ve N,, Rays, Separated by
.
90
-
91
Passes
13.4.3
.
Puncture Plots for -ve N 5 Rays, Separated by
.
.
.
NO Spectrum and Spectral Orientation Diagram Near
Center
13.4.5
.
.
Passes
13.4.4
.
72
.
.
.
.
-
-
93
N,1 Spectrum and Spectral Orientation Diagram Near
Edge
.
.
.
-
-
94
.
.
95
13.4.6
Orientation Spectrum Near Edge
13.4.7
Evolution of Coherence
.
-
-
97
13.4.8
Radial Power Profile
.
.
.
98
14.01
Orientation Spectrum Near Center
.
.
102
14.02
N,Spectra
.
104
17.2.1
Non-Orthogonal Coordinates in Scattering Plane
17.2.2
Introduction of Orthogonal Coordinates in
for
Restricted
Orientations
Scattering Plane
17.2.3
k-Resolution of Scattering Volume
19.2.1
Mixer Test Setup
.
-
7 -
. 122
.
.
123
.
.
124
.
.
130
19.2.2
Mixer Noise Temperature
.
.
19.2.3
Mixer Conversion Loss
.
.
19.3.1
133
.
133
Setup for Antenna Pattern Measurement
.
134
19.3.2
Detail of Detector
. 135
19.3.3
Sample Horn Pattern
19.4.1
Geometry for CW Power Transmission Measurement . 136
20.1
Richards' Filter/Absorber Feedthrough
20.2
Absorber-Filled Feedthrough
20.3
6-1/2 Stage LC Filter Feedthrough
20.4
Filter Transmission Test Setup
21.2.1
Scattering Geometry Plot from SBATPL2
-
8 -
.
135
..
.
.
.
138
.
139
.
140
.
141
.
143
Section [6]
9.1.1
LIST
OF
TABLES
Versator II Plasma Parameters
.
12.1.1
List of Experiments
.
12.5.1
Comparison
.
+90* and -90*
Between
Scattered Power P
.
.
29
.
64
Phasing
at the Plasma Center
.
on
.
77
.
87
13.3.1
Plasma Parameters Used in Ray Tracing Code
14.1
Plasma
Parameters
Used
for
Calculating
Frequency Broadening due to Scattering of Lower
. 103
Hybrid Waves from Low Frequency Fluctuations
14.2
Estimate of Terms in Eqn 14.03
20.1
Measured Transmission of 6-1/2 Stage LC Filter . 141
-
9 -
.
.
.
.
105
Section [7]
NOTATION
a
minor radius of plasma
a
subscript denoting plasma edge
a,b,c
coefficients in lower hybrid dispersion relation
constants used in k-resolution calculation
a,b,c,d
b
wall radius (theoretical model)
b
subscript denoting vacuum vessel wall
c
speed of light
e
electron charge
e
subscript denoting electrons
A
e
unit vector
f
wave phase
f(r) radiation pattern of transmitting antenna
f
lower hybrid wave frequency (0.8 GHz)
g(E) radiation pattern of receiving antenna
i
subscript denoting ions
j
square root of -1, used in wave phase terms
k
Boltzmann's constant
k
wavevector
kr ke components of k in scattering plane
ki, k, components of k relative to total magnetic field B
k1
wavevector of incident beam
kg
wavevector of scattered beam
W
wavevector of wave responsible for scattering
1
path length
me
electron mass
-
10
-
n ne electron density
-1,i1e line average electron density
ne
fluctuating
wave)
electron density (as due to lower hybrid
o0)
subscript denoting plasma center
r
minor radius coordinate in scattering plane
r
radial unit vector
r
spatial coordinate in scattering volume
rm
radius of magnetic surface (
ro
classical electron radius
t
time
ti
retarded time to first order approximation
v
fluid velocity
ye
electron drift velocity
magnetic coordinate)
in scattering
x,yorthogonal coordinates
horizontal and vertical)
xI
coordinate along incident beam
xS
coordinate along scattered beam
A
z
unit toroidal vector
AR
effective area of receiving antenna
Aw
cross-sectional
normal to r
plane
(not
area of lower hybrid beam, measured
A,B,C,D,X constants in k-resolution calculation
B BT toroidal magnetic field
B
bandwidth
BR
receiver bandwidth
BW
bandwidth of lower hybrid waves
C(K) Fourier transform of antenna pattern overlap f(_r)g( )
-
11
-
C
transmission loss of receiving waveguide
E
electric field
E'
designates fields
wave
E0
electric field amplitude
ES
total scattered electric field
Es
scattered electric field due to single electron
F
electronics calibration factor (dB/Volt)
F2
for (artificial)
complex incident
dimensionless quantity relating wave density amplitude
to electric field amplitude
F 3 dimensionless quantity relating electric field
amplitude squared to wave power (Poynting flux)
G
preamplifier gain
H(kL) lower hybrid dispersion relation solution for k,,
Hg
total scattered magnetic field
HS,
scattered magnetic due to single electron
I, Ip plasma current
I (NI
1 ) lower hybrid wave power per unit area,
per unit launched power
per unit Na,,
II
inductively driven part of plasma current
IR
RF driven part of plasma current
J
geometric factor related to k-resolution of scattering
volume
L
inductance of plasma current
L
mixer conversion loss
N
refractive index
NI,
parallel refractive index of lower hybrid wave
P
power
P,S,D
plasma quantities in Stix' notation
-
12
-
PC
CW transmitted power with system aligned
PL
launched lower hybrid power
PS
measured scattered power (absolute units)
A
PS
measured scattered power (in
power)
R
plasma resistance
R
units of receiver noise
R
A
R
unit vector in R direction
R
vector from scattering volume to (far) field point
RR
distance from scattering volume to receiving antenna
RX
distance from scattering volume to transmitting antenna
Se
lower hybrid wave Poynting flux in direction e
SI
Poynting flux of incident beam at scattering volume
SR
Poynting flux of incident beam at receiving antenna
T
time interval for received scattered power
Te
electron temperature
T.
ion temperature
TN
signal noise temperature
TR
receiver noise temperature
V
recorded voltage with 0.8 GHz system off (emission +
noise)
VL
loop voltage
VN
recorded voltage corresponding to noise level
V
recorded voltage with 0.8 GHz system on (scattering +
emission + noise)
X
constant in k-resolution calculation
orientation angle between k, and r
-
13
-
calculation of scattering volume's
in
ai
angle appearing
k-resolution
Aw
frequency broadening
density fluctuations
Fo
permittivity of vacuum
0
angle coordinate in scattering plane
o
halfwidth of receiving antenna pattern in E plane;
subscripts x for transmitting antenna and H for H plane
e
scattering angle
n Ee'.
n
e
i
(HWHM)
of lower hybrid waves by
form factors for density and temperature profiles
T
retarded time
T
optical depth for scattering of lower hybrid waves by
density fluctuations
$(w) (scattered) spectral intensity
W
(angular) frequency
oce electron cyclotron frequency
Wci
ion cyclotron frequency
WI
incident beam frequency
pe electron plasma frequency
" . ion plasma frequency
oS
frequency of scattered wave
-
14
-
Section
A
INTRODUCTION
[ 8]
as
phenomenon of lower hybrid current drive in tokamaks,
current for equilibrium;
toroidal
(parallel filaments of
force
pinch
radially
the
balances
other)
attract
current
due
outward force
However,
inductively.
tokamaks to be inherently pulsed devices.
this
the possibility of CW tokamak operation.
the
(DC)
RF
thus opening
CW operation,
tremendously enhances the attractiveness of
of course,
each
restricts
In contrast,
driven currents may be sustained indefinitely,
up
to
inductively driven
cannot be sustained indefinitely;
currents
inward
the radially
Conventionally this toroidal current is
pressure gradient.
generated
a
Tokamaks depend
means of obtaining steady state operation.
on
the
of interest in recent years has been focused on
lot
the
tokamak as a fusion reactor.
The basic idea of lower hybrid RF current drive is that
one
launches 'slow' lower hybrid waves (phase velocity less than
the
speed of light) travelling in the direction of electron
waves interact with the plasma and
These
drift.
momentum
to resonant electrons (enhancing the tail
transfer
of
the
electron velocity distribution), thus driving current.
Lower
hybrid
[Fisch.78],
Japan
current drive was proposed by Fisch
and
in
first observed experimentally on JFT-2
Versator II
and
[Yamamoto.80
-
15
-
in
the
1978
in
US
simultaneously;
sustained with both inductive and RF drives
loop voltage VL =
E-dl around the torus, with no attendant
The governing equation is
drop in plasma current.
V
hybrid
current
whence
the
3
6
x
101-2
MIT.
at
C
Alcator
can
current
plasma
et
Bernabei
kA
of
experiments
sustained
solely
al
plasma
for
current
-
16
-
s
obtained:
of
sustainment
the
3.5
indeed,
and,
been
have
document
[Bernabei.82]
RF,
with
that
shown
have
results
state
steady
impressive
some
be
Numerous
and
Princeton
at
(PLT)
Torus
Large
most
experiments,
tokamak
major
of
number
Princeton
the
notably
165
a
on
performed
were
experiments
drive
current
hybrid
lower
Subsequently
around
limits
density.
line-average
cr
experiments
These
density
showed
--
densities
high
limit.
density
GHz)
0.8
around
(both
a
of
concept
lower
that
observed
at
work
to
current
observed
also
failed
drive
tail
low-resistivity
experiments
early
These
increases.
the
that
assumes
experiments
Versator
The
electrons.)
the
of
external)
8.1
by
carried
is
resistance,
plasma
plus
-
components
driven
(Equation
current
driven
RF
8.1
effective
the
distribution.
current
plasma
R
(internal
inductance
the
is
L
and
I
inductively
and
is
R
~
+IR)
L(I
-
dt[
RF
the
current,
plasma
the
of
+
R
=I
L =I
are
I
and
IR
where
in
current drive effect was inferred from the drop
RF
the
was
current
experiments,
initial
In
[Luckhardt.81].
on
PLT;
the
time
limitation
RF
was due to heating of a ferrite isolator in
transmission system.
Experiments on FT
the
(Frascati)
at
2.45 GHz [Alladio.82] and Alcator C at 4.6 GHz [Porkolab.84a]
4x 10 1 3 cm-3
succeeded in driving 'flat-top' currents at
14cm-3
(line-average) and 1x 10
respectively, suggesting that
the current drive density limit scales with frequency.
has
now
been
a
on
Versator II
density limit.
(The 0.8 GHz system had
a
of 6x 101 2 cm-3 line-average [Luckhardt.82];
limit
system
the
shown
a new 2.45 GHz experiment has yet
where
[Mayberry.85],
find
conclusively
has demonstrated current drive at
experiment
is
This
limited
by
density
the
new
2.5 x10 1 3 cm- 3
available
power
to
and
-the
operating regime of the tokamak).
Aside from sustainment of the plasma current,
current
drive
has
up
and
ramping
demonstrated
capability
up
the
plasma
current.
saving in engineering.
0.3 s.
both
drive,
in
drive
a
substantial
Both Alcator C [Takase.85-b] and PLT
have demonstrated the ability
energy
1983
opening up the possibility of
increase the plasma current with RF drive;
magnetic
PLT
a tokamak with no inductive drive,
[Jobes.85]
for
the formation of 100 kA plasmas with RF
alone [Motley.84, Jobes.84] -building
hybrid
the plasma in the absence of inductive
starting
for
demonstrated the
lower
to
significantly
on Alcator C the
content of a 100 kA plasma was doubled
The "ramp-up" efficiencies of both experiments
in
(ie
the efficiency with which delivered RF power is converted to
-
17
-
stored magnetic energy) are in
excellent agreement with
theory [Karney.84].
A suitable review of lower hybrid experiments can be found
in
[Porkolab.84-b].
Despite
the progress
and
successes
experimental and theoretical,
in
the
field,
both
much remains to be learnt.
Between wave launching and wave absorption, a number of
The waves propagate in an
processes come into play.
inhomogeneous medium undergoing refraction and bounces; the
(at different initial
effects on different waves
locations and having different wavevectors)
varied.
spatial
can be quite
Toroidal effects are responsible for changes in the
spectrum of the waves.
Waves are scattered by density
fluctuations, causing spectral broadening.
and wave absorption are also present.
Mode conversion
Thus wave propagation
is a complicated process, and not very well understood.
While theories exist for various facets of the problem,
hybrid wave
on lower
experimental data
propagation in
contemporary devices is meager.
Current drive experiments are predominantly analyzed from
global
and
measurements
(current,
specific diagnostics
understanding
of
lower
are
loop voltage);
more detailed
necessary to
hybrid wave physics.
improve
the
Spatially
resolved X-ray measurements provide some insight into 'where
-
18
-
is the power going ?',
measurements,
RF
Nonetheless
the
propagation
is
as do density and temperature profile
probes
diagnostic
without
electromagnetic waves.
strength,
spatial
a
few
other
of choice
doubt
for
coherent
diagnostics.
studying
wave
scattering
of
A scattering diagnostic can look for
plasma
the
in
waves
the
and
distribution
and
their
measure
and
directly,
both
frequency
and
wavenumber spectra.
Coherent scattering diagnostics have been used to detect and
study
lower
Alcator A
hybrid
waves
on
other
[Slusher.82],
tokamaks,
Alcator C
such
as
[Watterson.85,
Takase.85-a] and WEGA [Ichtchenko.83], as well as previously
on
Versator II
[Richards.811.
The
Alcator
results
are
perhaps the most complete to date; Watterson et al have used
NH
a CO 2 laser scattering system to measure power,
and
radial profiles,
and have also studied the
spectra
parametric
decay of the lower hybrid waves and ion cyclotron sidebands.
The
WEGA
experiment
operated at 136 GHz,
geometry inside the vacuum chamber.
is
using
primarily
turbulence).
offers
It
to
is
study
low
a 139 GHz
frequency
microwave
of
Portions
experiment
this work have been
published [Rohatgi.85a].
-
19
-
Versator
drift
more geometric flexibility than the other
experiments.
fixed
The present experiment
an upgrade of Richards' previous experiment on
(used
a
wave
and
published
previously
Our
microwave
Interaction
scattering
Oscillator
Waveguides
experiment uses a
to
generate
power
are used to transmit the power to
7 W
Extended
at
139 GHz.
the
tokamak,
where a narrow beam is launched into the plasma.
oscillate in this radiation field;
An
electron
causing
some power is scattered.
density wave acts like a diffraction
coherent
scattering in directions
condition
kg = k1
grating,
satisfying
-4, -b-A
Bragg
Electrons
the
-A.
+ kW,
where
k1 and
kS
are
the
wavevectors of the incident and scattered radiation,
is
the wavevector of the electron density wave
for the scattering (see Fig 8.1).
is
also
shifted
in
frequency by
electron density wave.
by
a
and kW
responsible
The scattered
the
radiation
of
frequency
the
The scattered radiation is received
suitably positioned antenna,
and mixed down
to
the
intermediate frequency (IF) in a standard homodyne detection
scheme.
analyzer.
The
A
IF
is
signal
detected
using
a
spectrum
distinguishing feature of this experiment
is
the use of movable mirrors on both the transmitting (for the
Fig 8.1 SCATTERING WAVEVECTORS
Scattered
beam
incident
an
shows
(a)
impinging on an electron plasma.
The wave in the electrons results
in a scattered beam.
(b) The
relation between the wavevectors of
the
(k 1 ) ,
beam
incident
the
scattered
beam
(kg)
and
the
Beam
k
-
kI
-
Electrons
Incident
Beam
is
(kW)
density wave
electron
shown, as is the scattering.angle
(a)
(b)
kw
and
a
wave
with
that
6S.
[Note
-W;
and
is identical to one with ,-k
frequency w
consequently scattered power may exist with ks= r-kw too.]
-
20
-
incident
fair
beam) and receiving antennae,
which affords us
a
amount of flexibility in selecting scattering volumes.
(Scattering
radiation
volumes
patterns
are
of
defined by
the
the
overlap
transmitting
and
of
the
receiving
antennae.)
Before discussing the experiments we have performed,
to
necessary
a few words about
say
system
the
Versator II to launch lower hybrid waves.
consists
of
independent
4
adjacent
phase
open-mouthed
is
used
on
The antenna used
waveguides
The waveguides are
controls.
it
with
suitably
phased in order to produce an electric field pattern at
face
of
the antenna that couples to slow
less
than
plasma.
the
parallel to
the
during
wave propagation.
these
is
not conserved;
propagation
affects
N11 = c k1, / w ;
zeroth
and
the
NH has a poloidal component which
interaction
plasma.)
-
order
azimuthal
the consequent change in N11 during
the
or
by toroidal symmetry, or
cylindrical geometry because of axial
In a tokamak,
k11 ,
(N,, is conserved exactly if
magnetic field is purely toroidal,
symmetry.
spectrum
field,
quantities is conserved to
of
a
magnetic
the parallel refractive index
either
in
the
in
The waves are characterized by the component of
wavevector
equivalently
velocity
speed of light) lower hybrid waves
The launched power typically has a broad
in k-space.
the
(phase
the
21
-
between
waves
wave
and
With this setup we have sought to address the question of
propagation of externally launched 0.8 GHz waves in Versator
plasmas during current drive.
Specifically we have measured
the dependence of lower hybrid wave power on both radius and
(as well as on several other quantities.)
Nil
Our results
indicate the presence of a spatially defined resonance cone
near the edge of the plasma,
with very directional power
flow
agreement
that
modelling.
is
is
in
excellent
The N11 spectrum for the +900
with
theoretical
waveguide
in good agreement with the computed spectrum.
seen
to
reach
the
center
of
the
plasma.
phasing
Power is
A special
experiment has been conducted to look for wave absorption
during current drive; evidence of absorption is
seen.
The
measured frequency spectrum of the lower hybrid waves is
consistent with theory.
Some data has been taken at
densities above the current drive density limit; no dramatic
difference is seen.
The outline of this thesis is as follows.
The experimental
setup and procedure are described in Sections 9 and 10.
(A
single set of numbers is used serially to denote the various
sections
into
which
this
thesis
introduction is already Section 8.)
data analysis.
Section 12.
is
divided;
this
Section 11 covers the
The experimental results are presented in
Theoretical modelling was performed to compare
with the experimental results; the modelling and comparison
with experiment
are presented
-
22
-
in Sections
13 and 14
respectively.
appendices
aspects
15 is
Section
follow the references
of
measurements,
the
calculation,
hardware details,
the
conclusion.
(Section 16);
these cover
microwave
calibration
and computer programs,
are numbered as Appendices 17 through 21.
are suitably referenced from the main text.
-
23
-
Several
and
The appendices
Section [8A]
This
LOWER HYBRID WAVES
section
hybrid
Lower
provides a background on lower hybrid
waves
magnetized
plasma.
frequency
range
The name is applied to
just
above
i+ (Wce ci)
frequency wLH
2
normal
one of many
are
the
of
modes
waves
hybrid
in
the
resonant
w ci«W pi«wpe~ce).
The
cold
dispersion relation in this frequency range has
plasma
branches,
a
(We are assuming the typical
.
scaling for tokamak plasmas,
lower
waves.
two
one being a slow wave characterized by refractive
index N>>1 and the other a 'fast' wave with smaller N.
The
term
the
lower
former.
are
hybrid
The
driven
wave is usually used to
refer
name arises from the fact that the
both
by the electric field
and
the
to
electrons
magnetic
field.
-
-
'Lower
mn
dv
dt
=
q(
+vxB
E1 +1
)
0
8A.1
hybrid' refers to the mode where the
driving
-
terms
have opposite sign, and is the lower frequency solution; the
other
mode
frequencies
is referred to as 'upper hybrid' and exists
above
the
electron
plasma
and
at
cyclotron
frequencies.
As a consequence of large N, the magnetic field perturbation
associated with these waves is small (cB1 <<E), the magnetic
energy content of the waves is small,
approximation
may be used in the
-
24
-
and the electrostatic
analysis.
Electrostatic
analysis
yields the standard
Trivelpiece-Gould
dispersion
relation,
2
S.COS
2
2 .2Wsin
6
-
2 2
2
-
-c
c
j
where the summation
8A.2
is over the species e (electron) and i
and e is the angle between the wavevector k and
(ion),
-
the
Using the assumed scaling (above), this can
magnetic field.
be rewritten
-
-
-
-
-
-
-
-
-
-
-
-
Notice
-.
p2
-
-
-
-
-
i=
pe
-
-
-
-
-
-
-
-
-
- m .-
-
-
-
-
ce
-
that for cos 2 e~1,
-
-
-
---
-
-
22
i
. 2 /w 2 )
+(o 2 sin
-1
-
-
2
(1 + --Icos 6)
me
-
-
WoWpe.
-
-
-
-
-
-
---
8A.3
8A .
-
Since our interest is in
waves with o<<wpe, we may use sin 26e'1 and cos 2 e-(k /k ) 2 <<1,
whence
-
2
_
_
2
22
p.
1+ W
pe
2pi
/W
+im.+-k-
e k4
ce
8A.4
is the standard electrostatic lower hybrid
This
dispersion
relation.
The size of electromagnetic corrections is approximately 10%
in
k,
or
k.L;
we
do in
fact
use
the
dispersion relation in all our analysis -in
Appendix 18.
electromagnetic
this is discussed
Nonetheless the electrostatic
dispersion
relation is reasonably accurate, easier to grasp, and may be
used to illustrate two of the interesting characteristics of
lower hybrid waves.
-
25
-
It
is worthwhile to indicate the relative magnitudes of the
quantities
in
which
our
we see that the quantity in
approximately
wavevector
Typically for
experiments,
wpi/272O.5 GHz, wpe/27~ 20 GHz, wce/27Z35 GHz,
w/27=0.8 GHz,
from
Eqn 8A.4.
is
4.
mi/me=1 8 3 6 ,
Since
brackets
ks/kjj=25,
indeed nearly perpendicular to the
must
and
be
the
magnetic
field.
The
two interesting characteristics of lower
mentioned
(2)
the
hybrid
waves
and
above are (1) propagation in resonance cones
fact
that the group velocity of
nearly perpendicular to the wavevector.
consequence of the fact that,
these
waves
is
Both of these are a
at least in the electrostatic
approximation, the dispersion relation is independent of the
magnitude
of the wavevector k.
If the components of k are
(kek'4k) in spherical polar coordinates (with the
field as axis),
then w=w(ek) and
__k)
= k-
Sk-v
~
We
9
see
nearly
-0
k
3k
perpendicular
toroidal
W(ek
)=k
8A.5
have
that although lower hybrid waves
predominantly
to
toroidal.
components
B,
It
of v
the
is
wave
easy
to
a
show
that
and k are in the same
-
26
-
is
the
direction
This
wave propagating radially inwards has a k
radially outward.
-
wavevectors
propagation
and that the poloidal components are opposite.
that
magnetic
means
pointing
To
show resonance cone propagation,
same
plane
(say
with
ky=0).
consider waves in
Then
the
ratio
of
the
the
components of the group velocity
v
...
-
gti
gx
Dw/3k
k
_____x
Bw/3k X
8A.6
is determined by the dispersion relation and
which
is
same
for all waves,
with
different wavenumbers (and in general different
regardless of wavenumber.
velocities) follow the same trajectories.
-
the
Thus waves
group
This is resonance
we have already seen that the propagation
cone propagation;
is predominantly toroidal.
Further
elsewhere
discussion
of
lower
hybrid
waves
is
contained
Lower hybrid waves were already
in this thesis.
briefly touched on in the Introduction (p.21).
A discussion
of how the waves are launched in the plasma may be found
Section
[9.9].
The
electromagnetic
analysis
transport are both covered in Appendix [181.
-
27
-
and
in
power
Section [9]
[9.1]
This
EXPERIMENTAL
SETUP
Outline
section
setup
A
system
in
([9.3]
-
[9.2]
[9.3]
EIO Source
[9.4]
Transmitting/Receiving Antennae
[9.5]
Wedge Reflector
[9.6]
Microwave Receiver
[9.7]
Shielding
[9.8]
Electronics
[9.9]
Lower Hybrid System
[9.10]
Other diagnostics
the
of
is followed by more detailed
experimental
the
scattering
experiment.
have
[Richards.78,81;
sub-sections
Some procedures are mentioned, where they
to the setting up of the
the
operation
General Description
contains a description
[9.8]).
running
[9.2]
general description of the microwave
more
relate
Outline
for the detection of lower hybrid waves in
used
plasma.
[9.1]
and
The Versator II tokamak
adequately
been
than
experiment
Stone.79]
and
discussed
are
not
to
its
elsewhere
discussed
here.
Table 9.1.1 shows typical parameters of Versator II plasmas.
Versator
ports and diagnostics are shown in Fig 9.1.1.
lower
hybrid
system
is discussed
Other
diagnostics that bear on the present experiments
covered in [9.10].
-
28
-
in
sub-section
The
[9.9].
are
Table 9.1.1
VERSATOR II PLASMA PARAMETERS
Quantity
Symbol
Value
Major Radius
Minor Radius
R
a
40.5 cm
13.0 cm
Toroidal Field
BT
0.8 -
Plasma Current
Ip
20 -
Electron Density
Electron Temperature
ie
2 x 1012 - 3 x 1013 cm-3
Te
200 -
500 eV
Ion Temperature
Ti
100 -
180 eV
Shot Duration
1.5 T
60 kA
30 ms typ.
RF Systems:
Frequency
Max Power
Max Pulse Length
(1)
0.8 GHz
(2)
2.45 GHz
100 kW
20 ms
100 kW
40 ms
Fig 9.1.1 VERSATOR
600MHz
;
PORT ALLOCATION
Top view of Versator II
showing the microwave
the
scattering port,
lower
hybrid
(LH)
RF
ION GAUGE
other
and
ports,
and
equipment
The
diagnostics.
scattering
microwave
port
is
450
p
EMISS
PumpaRGA
RUBYLASER
toroidally
from the 0.8 GHz
port.
LASER DUMP
LHRF
To
GAS PUFFING
HARD
ANO
CHARGE
X-RAY
0
10cm
-
29
-
[9.2]
An
the
General Description
experimental schematic is shown in Fig 9.2.1.
equipment
Much
used for this experiment was inherited
of
from
previous microwave scattering experiments on the Versator II
tokamak
[Richards.81].
An extended interaction
oscillator
(EIO) made by Varian is used as a 7 W CW source at
Most
of
tokamak,
the power is transmitted through waveguide to
where a horn and lens are used to launch a
(approx 4.5* FWHM) incident beam.
off
an
139 GHz.
beam
is
received
by
similar
vessel.
The
rotation in
the poloidal plane and translation along the ports on
are mounted.
The
apparatus.
adjustable mirrors have two degrees of freedom:
they
narrow
The incident beam bounces
adjustable mirror and into the vacuum
scattered
the
which
This system permits complete flexibility
COMPUTER
SCOPE
R F SHIELDED CABINE T
APLI FIER
FIL
AMPLIFIER
TER
RECEIVING
ANTENNA
800MHz
SPECTRUM
ANALY ZER
A
USTABLE
MIXERL
PREAMP
WE DGE
REFLECTOR
TOR
MON I9
DIOD E
PLASM
VAR.
ATTEN.
L-V
POWER
SUPPLIESANE
EIO
WAVEGUIDE
TAN
TUNER
N
TT
A
G
Fig 9.2.1 EXPERIMENTAL SCHEMATIC
-
30
-
in choosing scattering geometry
(location of scattering
volume, scattering angle, and poloidal orientation) limited
only by port access. A wedge shaped reflector inside the
vacuum vessel is used to deflect unwanted microwave power
and reduce stray signal.
The power scattered by the 0.8 GHz lower hybrid waves is
139+0.8 GHz.
The received scattered power is
at
transmitted by
waveguide back to the main cabinet, where it is mixed with a
local
oscillator
signal
forward power line),
(This is
signal
(taken
by
a
20 dB
tap
off
the
to produce an IF signal at 0.8 GHz.
the standard homodyne detection method.) This IF
is
amplified,
analyzer which is
and
then
detected
by
set to a fixed frequency
a spectrum
(0.8 GHz)
and
The purpose of the amplifier is
used as a tuned detector.
to boost the signal power above the spectrum analyzer noise
level.
This receiver
has a noise temperature of 6600 K,
which corresponds to a sensitivity of about 3x10-1
(this
bandwidth of 300 kHz
bandwidth
experiments except frequencyspectrum
detected signal
is
4
W in a
used for all
measurements).
(output of the spectrum analyzer) is
The
driven
by an amplifier through microwave filters and a triax line
over to the control room, where it is smoothed and then
stored in our computer.
[9.3]
EIO Source
The 139 GHz source used in this experiment is a Varian
-
31
-
VKT 2438 El Extended Interaction Oscillator.
linear
The EIO is
beam tube which offers a significant advantage
conventional
klystrons)
millimeter
wave
sources
(such
as
over
reflex
in that the beam power is not dissipated by
delicate
RF
structure
within
the
tube.
sustained high power operation is feasible.
a
the
Consequently,
Our model is
a
water-cooled tube rated at 20 W nominal, although it is used
at
a more modest level of 7 W in order to prolong the
tube
lifetime.
as well as
The EIO requires 3 power supplies for operation,
A Hipotronics 10 kV
protection against high-voltage faults.
300 mA
regulated
supply;
smaller
operation
at
supply
is used
for
anode
supplies are used for the
5 kV,
cathode
the
(typical
< 1 mA) and filament (typical
1 A
at
anode power supply is used to switch the tube on
The
6 V).
power
The power circuit is shown in Fig 9.3.1. Also, Fig
and off.
9.3.2 shows the cooling system for the tube.
An
important consideration is how to get the
into
power
through
a
transmission
with
10 kV
iron-loaded
eventually
that
worked
since any wire
the RF shielded cabinet,
hole
in
line.
the
cabinet
looks
like
What is needed is a
standoff.
Our experiences
compounds
were
not
voltage
high
a
microwave
with
entirely
going
co-axial
filter
graphite- and
satisfactory;
we designed and built multistage LC-type filters
very well.
These are
-
32
-
further
described
in
RF Shielded Cabinet
1.
G
u
Cathode
Power
Supply
.0
.0
u
kLine
1.v50WT
iExternal
Interlock
to
Shielded
Cooling System
.Anode
Power
Supply
Filter
-al
I--
Bundle
Voltage Filte
-Hig
Heater
12V DC from
control room
for turn on
12V relay
Local
Switchh
P.S.
F
Interlock
I
EO
truh
RF
Fig 9.3.1 EIO POWER CIRCUIT
Note that the ground (= HV return) connection is through t1 e
line cord supplying AC power to the RF shielded cabinet.
to Cathode Power Supply
Pump
Heat Exchanger
RF Shielded Cabinet
Fig 9.3.2 EIO COOLING SYSTEM
The two stage cooling system has a tap water primary and a
distilled water secondary coupled through a heat exchanger.
-
33
-
Appendix [20].
By
and large our EIO has served us well.
the tube gave some difficulty turning on;
A couple of times
we found in
cases
that running the tube for a couple of hours with
anode
voltage
(well below turn-on,
typical
beam
such
low
current
about 15-20 mA) was quite effective.
Transmitting/Receiving Antennae
[9.4]
Gain
standard
horns with 25 dB gain are
rectangular horns flared in both planes.
the
horns
Quartz
at
[CRC.79]
are
As mentioned above
them.
and
good
were
for
chosen
availability
transmission properties.
25 GHz
These
have focussing lenses mounted in front of
lenses
microwave
used.
[von
and
Hippel.54]
The refractive indices
at
frequencies
optical
focal
were used to estimate a desirable (optical)
length. (Suitable information at 140 GHz was not available.)
The
gain patterns of the horn + lens combination have
measured;
been
this measurement is further described in Appendix
[19.3].
The
adjustable
scattered
assemblies.
on
the
used to reflect the
mirrors
beams are simple aluminum mirrors
One is shown in Fig 9.4.1.
incident
on
and
plexiglass
A protractor scale
the assembly permits the mirror angle to be set to 0.50;
position is held by friction at the pivot.
The
assemblies bolt onto a plexiglass track (which has
-
34
-
mirror
threaded
-
35 -
holes) that is mounted on the tokamak port. The position may
be set to 0.5".
The
overlap
of the incident and
scattered
beam
patterns
(which
are reflected by the mirrors) defines the scattering
volume,
ie the volume from which electron density waves are
detected.
Some of the scattering volumes possible with this
setup are shown in Fig 9.4.2.
volumes are not small;
this
experiment.
As is evident, the scattering
spatial resolution is a problem with
Typical scattering volumes
are
diamond
shaped, with the long diagonal vertical and ~10 cm long; the
short
diagonal is typically ~5 cm.
sizes
vary
scattering
from one scattering volume
volume
scale lengths,
somewhat
to
the
volume,
a
given
spread
in
dimensions are comparable to the
the
than
comparisons
spread in density
across
scattering angle also
values
Nonetheless
The
plasma
of
parallel
scattering
the
plasma
between
scattering
parameters
computed
at
the
vary
refractive
volumes
scattering
corresponds
are
cross-section,
different regions of
different scattering angles may be made.
volume;
another.)
over the plasma volume (especially near the edge).
of
values
the exact
consequently the plasma parameters may
Because
smaller
(Of course,
index
still
and
the
a
(Nil).
somewhat
meaningful
plasma
and
Values quoted for
in this thesis always refer
the nominal center of
to
the
to
the
scattering
the nominal center is the point of intersection of
the central rays of the incident and scattered beams.
-
36
-
The entire geometry is aligned using a CW beam, by adjusting
the
horn
and
mirror
positions
until
maximum
power
is
received
at
[19.4]).
The receiving waveguide is attached to the machine
by
the end of the receiving
waveguide
(Appendix
a 2-D sliding dovetail bracket (Fig 9.4.3) to facilitate
this
adjustment.
system
are
copper
losses,
Waveguide
transmission losses
approximately 5 dB:
in addition
there are losses at waveguide
for
to
this
waveguide
flanges
and
losses associated with transitions to and from the overmoded
waveguide.
Fig 9.4.3 SLIDING
DOVETAIL BRACKET
ciamp
to
Tokamak
Allen lea
Set Screws
--
M'Horn
A
cy
Waveguide Clamp
-
37
-
+ Lens
[9.5]
Wedge Reflector
A wedge reflector,
vacuum
stray
shown in Fig 9.5.1,
is installed in the
vessel in order to minimize problems associated with
multiply reflected signal getting into the
receiver.
The idea is that a multiply reflected beam will impinge once
on
the wedge (located on the inside wall) and be
toroidally away from the scattering port.
of
deflected
A salient feature
the design is the absence of electrical contact
various pieces and the vacuum vessel.
eliminate
between
This was necessary to
eddy currents and associated forces
that
ruined
two previous assemblies.
Insulating
Block Macor)
Bushing
(S.S.
Horizontal
Member (S.S.)
Vertical
Member (S.S.)
(b)
(a)
Fig 9.5.1 WEDGE REFLECTOR
(a) shows wedge reflector and frame as assembled inside the
tokamak. (b) shows corner detail.
-
38
-
[9.6]
Microwave Receiver
The
microwave receiver comprises a mixer,
and
a
mixer
spectrum analyzer and is shown in
is an Alpha/TRG model F9100.
a
pre-amplifier
Fig
9.6.1.
The
Local oscillator drive
at the 3 mW level is provided by a 20 dB tap off the forward
power line,
diode
adjusted with a variable attenuator.
is used to monitor the L.O.
drive level;
serves as a convenient power monitor.
at
low-noise
MITEQ
boosts
This
pre-amplifier with a 35 dB
the signal above the spectrum
also
output
(10-1000 MHz)
nominal
gain.
analyzer
noise
The spectrum analyzer (Tektronix 7L12) is used as
level.
fixed
this
The mixer IF
is fed directly into a broadband
0.8 GHz
A crystal
frequency detector,
with usually 300 kHz
a
bandwidth.
Owing to the wide dynamic variation of the scattered signal,
10 dB/div
the
Care
log scale on the spectrum analyzer is
taken to protect the spectrum analyzer with
is
block and a DC short on the RF input.
mixer
used.
a
Calibrations of
DC
the
and preamplifier are covered in Appendices [19.21 and
[19.5] respectively.
It
is worth pointing out that the receiver is sensitive
suitably polarized radiation at 139+0.8 GHz,
scattered
the plasma.
noise,
it
and aside from
power there is also some background emission from
Thus the detected signal has three components:
and scattered signal.
plasma emission,
is the plasma emission and not the noise
limits
to
the detection sensitivity.
-
39
-
In practice
which
usually
The plasma emission
is
Fig 9.6.1 MICROWAVE RECEIVER (disassembled view)
-
40
-
tail
be 4-5th harmonic cyclotron emission from
to
thought
(ie energetic) electrons.
Shielding
[9.7]
Excellent shielding is necessary for this experiment because
we are trying to measure extremely weak (~10-1 3 W) signals at
the
same time as we are pumping ~50 kW of power at the same
Shielding also serves to isolate
frequency into the plasma.
the
noise
electromagnetic
from the substantial
apparatus
associated with a tokamak discharge.
The entire microwave system is housed in a RF-tight cabinet,
with
finger-stock along the door
Power
inside.
are
all
the
lines going in and signal lines coming
out
filtered.
This
box
is
good
preamp,
are
housed
holes
60+ dB
namely the mixer
in
along with their batteries
second shielded box within the first.
(Fig
about
for
The most sensitive components,
isolation.
and
sheets of microwave absorbing foam on
and
hinge,
strips
a double layer of aluminum foil along
along the door frame,
the
absorber
joints,
9.6.1) has a 32-screw lid,
box
This small brass
and 3 ports.
a
tubular
Two
are for turning the devices on/off and for a battery-
status LED indicator. These are 'safe' because the tubes are
cut-off at 0.8 GHz. The third port is for the output signal.
Unfortunately
that
we
filtered.
are
the
preamp output is at the
trying
to
shield
against,
same
and
frequency
cannot
Instead there is a 6 dB attenuator on this
-
41
-
be
port.
Since the preamp output noise level is still higher than the
spectrum
analyzer
adversely
noise level,
affect
sensitivity.
The
the
this attenuator
signal
to
noise
ratio
does
not
or
the
shielding described above is adequate
to
provide a clean signal, free from pickup.
[9.81
The
Electronics
detected
analyzer
scattered
goes
power
signal
through a simple
from
amplifier,
the
spectrum
shown
in
Fig
9.8.1, whose purpose is to provide a low impedance signal to
drive
a microwave filter and 75' triax cable,
isolate
and also
the control room and shielded cabinet grounds.
to
The
amplifier is grounded at the control room through the middle
triax conductor.
shielded
The triax outer shield is grounded at
cabinet.
In
the
control room
the
I
RF SHIELDED CABINET
10k
nput From
I
CONTROL ROOM
n
0
LF
10k
goes
Filter
Feedthroughs
10k14N
Spectrum
aly+351
I
signal
the
31'Cotti1N
4148
-:~b10k
Cainet
75'1 triax
390
3906
2k
Ground
J-
BNC out
I
Cabinet
Ground
-
.47
*
Ou
-12
Ou
0 +12
Floating
Power
Supply
Fig 9.8.1 SIGNAL AMPLIFIER AND TRANSMISSION LINE
-
42
-
Contraol
Room
Ground
through
a
boxcar
integrator set up as a
filter with a 0.1 ms time constant,
signal
is
computer
displayed
via
integrator
analyzer
a
also
10-bit
low-pass
typically. The smoothed
on a scope and
12.8 kHz
simple
also
goes
digitizer.
into
The
compensates the DC offset of the
boxcar
spectrum
and amplifier so as to make efficient use
digitizer's
+5
from
calibrated
Volt
the
input
range.
spectrum
The
analyzer
our
of
electronics
is
the
to
through
the
computer, 4.60 dB/Volt.
[9.9]
Lower Hybrid System
A single 150 kW Varian klystron is used to power the 0.8 GHz
lower hybrid RF system on Versator.
fundamental
is
grill,
through
mode waveguides,
used
An array of 4
adjacent
commonly called a 4 waveguide
as an antenna.
The
fed
are
waveguides
power splitters with independent phase controls for
each line.
Fig 9.9.1 shows the antenna,
together with the waves in the
4 waveguides for the case of +900 relative waveguide phasing
(waveguide
2 is 90* in phase ahead of waveguide 1,
so
The field pattern at the face of the antenna is shown
on).
for 4 successive time points a quarter period apart;
seen
and
it
is
that the field pattern appears to move across the face
of the antenna from right to left.
array
(phase
In this way, the phased
of waveguides is able to couple power to
velocity
less than the speed of
-
43
-
light)
slow
waves
travelling
Fig 9.9.1 LAUNCHING
LOWER HYBRID WAVES
Top View
A top view of the
tokamak
and
the
hybrid
lower
launching antenna is
shown. The waves in
each waveguide are
shown for the case
of
+900
e
t=3T/4
t=T/2
relative
waveguide
phasing.
The field pattern at
the
antenna
shown
at
period
intervals.
shown
face is
quarter
(T/4)
Also
are
4 Waveguide
Grill
1
the
2
3
4
directions
of
the
plasma current-I,
the electron drift ye and
magnetic field B.
the
toroidal
direction.
The
component of the wavevector of the launched
waves
is to some extent determined by the wavenumber of the
field
preferentially
toroidal
pattern
in
the
electron
drift
moving across the antenna face,
broad spectrum of waves is launched.
shown,
30%
but in practice
a
(In fact for the case
of the power is coupled to waves travelling from
0.30
Fig
9.9.2
SPECTRUM
LAUNCHED
FOR
-
+900
PHASING
0.20
This
spectrum
is
computed as described
in Section [13.2].
0
0
4
-0-10
0
0.00
-15
-10
-5
0
5
Parallel Refractive Index
-
44
-
10
NO
15
left to right.
be
seen
in
launches
The computed spectrum of waves launched may
Fig 9.9.2.)
waves
direction,
is
The
+90*
preferentially
associated
with
in
the
current
(The 180* phasing,
phasing is not.
phasing,
because
electron
drive;
it
drift
the
with a symmetric
-90*
wave
and higher wavenumbers is associated with electron
spectrum
heating.)
It is conventional to speak in terms of the
index
refractive
N = c k / w
,
where
and
k
are
w
wave
the
wavenumber and (angular) frequency of the lower hybrid wave.
The
subscripts , and I
components
the
are used to denote
(as in NU or k,)
parallel
and
to
perpendicular
the
(predominantly toroidal) magnetic field.
Other Diagnostics
[9.10]
The
loop
primary
(utility) diagnostics are the plasma
voltage,
In
monitor.
density interferometer and
the
addition,
second
current,
in/out
harmonic
position
cyclotron
(2wce) diagnostic provides valuable information on
emission
plasma emission.
The plasma current is measured by a Rogowski coil encircling
the
plasma
voltage
across
derivative
as shown
cross-section
of
this
the
coil
is
encircled
in
proportional
(the
loops
at the corners of the vacuum
-
45
-
The
the
time
signal
is
Figure 9.10.1 also
the toroidal loops used to measure the
4
9.10.1.
to
the
current;
integrated to yield the plasma current.
shows
Fig
loop
voltage
vessel
cross-
section are in series).
Fig
9.10.1 PLASMA CURRENT
AND
LOOP
WINDINGS
The
VOLTAGE
return
COIL
conductor
of
,.-Rogowski
the Rogowski coil is fed
back through the middle of
Coil
for Plasma
Current
the coil.
Diagnostic
Vacuum Vesse
One of 4 turns of
Loop Voltage Diagnostic
(series wound)
The
density
is measured by a
80 GHz
interferometer.
An
O mode beam is launched from the bottom of the machine;
the
transmitted beam is received at the top.
the
transmitted
sampling
rate.
The phase shift of
beam is measured modulo 27
This
at
a
phase shift is proportional
100 kHz
to
the
electron density averaged over the line of propagation.
The
calibration
constant for our instrument
(line average) per 2r phase shift.
is
2.26 x10 1 2 cm-3
(A phase shift of 2r is
commonly known as a fringe.)
The
in/out position monitor consists of two sets of
coils,
each oriented to measure the poloidal magnetic field, one on
the
inside
difference
signal
of
of
the machine and one on
the two signals upon
proportional
to
the
displacement
46 -
The
outside.
integration
current column from the geometric center.
-
the
of
yields
the
a
plasma
Our
second
harmonic
a
cyclotron
emission
horn antenna feeding
consists
of
receiver
[McDermott.84].
a
This radiation
(2 wce)
71 GHz
detector
heterodyne
comes
primarily
from electrons with substantial perpendicular energies,
Its usefulness for
provides information on tail electrons.
the
that
microwave
the
2 wce
and
scattering experiments stems from
the
signal correlates quite well with the
fact
plasma
emission seen by the receiver of the scattering system, thus
providing
an
monitor
indirect
emission.
-
47 -
of
the
139 GHz
plasma
Section
Outline
[10.1]
[10.1]
Outline
[10.2]
Setting Up Equipment
[10.3]
Planning Datapoints
[10.4]
Running the Experiment
[10.5]
Shutting Down
Setting Up Equipment
[10.2]
Three
EXPERIMENTAL PROCEDURE
[10]
are
systems
experiment --
required
to be
the 0.8 GHz RF System,
the tokamak,
this
for
operational
and
the
139 GHz scattering system; all require some setting up.
Setting
the
up
the
tokamak involves (1) keeping
machine
clean between runs (2) turning on various power supplies and
the
keeping
clean:
machine
gettering.
titanium
(3) tuning
discharge
cleaning
The latter introduces changing
and wall conditions on a 1 - 2 hour timescale,
In
run,
consistent
retuning
the
on
conditions.
With discharge cleaning prior to
hand,
other
quality
and
plasma
gradual increase of the ohmic heating drive
particular,
is necessary during a run.
a
and
and requires
retuning in order to maintain plasma
continual
the
Two strategies are in use on Versator
machine during a run.
for
before a run and
immediately
diagnostics
we
were
shots for several
no increase in the ohmic
-
48
-
hours
maintain
to
able
with
heating
minimal
drive.
We
naturally
preferred to rely on discharge cleaning (4 second
discharge
out of a 12 second cycle;
approximately
also
cold
hydrocarbons
time
is
It
is
3 seconds) to keep the machine clean.
necessary
nitrogen
the pump-out
to
trap,
monitor
the
vacuum
to prevent
system's
backstreaming
liquid
of
water,
and other impurities if and when the cold trap
runs dry.
A number of power supplies and diagnostics need to be turned
on prior to a run. These include power supplies for the main
field,
the vertical field,
breakdown
oscillator,
the ohmic heating
the
the
filament,
interlock and control system,
system,
the
sequencer,
the
and the water cooling system.
diagnostics include a 80 GHz (4 mm) interferometer,
Utility
a second harmonic cyclotron emission (2wce) detector, a hard
X-ray
crystal
monitoring
voltage.
currents,
It
plus
detector,
plasma
wire
various
position,
and
loops
for
plasma
loop
is standard practice to test fire the
magnetic field systems before a run.
various
The computer must also
be set up for data acquisition.
Tuning the machine in order to get suitable plasmas may take
from one to several hours. (Versator runs one shot every 120
seconds,
field
typically.) The main tuning knobs are the vertical
system
controls and the gas
puffer
features
of good shots are density and
centered
position,
reproducibility,
-
49
-
controls.
current
low
level
Some
flat-tops,
of
2 wce
emission (more on this later),
absence
of
disruptions.
low level of hard X-rays, and
Attaining such shots is
an
art,
often difficult.
The
RF
system requires
preferably,
purpose
but
not
periodic
necessarily,
waveguide
before
each
sending
The
This is done
by
short pulses of power (typically 1 ms every second)
through the system into vacuum,
increasing the power levels
keep up with what the waveguides will
pressure
order
run.
of this is to clean the waveguide walls and improve
the waveguides' power handling capability.
to
conditioning,
handle.
waveguide reflected powers are
and
to watch for plasma breakdowns in the
The
gas
monitored
in
waveguide.
0*
relative phasing between waveguides is used for conditioning
because it couples well to vacuum.
up
setting
and
the RF system requires going through a
warm-up procedure,
appropriately
It
Other than conditioning,
and setting the
(usually +90*
waveguide
turn-on
phasing
for current-drive experiments).
is also necessary to have the radial position of the
4-
waveguide grill suitably adjusted for good coupling of power
to
the
plasma.
In
practice
this
position
is
not
too
critical, and once set needs no adjustment.
Setting up the scattering system is straightforward. The EIO
power
supplies
are turned on slowly and the EIO
checked.
The
on;
spectrum
the
power
electronics and spectrum analyzer are
analyzer is locked to an 0.8 GHz
-
50 -
is
turned
signal
taken from the RF system.
Mixer and preamplifier are turned
on; their batteries are replaced if necessary.
.[10.3]
Planning Datapoints
An experiment may be thought of as measurement of
power
over
specified
magnetic
namely
a
by
set
of datapoints,
(1) the
field
plasma
where
a
conditions,
and density (2) the RF
scattered
datapoint
especially
is
the
system
parameters,
the RF power and the waveguide phasing,
and (3) the
parameters characterizing the detected wave, namely parallel
N,, ,
wavenumber
In
location.
perpendicular orientation and
one
experiment
the
one
usually only
spatial
of
these
parameters
is varied.
parameters
are chosen and may be set more or less directly,
but
the
situation
regarding
the
specification
is more complicated.
scattered
wave
waves
terms
in
The plasma conditions and RF
of
order
[Brambilla.76]
are
variable
in
expressed.
so
However,
spectra
the scattering angle is related to Nfl,
that a given Nil will correspond to different
angles
different locations in the
at
complication
is
to
needing
The
the
for a chosen spatial location
necessary
scattering
volume.
(described
more fully in Appendix [21])
mirror
scattering
plasma.
back-calculate
positions
the
is
the
during propagation and also because this
computed
Nil
is
conserved
which
the
specify
We prefer to
of N11 , both because to Oth
system
computer
these reasons a
For
second
mirror
of
the
program
used
determine
positions for a given N,, and spatial
location.
-
51
-
is
The program uses the cold plasma electromagnetic
relation
the
to determine the scattering angle,
dispersion
and then
does
coordinate geometry calculation to determine the mirror
positions. The program also draws a sketch of the scattering
geometry
and
computes some quantities
required
for
data
the mirror positions
for
each
desired datapoint are determined at the beginning of a
run.
analysis.
Of
In
course,
this
manner
some experiments (frequency scan,
comparison
of
waveguide
power
phasings) require only
scan,
a
single
scattering geometry.
[10.4]
Once
Running the Experiment
things
collection
for
of
a
may begin.
as
waveguide
is
tuned,
a
except for breaks. The usual
this takes
about
5
positions
positions
or
changing the spectrum analyzer frequency
and may be accomplished
cycle;
the
where
Some
minutes.
changes do not require changing mirror
phasing)
data
continuous
breaks is needing to change the mirror
disrupting
without
machine
The tokamak is run on
new datapoint;
datapoint
(such
set up and the
typically 120 seconds,
cycle,
cause
are
between
the
shots
is
this
possible
preferable, as breaks affect shot reproducibility. After a 5
minute
break,
normal.
Other
fault
it typically takes 1 or 2 shots to return to
causes of breaks are less
of some sort,
required
a need to check something,
by some other concurrent experiment --
means infrequent.
-
52
-
--
predictable
a
or a break
but
by
no
Most shots taken are for data,
scattered
power.
These
ie with the aim of measuring
shots
are
judged
good
or
bad
good shots are used for analysis, bad ones are
immediately;
ignored. Shots may be judged bad for a variety of reasons:
(1) wrong density
(2) poor plasma position
(3) misfire of some system
(4) high
The
2 wce
emission
last merits some elaboration.
the
[9.6],
As mentioned in section
scattered
to
emission
may
blocking
off the incident scattering
be seen independently of scattered signal
2 wce
well with the
beam.
The
in
plasma
background
This
signal.
addition
correlates
emission
system detects plasma
scattering
by
emission
emission and is thought to be
4-5th harmonic cyclotron emission from tail electrons. Since
the
the
scattered signal sensitivity is limited by
may
emission
high
emission,
make
the
scattered
plasma
power
measurement meaningless, especially if the emission jumps up
when
the RF turns on.
Fortunately it is generally possible
to run with emission levels low compared to scattered signal
levels.
large
Unfortunately,
tail
populations
emission levels are good for current drive and
wave
absorption,
regimes
where
so
and
high
lower-hybrid
that our measurements are limited
effects
current-drive
strongest.
-
53
-
are
not
at
to
their
RUN 4006
RUN 4006
VERSATOR
VERSATOR
SHOT
SHOT
233
233
3S.
0.
1.
-0.1
T I M E
M I L L I S E C O
I N
N D S
Fig 10.4.1 TYPICAL LOW DENSITY SHOT (+90* phasing)
-
54
-
the plasma discharge has an
current trace,
plasma
shown
As
typical shot is shown in Fig 10.4.1.
A
the
by
initial
turn-on phase of about 3 ms followed by a quiescent phase of
22 ms during which the plasma current decays
about
The
density
circuit,
fringe
for
and
from a
is
trace
(one
shows the fractional part of the fringe
beam);
is a phase shift of 27 in the interferometer
The loop voltage and
2.26x1012cm- 3 line-average per fringe.
position
is
factor
our interferometer the (linear) calibration
in/out
counting
fringe
so-called
slowly.
radius)
coils (for the plasma major
were
The hard X-ray trace comes from
described in section [9.9].
a portable detector consisting of a NaI crystal coupled to a
and measures bremsstrahlung radiation
photomultiplier tube,
the limiter.
at
plasma
boundary
(The stainless steel limiter defines
is subject
and
to
substantial
the
particle
bombardment.)
The
traces of particular interest to our experiment are the
at
three
Tokamak Bottom Port
I
The
scattered signal is shown on a
log
scale;
clearly
Piece of
Aluminum Foil
ALUMINUM FOIL TO DEFLECT
INCIDENT BEAM
-
during
-
the
is
RF
frame
is the signal seen with
incident scattering
(by Aluminum foil
see Fig 10.4.2),
55
signal
Also shown on the same
blocked
USE OF
seen
the
pulse.
the
Fig 10.4.2
bottom.
the
so that
beam
--
the
receiver
sees noise and plasma emission,
signal.
This
shows
that (1) there is
but no
significant
emission
(2) the
emission
(3) the scattered signal is detectable
level
of
pickup
scattered
emission correlates well with
It
2wce
the
above
the emission and (4) the system is free
problems.
plasma
the
from
is worth pointing out that the
RF
usual
procedure is to measure the scattered power during the first
after
millisecond
measured
during
this
During
rising,
2 wce
RF
turn-on and
subtract
the last millisecond
before
the
emission
RF
turn-on.
first millisecond the plasma emission
may
be
but not so as to introduce serious error. Where the
and 139 GHz emissions jump is usually later in the
RF
pulse, say after 2 or 3 ms.
Typically,
and
we take 2 or 3 good data shots at each datapoint
move on to the next datapoint.
then
In cases where
a
break is not necessary between datapoints, datapoints may be
changed each shot.
Besides data shots,
shots are occasionally taken.
matter)
receiver.
that
This
of
The first are baseline shots,
no plasma (with or without the fields does
with
shots
two other kinds
are used to measure the noise
level
of
not
the
is necessary since our system is calibrated
for
the scattered power measured in units of
noise
The
second kind of shots are 'Aluminum foil'
shots,
power.
where
the incident beam is blocked off by a piece of Aluminum foil
(see
Fig 10.4.2).
This
serves to check
that
our
system
remains 'clean' and free from RF pickup, and also to monitor
-
56
-
the
plasma
emission and ensure that our
meaningful.
Aluminum
Care
foil
the
EIO,
the
tokamak.
analyzer
is
taken
with
the
measurements
placement
of
so as not to reflect the beam power back
but rather to deflect it downwards and away
Another precaution is to check
frequency every once in a while;
it
the
are
the
to
from
spectrum
occasionally
drifts a little.
[10.5]
Very
Shutting Down
little
equipment off.
for
the
usually
is involved in shutting down
besides
As a matter of good practice,
scattering
recorded.
system and the 0.8 GHz RF
The
EIO power,
the
the
57
-
settings
system
spectrum
frequency and the mirror positions are checked, too.
-
turning
are
analyzer
Analysis
Section [11]
The
purpose of the analysis is to take the measured
and
compute the lower hybrid wave power,
signal
since this is the
quantity of interest.
Consider
are
accelerated in the electric field and consequently
radiate.
For
a
straightforward
to
kg
beam.
electron
waves
re-
density
power
are
radiation
with
and
Scattered
from
with
wavevector
where k, is the wavevector of the
incident
in the regions of higher
electron
electrons
Those
of
fields
compute.
arises
kw = +(kg - k1 )
n(k,w)
scattered
the
fluctuations,
wavevector
spectrum
of
electrons
The
Wo.
frequency
at
radiation
(0 mode)
S,
plasma illuminated with a Poynting flux
a
density contribute scattered fields in phase, which are only
by
cancelled
incompletely
fields
the
electrons in the regions of low density,
wavevectors
scattered
radiation
frequency
of
the
was
indicated
also
is
fewer
the
giving rise to net
(The relationship between the
coherent scattered radiation.
various
from
scattering
in
frequency
wave.
Fig
8.1.)
shifted
The
by
calculation
The
the
is
performed in Appendix [17]; the result obtained there is
I R
-l)
-
where
$ (w)
frequency w,
is
_6q
R)(21)
T
power per unit area per unit
-
11-01
(17.1.32)frequency
at
ro is the classical electron radius, RR is the
-
58
-
distance between scattering volume and receiving antenna,
is
a
geometric
factor
computed
in
Appendix
J
[17.2],
n2 (i ,w-w1 ) is a quantity related to the Fourier transformed
wave
amplitude squared (defined in Eqn 17.1.28),
the
time
over
which
the
receiver
measures
and T
power.
is
The
receiver sees power P
5
PS = AR CL l(w) dw
B
R
11.02
where AR is the effective area of the receiving antenna,
is
the
receiver
analyzer),
bandwidth
(determined
we measure PS,
practice
In
scattered power to the noise power.
the
instrumental
referred
the
BR
spectrum
and CL is the transmission loss of the receiving
waveguide.
to
by
-
noise
to the input.
of
the ratio of
the
Here noise power refers
the
microwave
receiver,
This noise is primarily associated
with the mixer and preamp.
The
density amplitude of the lower hybrid wave can also
used to calculate the lower hybrid wave power.
electromagnetic
amplitude
Poynting
theory
is
used
to
relate
to the electric field amplitude,
be
Cold plasma
the
density
from which
the
The calculation is performed
flux is calculated.
A.i
in Appendix [18]; the power flow Se in direction e is
2Ec
~
0
Se ~
(27)
da wo
cos,,da
27c
27
o
o
____
5
0-
-
cB 2A
F
3
n
e 2
A
(**kldk,
d 11 dki
-
59
2d0
n
(k"Wo
T
-
-
11.03(18 .2. 08) -
where
is the frequency of the lower-hybrid waves,
ne,
60 ,
are
dimensionless quantities depending on plasma
B,
kill kL have their standard meanings, and F2 and F3
parameters
(Eqns 18.1.13 and 18.1.17).
angle between k. and e.
power
c,
w,
and Nil,
11.03 to calculate the total power.
and
spectrum
of
measured
--
The angle
wave
is
compromises
are
and then use
Eqn
In practice this is not
necessary.
The
frequency
the lower-hybrid waves in the plasma has
the
the
Ideally one would measure scattered
for many values of a,
feasible,
and
been
used
measured bandwidth of 300 kHz is
to
perform the w integral. The a integral is performed by using
the
neutral
inwards
have
the
waves
same amplitude
radially
propagating
that
assumption
outwards
for
have
radially
propagating
all
zero
a,
and
waves
amplitude.
(In
practice this semi-isotropic assumption is found to be poor;
this
will be the subject of further discussion in
[12]
and
[14]).
The Nil integral is left
Sections
undone;
we
are
content to calculate lower hybrid wave power per unit Nii.
We
eliminate
equations
power,
and
the
lower hybrid
wave
amplitude
from
the
for the scattered power and the lower hybrid wave
use (1) the transmission system calibration
of
Appendix [19.4] to eliminate SI AR CL in favor of measurable
quantities and (2) the mixer calibration of Appendix
[19.2]
for the noise power. Thus the master equation is obtained
-
60
-
2 (27) 3/ 2
.I()
I(N11
2
c
-FcB
F
-
-n
PL
2. N, dN.
dN
)
1[i/RRRX
JJX,
F2.
(R R+RX )rO
BRBW ~ kTR
VB 4+B /
PC P
R W
S
11.04
-
per
I(N1 ) is the lower-hybrid wave power per unit N,,
where
unit area per unit launched power, and most other quantities
kTRBR is the noise power in the
been mentioned above.
have
the wave bandwidth BW=3 0 0 kHz, PL is
receiver bandwidth BR,
RX is the distance from the
measurement of Appendix [19.4].
This
volume.
scattering
the
to
antenna
transmitting
calibration
the
from
power
transmitted
CW
139 GHz
the
is
PC
and
lower-hybrid power
0.8 GHz
launched
the
equation is of the form
parameters
and
is
calculated
in
Appendix
1
the
emission
log
and
and
the
of
-
61
-
interactive
scattered
the
subtracting
and
units,
before
get
involves
power
scattered
to
C
by
multiplies
just
(measured
noise
CPL
(described
an
using
'real'
to
signal
measured.
experiment.
calculates
signal
measured
is
SBATPREP2
done
program
computation
The
).
converting
the
the
from
power
an
is
This
PL
and
planning
analysis
2MM4016.
program
and
-
plasma
known
from
computed
be
SCATBACL
while
data
11.05
geometry,
programs
[21])
actual
The
I(N
scattering
by
11S
can
CPL
product
the
where
P
C
=
)
I(N
the
0.8
GHz
system
is turned on.)
Details on 2MM4016 may be
found
in
Appendix [21.41.
The
significance
of
the quantity I(NO) is
that,
to
the
extent that the model assumptions are valid,
AW dN I(Nl)
=
1
11.06
where
AW
is the cross-sectional area of the
lower
-
hybrid
beam measured normal to r.
Data are presented in terms of I(N,), except for experiments
such
as the power scan where the scattering geometry is the
same for all datapoints.
-
62 -
Section
[12.1]
A
EXPERIMENTAL
[12]
RESULTS
Introduction
[12.1]
Introduction
[12.2]
Radial Scans
[12.3]
N 11 Spectra
[12.4]
Orientation Scan
[12.5]
Absorption Test
[12.6]
Other Experiments
number of experiments have been performed,
variation
of
lower
hybrid
wave
power
with
The radial scans and N11 spectra
parameters.
measuring the
different
(sub-sections
[12.2] and [12.3]) constitute the core of this thesis.
section
of
the
[12.41 covers an experiment that tests the isotropy
lower hybrid power flow,
subject
the lower hybrid
of
of [12.5].
power
antenna;
frequency spectrum,
was
+900
and
is
the
describes
poloidal scan
The experiments are summarized in
scan.
of
power
this
sub-section [12.6]
Lastly,
three other experiments:
and
wave
by comparing cases with
indirectly
phasing
by varying the orientation
Absorption of
wavevector.
detected
investigated
-900
Sub-
Table
12.1.1.
The
drive
current
0.8 GHz
is
6
-
density limit observed on
[Luckhardt.82].
7 x1012cm-3
Versator
Almost
at
all
experiments were performed at low density (4.5 - 5 x101 2 cm-3
line
average,
in the current drive regime) and
-
63
-
with
+90*
Table 12.1.1
LIST OF EXPERIMENTS
Experiment
Conditions
Run#
Figure
Radial Scan
Low Density N11=3
4003
12.2.1
Radial Scan
Low Density N11=5
4003
12.2.2
Radial Scan
High Density N,,=3
4004
12.2.3
Radial Scan
High Density N 11=5
4004
12.2.4
Nil
Spectrum
Low Density r/a=0.85
4006
12.3.1
Nil
Spectrum
Low Density r/a=0.0
4006
12.3.2
Nil Spectrum
High Density r/a=0.85
4015
12.3.3
Nil Spectrum
High Density r/a=0.0
4015
12.3.4
Nil Spectrum
1800 Phasing r/a=0.85
4018
12.3.5
Nil Spectrum
1800 Phasing r/a=0.0
4018
12.3.6
Orientation
Scan
r/a=0.5 N11=3.1
Low Density
4122
12.4.1
Absorption Test
r/a=0.0 Nii=3,5
4030,
+-90* Comparison
Low Density
4103
Frequency Spectrum
r/a=0.5 N11=3
Low Density
4204
12.6.1
Power Scan
r/a=0.5 N1,=3
Low Density
4125
12.6.2
Poloidal Scan
r/a=0.82 N,1=3.2
Low Density
4124
12.6.3
-
64
-
Table
12.5.1
phasing
of
current
drive
the 0.8 GHz lower hybrid antenna (this
phasing).
A
set of radial
is
scans
the
and
Ni,
spectra was measured at a density (8 x 101 2 cm-3 line average)
above the density limit.
Exceptions to the +90* phasing are
a pair of Nil spectra measured for 1800 phasing, and the -90*
phasing used in the absorption test.
Other
the
parameters also assumed some 'standard'
course
toroidal
field
horizontal
scan
of
1.2 T
Scattering
typically.
and
plasma
volumes
were
over
run
with
were
currents
of
25 kA
on
centered
the
midplane for all experiments except the poloidal
(sub-section [12.5]).
oriented
Plasmas
the experiments.
of
values
to
look
for
The scattering
waves
propagating
(specifically with k. within 1.20 of the
geometry
was
horizontally
horizontal);
this
The obvious exception to this
is illustrated in Fig 12.1.1.
is the orientation scan of sub-section [12.4].
[12.2]
Radial Scans
Radial scans were conducted at two values of Ni , nominally 3
and
5.
size
of the scattering volume;
detect
values.
finite
The parameters are 'nominal' because of the
waves
over
Radial
any scattering volume
a spread in spatial
and
locations
were performed with +90*
scans
-
65
-
Nil
waveguide
phasing at densities both above and below the current
density limit, as discussed above.
will
drive
I
-
I
I
M
50a45 x1
N -345 l
l~m
|
1
I
I
10-
-
I
ng=4.5x10
3-
SNi
+90* WVGO PHASING
BT
-
5
+90* WVGD PHASING
I
.19T
B
RUN 4003
-
1.19T
RUN 4003
I.
I
I
12 - 3
cm-
10-2
--
0/\
/
/
-
--
io-3
p
-"
"/ "
0.5-
10-4
X
-
Noise Level
I
x
-
NoseLee
-
I-I
10-5
0.5
I.C
r/o
Fig 12.2.1 RADIAL
Low Density,
N,,=3,
Phasing
Fig 12.2.2 RADIAL
Low Density,
N,1=5,
Phasing
SCAN
+900
SCAN
+900
which is a measure of tne normalized
The graphs show I(N,,),
lower hybrid power flow, and C, a scaling factor numerically
equal to the noise level of the system, versus normalized
minor radius r/a.
-
66
-
10~'
~
12
I
I
I
I
I
fe =79 x 10 cm-3
As =-79x I
Nil = 3
5
Ni-I-C
+90 * WVGD PHA SING
+90*WVGD
BT
PHASING
2
cm-
I
I
I
-
3
-
By= 1.30T
RUN 4004
1.30T
RUN 4004
10-2
10-2
It
/0
-
-
x
10-3
-x
x.1/
-Noise
Level
x
x
x
x
10-5 L
0
:
x
Noise Level
10-4
i
x
0
0.5
r/a
Fig
Fig 12.2.3 RADIAL SCAN
High Density, +900
N,1=3,
Phasing
12.2.4
N11=5,
RADIAL
SCAN
High Density, +900
Phasing
The graphs show I(Na ), which is a measure of the normalized
lower hybrid power flow, and C, a scaling factor numerically
equal to the noise level of the system, versus normalized
minor radius r/a.
-
67
-
12.2.1 shows the low-density radial profile for NH = 3.
Fig
Before discussing the data,
in
order.
quantity
First,
I(N11),
the
a couple of general remarks are
quantity
plotted
is
the
a measure of the lower-hybrid
discussed in section [11],
derived
wave
power
versus r/a, the normalized minor
radius.
Also
convert
scattered power to lower hybrid wave power via
shown for reference is the quantity C used to
Eqn
11.05.
(11.05)1 -
I(NI) = C PS
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
--- (1
When PS = 1 (scattered power equals noise power),
so that
. -5
I(N1 )
the location of C on the plot may be used to
the noise level of the system.
Second,
=
C,
judge
one notices a shot-
to-shot variation in the signal levels by a factor of 1.5 to
2.
This
variation
independent
The
is always present,
and is
essentially
parameter.
of signal level or any experimental
variation does increase for smaller
spectrum
analyzer
bandwidths, however, and is thought to be principally due to
spectrum analyzer noise. The mean of several shots should be
a
reliable
indicator of the true
signal
level;
also,
a
A
factor
of 2 is not serious when I(No ) varies by factors
of
10 or more between different datapoints in an experiment.
Returning to Fig 12.2.1, we see a strong peak at r/a = 0.65,
with the power level decaying by about 2 orders of magnitude
from there to the plasma center.
thought
to
be
The peak in the power
the 1st pass resonance cone
-
68
-
of
rays
is
with
positive
(450)
N
from
travelling
the short way around
the
hybrid
scattering plane,
(sections
observe
the
and
and
noise
level,
to
of
the
discussed
broadening
reach
The measured
resonance
cone
300 cm 2
beam
and
refraction
and
to
drop
even if all the wave power
center of the plasma.
might have an area (normal to r)
did
that
Consider
(this is the area of the face of the
antenna),
is
quantity
would cause the measured signal
the
to
the
Saying how much reaches the center is
from edge to center,
penetrate
We
the signal is 10 dB above
and loss of directivity (due to
scattering)
going
highly
below).
the directional power flow per unit area,
really
the
calculations
and conclude that power does
another matter.
quite
tokamak
grill
because
power flow (Fig 12.4.1,
center of the plasma.
wave
[14])
that even at the center,
however
waveguide
both because of ray-tracing
[13]
directional
lower
the
of
lower
a
about
hybrid
a magnetic surface at r = 5 cm has a surface
and
area of around 8000 cm2 , so that beam broadening alone could
account
for
Therefore
a
drop
by a factor
of
25
- 30
in
I(N1 ).
we are unable to conclude from the radial profile
whether or not the bulk of the power reaches the center.
separate
the
to
experiment was performed specifically
question
of
absorption during current
(A
address
drive;
it
is
discussed below in [12.5].)
For
same
comparison,
run,
but
Fig 12.2.2 shows a radial profile from the
for N11 = 5.
-
69
The power level
-
is
generally
computed
the
of
our knowledge
from
expected
as
lower,
peak
and the
(shown in Fig 9.9.2),
is
launched
spectrum
missing.
I(N1 ) does drop by an order of magnitude from edge
to center.
and 12.2.4 show radial profiles for
12.2.3
Figs
density case,
at N,, = 3 and 5 respectively.
that
the
reproduced
experiment
of
rapidly
Consistent
the point
to
and
It would appear that the lower
extremely well.)
at N,, = 5 the signal
Ni penetrates further into the plasma,
drops
mentioning
repeated,
was
12.2.1
Fig
graph
Neither
the peak of Fig 12.2.1 (It is perhaps worth
has
high
the
where
equals
signal
noise.
the observation for the low density
with
case,
the power level for N,, = 5 is lower than for N11 = 3.
N11 Spectra
[12.3]
Fig 12.3.1 shows an N11 spectrum for the low density case
at
Except for a couple
of
exponential
is
a
location near the outside edge.
shots
at
one
datapoint,
the
fit to
an
excellent.
The computed launched spectrum is also shown for
comparison
(this
match the data).
factor
The agreement is quite good.
Fig 12.3.2
shows the spectrum measured at the center of the plasma.
expected,
we see less power than at the edge.
at the center is noticeably flatter, too.
farther into the plasma.
-
70 -
As
The spectrum
This would appear
hard to reconcile with the previous statement that lower
penetrates
to
has been scaled by a constant
However a look at
N11
the
I~*~- I
I
I
10- 2
f
I
-
J
I
liq
5 x 10 cm-3
I
12
5 x 0
r/ =0.0
+90*WVGD
r/a =Q85
#90*WVGD
I
PHASING _
1.23T
BT a 1.23T
RUN 4006
RUN 4006
BTy
I
I
cm-
-
3
PHASING
10-3
'I
computed
spectrum
exp(-Nu /1.85)
xi0-
x
4
xX x
-x
X~
x
Noise
Level
10-61
X
xx
10~
X
i
i
|
Fig
12.3.1
NU
X-
x
X
0
10
0
Low
r/a=0.85,
+900 Phasing
-
Noise
Level
SPECTRUM
Density,
Fig
12.3.2
r/a=0.0,
+90*
N11
Low
SPECTRUM
Density,
Phasing
The graphs show I (N11), which is a measure of the normalized
lower hybrid power flow, and C, a scaling factor numerically
In Fig
equal to the noise level of the system, versus Nl,.
12.3.1 the exponential fit
(....)
are also shown.
-
(-
71 -
-
-) and the computed spectrum
10
I
I
I
-
I
I
10 21
I
'
I
'
I
I
I1
I
-
2
n\ = 79 x I02 cm-3
A,= 79x 10 cm-3
r/o =0.85
+ 90* WVGD PHASING
BT= 1.34T
UN 4015
r/a =0.0
+90*WVGD PHASING
34
BT= 1. T
RUN 4015
IP\
**
10-3
10-3
-
x
Noise
E
0
x
Level.
-
U
x
10-4
x-
10-45-
x
xx
-
-
Noise Level
I
10
0
10-6
1
5
Fig 12.3.3 N 1
r/a=0.85, High
+90*
x
5
0
Fig 12.3.4 N11
r/a=0.0,
High
SPECTRUM
Density,
+90*
Phasing
II
SPECTRUM
Density,
Phasing
The graphs show I (NII) , which is a measure of the normalized
lower hybrid power flow, and C, a scaling factor numerically
equal to the noise level of the system, versus N,,.
-
72
-
I '.- *I
F
I
I
I
I
10-2
-
395
x 10
2
cm-
r/a 20.0
180* WVGD PHASING
BT a 1.24T
RUN 4018
10-3
n.-
5 x 10
2
mn-3
ri/oa 0.85
180* WVGD PHASING
E
BT'. 1.2 4T.
RUN 4010
E
U
x
x
-
10-4
-
x
x
-5
10-
Noise Level
-x
x
x
Noise
i
1
1
K
Level1
10-6
106 1
0
-
.
Nil
Fig 12.3.5
Low
r/a=0.85,
1800 Phasing
1
0
5
Fig 12.3.6 Nil
Low
r/a=0.0,
1800 Phasing
SPECTRUM
Density,
5
SPECTRUM
Density,
The graphs show I(Nii),, which is a measure of the normalized
lower hybrid power flow, and C, a scaling factor numerically
In Fig
equal to the noise level of the system, versus N .
(....)
12.3.5 the computed spectrum
-
73
-
is also shown.
radial
profiles Fig 12.2.1 and 12.2.2 shows that the shapes
of the two radial profiles are quite
that
different,
indicating
comparison of edge and center Nil spectra is not a good
indicator
of how far the various waves penetrate
into
the
plasma.
Figs
12.3.3 and 12.3.4 show likewise the Nil spectra for the
high density case,
for r/a = 0.85 and r/a = 0 respectively.
The
remarkably similar
spectra
look
to
the
low-density
spectra.
Figs
12.3.5
experiments
reasonably
spectrum
12.3.6 show Nil spectra
from
a
pair
of
In the light of
the
fit between experiment and theory for
the
which in a sense failed.
good
of Fig 12.3.1,
computed Nil
phasing;
and
an attempt was made to verify
the
spectrum for the case of 1800 relative waveguide
this
spectrum should have a peak
around
Nii = 6.
Fig 12.3.5 shows the experimental result near the edge, with
the computed spectrum also marked in.
spectrum
makes
one
at the center.
wonder
Fig 12.3.6 shows the
The failure of these
about
the validity of
the
experiments
N
spectra
measured for the +900 case (Figs 12.3.1 through 12.3.4).
is
natural to speculate whether the experiment is
in
It
some
way biased towards small Nil or small scattering angles. This
is
the subject of further discussion in Section [14].
other point to be noted about the Nil spectra is that by
definition of I(N11 ),
-
74
-
The
the
AW fdNi 1I(Nil) = 1
12.3.1
(11.06)
yet even using 1 m2
the
-
(the area of a magnetic surface) for AW,
discrepancy between Eqn 12.3.1 and Fig 12.3.1
is
over
one and a half orders of magnitude.
[12.4]
The
Orientation Scan
orientation scan,
shown in Fig 12.4.1,
is perhaps the
most exciting result to emerge in our experiments.
Here
set
spatial
of
scattering volumes was taken with the same
location
and
orientation.
directional,
100.
40
scattering
The
wave
angle,
power
but
is
with
seen
varying
to
ki
highly
be
dropping by an order of magnitude in less than
There is also a noticeable offset in the peak,
from horizontal.
poloidal
a
Other orientation scans at
locations also showed the steep drop,
cleanly on both sides.
-
75 -
about
different
though
not
10
1
0
100
Noise Level
x
10-
31
1
-100
00
Angle
a
10"
(deg)
Fig 12.4.1 ORIENTATION SCAN
r/a=0.5 N11=3.1 Low Density and +90* Phasing.
A set of scattering volumes was chosen at the
same
spatial location,
with
the
same
scattering angle, but oriented differently in
the scattering plane.
[The inset shows the
scattering geometry for a positive angle a.]
which is a measure of
The graph shows I(N,,),
the
normalized lower hybrid pgwer flow,
versus a,
the angle between k., of the
detected wave and the horizontal.
-
76
-
Absorption Test
[12.5]
A
special
experiment
was
performed
absorption during current drive.
phasings of +90*
and -90*
opposite
directions.
absorbed
during
scattered
and
so
infer
look
for
launch identical spectra,
Waves
with
positive Ni
so that
from shots with +900
something
wave
The idea is that waveguide
current drive,
signals
to
about
one
and
but
in
should
be
compare
may
900
phasings,
The
absorption.
wave
measurements were performed at the plasma center,
get away from the strong resonance cone near the edge.
basic
assumption
in
refraction,
scattering
and
toroidally
symmetric
(This
The
due
to
the wave power is diffuse
and
experiment
this
to
so as
by the time it
that
is
reaches
the
center.
assumption is neither clearly good nor clearly
bad.)
Table 12.5.1 shows the results gathered over three runs with
two different values of Nil; we see that the signal from -90*
shots
higher
consistently
is
Table 12.5.1
than
BETWEEN +90*
COMPARISON
from
+90*
shots
AND -9 0 * PHASING
<Expectation
SCATTERED POWER PS AT PLASMA CENTER.
and standard deviations are indicated.
RUN
<P3(+900)>
P5
<43(-900)>
Ps
(+900)
(-90*)
<Pg(- 9 0 *)>
<Pg(+90*)>
8.73+0.28
8.73+
0.88
10 shots
6.21+0.22
6.21+
0.72
11 shots
1.40+0.07
4103
N 11=3
7.97+0.84
7.97+
2.51
9 shots
5.87+0.31
5.87+
0.81
7 shots
1.36+0.16
4103
N1=5
3.54+
1.40
1.95+0.21
1.82+0.28
__
13
1.95+
0.71
11
shot_
-
77
-
shots
ON
Values>
4030
Ni=3
3.54+0.39
--
If our assumption is
valid,
this
is evidence for wave absorption during current
drive.
Also,
by much (40%).
not
although
the
wave
absorption
is
not
strong
first
absorption (if it were, the difference between -90*
pass
and +90*
would have been greater).
Other Experiments
[12.6]
Several
other
12.6.1
a
basic experiments were
In
Fig
spectrum
was
performed.
frequency spectrum is shown;
this
measured with the receiver set to a 30 kHz
bandwidth.
The
figure also shows two fitted spectra; one a Gaussian and the
a peaked spectrum characteristic of weak
other
The
as
the
FWHM of the Gaussian spectrum is 400 kHz,
not the same
for
from an older experiment) used
the value (300 kHz,
data analysis,
scattering.
but the systematic error introduced
is
inconsequential.
A
power
verify
launched
scan was performed,
linear
dependence
power
(although
as shown in
between
differs
suggests
of magnitude is excellent;
from unity by nearly 20%.
12.6.2,
power
high
to
and
power
The log-log fit over two
unfortunately the
The excellence
slope
of
fit
that the problem lies in calibration of either the
scattering system or the RF system.
the
scattered
parametric decay at
levels may affect the dependence).
orders
Fig
scattering
returned a
system
A repeat calibration of
value
of
4.90 dB/Volt
instead of the old value 4.60 dB/Volt; this is not enough to
-
78
-
10- 1
1
1
Frequency Spectrum
Run 4204
N,, a 3.0
r/a Z 0.50
Low Density
0
g
+90* Phasing
1%1
0
Gaussian Fit
exp -(:of
10-2
I.0
0
0
Jo:
0
-0.6
-0.3
0
Frequency Offset
f-f0
0.3
(MHz)
0.6
(f =800MHz)
Fig 12.6.1 FREQUENCY SPECTRUM
r/a=0.5 N,,=3.0 Lgw Density and +90*
Phasing.
The graph shows I (N,,),
which is a measure of
the
normalized power flow,
versus
the
frequency difference between detected wave
and pump wave. Measurements were made with a
30 kHz bandwidth.
The inset shows
the
scattering geometry used.
A fitted Gaussian
is shown
(- - -) as well as a more peaked fit
-
79
-
1000
I
I
I
i
I
I
I
I
I
0
0
oo
0
Ln
I
00
Power Scan
o
Run 4125
=3.0
0N
100
I-
r/a
0Low
0=.50
Density
+90* Phasing
L
Lo
-
010
~
10 ~~
~~
1
N
Launched Lower Hybrid Power
P
100
3.0
(kW)
Fig 12.6.2 POWER SCAN
r/a=0.5 N11 =3.0 Low Density and +90
Phasing.
The
normalized scattered power is shown as a function of
the
launched lower hybrid power PL.
The inset shows
the scattering geometry used.
-
80
-
10-1
I
I
*1
II
II
I
Poloidal Scan
Run 4124
NUe
3.1
-
3.4
0.81 -
r/a
0.84
Low Density
+90* Phasing
-90*
10-
3
L
(b
0
0
8
10-
-900
0
-60*
-30*
POLOIDAL
If
00
I
+300
I
+600
i
+90*
ANGLE
Fig 12.6.3 POLOIDAL SCAN
r/a=0.81-0. 8 4
+900
Nii=3.1-3.4
Low Density
and
A set of scattering volumes
Phasing.
was chosen with the same scattering angle
and orientation, at the same distance from
different
but at
plasma center,
the
the
shows
[The inset
poloidal angles.
scattering
7
detected wavevectors for the
The graph shows I(Nii),
volumes used.]
which is a measure of the normalized lower
hybrid power flow, versus poloidal angle.
-
81
-
account
for the discrepancy in the power scan,
so
at
the
present time the RF system calibration is still suspect.
Results from a poloidal scan are presented in Fig 12.6.3. As
shown
in the inset,
several scattering volumes were
the plasma periphery (r/a = 0.85),
around
look for waves with horizontal wavevectors.
graph
is
waveguide
poloidal
taken
all oriented
to
The flat peaked
entirely reasonable in view of the fact that
the
grill
the
is
angles -46*
in contact with the
<
e<
460
of Fig 12.6.3).
-
82
-
plasma
over
(this is shown in the
inset
Section [13]
[13.1]
THEORETICAL
MODELLING
Outline
[13.1]
Outline
[13.2]
Launched Wave Spectrum
[13.3]
Ray Tracing
[13.4]
Results
[13.5]
Computation Details
In order to relate the experimental results to theory, it is
necessary to compute from available theories quantities that
be
may
related to experiment.
numerical
in
This section
describes
study of the lower-hybrid wave power distribution
a poloidal cross-section of the tokamak (the
plane).
are discussed;
in
scattering
details of the model, and results
The computation,
covered
a
comparison between experiment and theory
the following section.
The idea is
that
is
the
lower
hybrid power flow can be thought of as a composite of
rays;
each
the
ray can be followed independently to
power
flow.
of
computation
followed
tracing.
in
the
Sub-section
[13.2]
initial spectrum
of
discusses
the
waves,
launched
sub-section [13.3] by a discussion of the
Results are presented in [13.4],
miscellaneous
determine
computation
details
in
too voluminous to permit
ray
followed by some
[13.5].
inclusion
Program
in
this
listings
are
thesis:
listings and more computation details are provided
in a separate document [Rohatgi.85b].
-
83
-
[13.2]
A
Launched Wave Spectrum
code
used
due to M Brambilla [Brambilla.76,
to
hybrid
compute the wave spectrum launched
4
assuming
waveguide antenna.
plasma
density)/24cm.
ignored.
are
the
calculated
at the grill
mouth)
magnetic
-15 < N11 < 15
total
a
chosen arbitrarily to be (central
field
and
grill
mouth
curvature
Vacuum is assumed inside the waveguides.
-1 < N11 < 1 );
an
with
the
are
Fields
matched using 4 evanescent waveguide modes in
range
lower
The launch geometry is shown in Fig 13.2.1.
addition
the
Plasma waves are computed over
to the launched waves.
the
This spectrum is
(w2e/2=10
density gradient,
Poloidal
by
is
a finite waveguide grill mouth in contact with
overdense
linear
Knowlton.85]
(no
lower
hybrid
waves
exist
in
wave powers are normalized so that
the
launched power equals 1.
The computed spectrum
case of +900 relative waveguide phasing
was
for
presented
The phase of the launched waves is
previously in Fig 9.9.2.
also computed, for subsequent use during ray tracing.
Fig 13.2.1 GEOMETRY FOR
SPECTRUM COMPUTATION
BRAMBILLA
decreases
linearly
The
density
towards the mouth of the 4 waveguide
grill.
-
84
-
slope
n
W
=
[13.3]
Ray
Ray Tracing
tracing
is
used to follow a
keeping
track
through
the scattering plane.
large
number
of
rays,
of what the rays 'look like' when they
Paul Bonoli's
ray
pass
tracing
code ZIPRAY [Bonoli.82] was suitably modified and used.
The
geometry is shown in Fig 13.3.1.
Waves
are launched at the grill mouth,
lie along a magnetic surface.
0;
kr
is
which is assumed to
ke is initially taken to
determined from N11 and the dispersion
relation.
The initial power of the various waves is chosen to fit
(previously)
spectrum.
During
into account;
parametric decay and
low-frequency fluctuations are not.
tracing,
Phased 4-Waveguide
Grill
B
z=O
e
Scatterin
$=1T/4
GEOMETRY FOR RAY TRACING
-
85
-
scattering
from
Most rays are followed
till they damp (more on this in [13.5]).
Fig 13.3.1
ray
the
damping and electron and ion Landau damping are
collisional
taken
computed
be
The
ray
tracing code assumes the density
and
temperature
profiles within the plasma
n
-e
=
(neO -n
e
ea)
(r /a)2
-e n
+n
E
ea
13.3.1
e n-1
-(r
T
e
=
(T -T )- e
0Oa
1
-
-
/a) 2 M
-E-_-E
-
+ Ta
e
13.3.2
-
13.3.3
-
13.3.4
-
and outside the plasma
-
e
e
-
ea
-rm /1.5cm
-b/1.5cm
- e
-a/1.5cm
-b/1.5cm
- e
e
T (b-r ) + T (r -a)
Tb mm
_a
T
-
-b
a
1
-
where
rm
is the magnetic surface radius,
minor radius, and b is the wall radius.
a is the
plasma
Other parameters of
the plasma model, including the profile factors E, are shown
in
Table 13.3.1.
shifts,
axis
incorporates
flux
Shafranov[.67] in the small displacement
following
approximation.
magnetic
The magnetic geometry
For
is
the
parameters
displaced
by
of Table
about
a/8,
approximation is not good near the plasma edge.
13.3.1
the
and
this
Also,
the
model assumes a circular vacuum vessel, whereas the Versator
cross-section is square.
Following ray tracing, a number of analyses can be performed
These form the subject of the next
on the computed dataset.
sub-section.
-
86
-
Table 13.3.1
PLASMA PARAMETERS USED IN RAY TRACING CODE
Value
Quantity
Symbol
Toroidal Field
BT
Plasma Current
Ip
Electron Temperature
Center
Edge
Te0
Tea
300 eV
10 eV
Wall
Teb
5 eV
Profile Factor
(e
3.5
Tio
150 eV
Edge
Tia
10 eV
Wall
Tib
5 eV
Profile Factor
Ei
3.5
Ion Temperature
Center
Density
Center
1.2 T
25 kA
ne
1
6.78 x 10 23 or
cm-3
1.19 x 101
Edge
nea
0.10 x neO
Wall
neb
0.0
Profile Factor
En
-0.571
Major Radius
R
40.5 cm
Minor Radius
a
13.0 cm
Wall Radius
b
15.0 cm
Impurity Atomic Number
Zimp
6
Effective Atomic Number
Zeff
1.5
-
87
-
[13.4]
Results
Four cases were run: low density (6.78 x1012 cm-3 peak) with
waveguide
relative
phasing),
-90*
peak)
phasings
and 1800,
at +90*.
of +90*
(the
current
drive
and high density (1.19 x101 3 cm-3
(These densities correspond closely to the
'low' and 'high' densities of the experiments.)
Variations
from case to case, while noticeable, were not dramatic.
results
presented in this sub-section are restricted to the
low-density
launched
+900
case,
spectrum.
terminated
several
The
which
Fig
As indicated above,
normally
toroidal
for
via
damping,
passes.
9.9.2
most
but not
shows
rays
(84%)
before
The ratio of total
the
making
power
flow
across the scattering plane to the total launched power,
in
some sense the Q of the tokamak, was typically about 5.
Fig 13.4.1 shows a power map in the scattering plane for the
low-density
spectrum.
while
do
+900
The
case;
the
inset
shows
the
launched
power map may be characterized as
splotchy;
wave power does penetrate to the center,
so evenly,
it does not
despite making a number of toroidal
passes.
(A mechanism such as scattering of lower hybrid waves
low
frequency
map.)
to
fluctuations could greatly smooth the
Figs
13.4.2 and 13.4.3 which
toroidal
towards
power
To identify the rays in the brighter regions, we turn
negative NH rays respectively,
by
from
show,
for
positive
puncture plots separated out
We see that the bright
pass number.
the outside is caused as expected by the
-
88
-
and
crescent
1st
pass
1.0
0.3
0
OUTSIDE
INSIDE
Fig 13.4.1
POWER MAP IN SCATTERING PLANE
Contour plot of computed power density in scattering plane.
Contour levels are separated logarithmically as indicated.
The peak power density has been arbitrarily scaled to 1.10.
-
89
-
4 PASS PUNCTURE PLOT
--
RAYS WITH POSITIVE N
Top
-
;-/
Pass 2
Pass 1
*-
Pass
Pass 3
Fig 13.4.2
PUNCTURE PLOT FOR +ve N11 RAYS, SEPARATED BY PASSES
One dot corresponds to one ray.
-
90 -
4 PASS PUNCTURE PLOT
--
RAYS WITH NEGATIVE Ni
Top
-.
Pass 2
Pass 1
as
**-
-
Pass >4
Pass 3
Fig 13.4.3
PUNCTURE PLOT FOR -ve Nil
RAYS, SEPARATED BY PASSES
One dot corresponds to one ray.
-
91 -
positive
Nil
rays,
together with some contribution from the
2nd pass negative Nl
center
is
due
rays.
The bright region at the
to 1st pass negative Nil rays and
positive Nfl rays.
plasma
2nd
pass
To further study the rays near the center
we look at Fig 13.4.4 which shows the local N H spectrum
and
a spectral/orientation diagram. The latter diagram shows the
rays in the chosen spatial region (2cm square,
center)
of
on a diagram of N1 vs orientation.
2cm from the
The orientation
a ray is the direction of the poloidal component
with
0*
as
important
outward
and 900
as
upward.
for a scattering experiment,
experiment is orientation-specific.
of
k,
Orientation
is
since a
Notice,
scattering
though,
that
the lower-hybrid wave is a backward wave and so the poloidal
component of the group velocity is exactly opposite to this.
The
positive
Nil
directions.
(The
diagram
the
and
13.4.4
mostly propagating in
rays
area
of
the
- 2400
1800
the
the
shows
rectangles
on
a
proportional to
the
ray
is normalized so that the strongest ray on
any
spectral/orientation
power,
in
diagram
spectral/orientation
diagram
is
One may wonder what happened
is a fixed size.)
first pass negative Nil
rays that should show up at
to
the
center;
they do, but in a spatial location adjacent to that
of
13.4.4.
Fig
Fig
spectral/orientation
the
narrowly
the
the
0*.
about
-
spectrum
and
where
both
and 2nd pass negative Ni rays
positive Nil rays appear to
centered
Nil
diagram near the outside,
1st pass positive Ni
visible;
shows
13.4.5
92
-
A
have
closer
are
orientation
look
at
the
1.0
Spectral Orientation
NSpectrum
(a)
10
Diagram
(b)
8
6
1.6
i
.Q
44
02
0
00
.0
o
o
-2
to
-4
(c)
2
T/
Top
-6
Region of
Interest
TT
-8
0 ,21T77
n'J
-10
Outside
-1?
Orientation of k.L
Plasma Cross-Section
(radians)
Fig 13.4.4
Nil SPECTRUM AND SPECTRAL ORIENTATION DIAGRAM NEAR CENTER
(c))
Rays passing through the region of interest (shown in
are plotted on two diagrams.
(a) shows the Nil
spectrum.
(b) is a spectral orientation diagram, where a rectangle is
plotted for each ray at a coordinate determined by the Nil
The area of the rectangle is
and orientation of the ray.
proportional to the power in the ray.
The relation of the
orientation angle to spatial direction is also indicated in
(c).
-
93
-
1.0
Nil
Spectrum
10
(a)
4J
8
.4i
(a
Spectral Orientation
Diagram
(b)
(a
.6
21
2
13,
04
-
0
(c)
u/2 Top
-6
Region of
Interest
-8
+
0,27r
Outside
-10
-12
I
-
('4
,
Orientation of k,
Plasma CrossSection
L
(radians)
Fig 13.4.5
Nil SPECTRUM AND SPECTRAL ORIENTATION DIAGRAM NEAR EDGE
(c))
Rays passing through the region of interest (shown in
spectrum.
Nil
the
shows
(a)
diagrams.
two
are plotted on
(b) is a spectral orientation diagram, where a rectangle is
plotted for each ray at a coordinate determined by the Nii
is
The area of the rectangle
and orientation of the ray.
The relation of the
proportional to the power in the ray.
orientation angle to spatial direction is also indicated in
(c).
-
94
-
1. 0
90* Top
Region of
Interest
+
1800
00
Outside
270*
Plasma Cross-Section
0
0
Orientation of k. (degrees)-
Fig 13.4.6
ORIENTATION SPECTRUM NEAR EDGE
Plot of power vs orientation angle for the rays passing
The
through the region of interest (shown in the inset).
plot is restricted to rays with N1i between 2.5 and 3.5.
-
95
-
orientation
spectrum,
width of 10*,
the
in Fig 13.4.6,
peaked at +3*.
shows a 10 dB
full-
Noticing from Fig 13.4.2 that
1st pass rays are shifted upwards (as expected for rays
following
the field lines),
component
of
k
corroborated
remains
by
this means that
essentially
orientation
the
poloidal
radial.
spectra
This
further
is
from
the
midplane.
One question of interest is how loss of coherence depends on
Ni.
To
address this question,
a quantity related to
the
wave coherence called the cell size is defined
-
-
-
-
-
-
-
A
=
-
-
-a
f
IN
-
-
-
-
-
-
-
-
-
-
-- -
-
-
-
---
-
3f 3f1
3y
z
13.4.1
ray
where f is the wave phase and y and z are the launching
coordinates
as
shown
in
Fig
13.3.1.
(The
phase
-
f
is
corrected to lowest order for the phase difference k-Ar that
should
exist between coherent waves.)
interest
for
a
scattering
This quantity is
experiment
since
of
scattered
electric fields add for coherent waves, but scattered powers
(Incoherent waves have a broader
add for incoherent waves.
k
spectrum.)
coordinate
space)
of
number
The
waves
retaining coherence
(in
at
launching
the
the
scattering
plane is directly proportional to the cell size.
grouped according to their Nil
(0 to 3,
Rays
were
etc)
and the evolution of cell size from pass to
studied.
The
results
are shown in Fig
-
96
-
13.4.7.
3 to
pass
It
6,
was
would
Pd
102
I
I
-1
2
+++
4--I+
-
i
i- +
10
+PP4
_r -t-a
4
-'~,-
3
w
N
U,
0
~
~ 10
N
w
'3
-I+
w
U
0
U
1-4
2
I
-12
Fig 13.4.7
I
I
I
-9
-6
-3
I
3
I
6
I
I
9
12
EVOLUTION OF COHERENCE
For each pass, rays are grouped according to their
N11 and the coherence cell size is plotted versus
Ni1 .
The correspondence between symbol and pass
is
shown in the key at the right, which
number
also shows the average cell size for all rays.
-
97
-
appear
that
lower Nil rays are consistently
than higher Nil ,
more
less
coherent
perhaps because longer wavelength waves are
affected by spatial gradients of density and
magnetic
13.4.8 shows a radial profile of power for IN1,
between
field.
Fig
2.5 and 3.5, and orientation within 100 of horizontal.
E-01
(a)
top
3 -
a te
2
E-02
0
"4
S 2
(b)
b E-03
4
0
4
3 3
2
E-04
2
E-05
-
-
I
I
(inside)
Fig 13.4.8
I
1
-
x (cm)-.-
--
(outside)
RADIAL POWER PROFILE
The power density is plotted in (a) across the horizontal
chord shown in (b).
The plot is restricted to rays with
N1 |between 2.5 and 3.5, and with kL orientations within
100 of the horizontal.
-
98 -
[13.5]
The
Computation Details
computation proceeds in 5 stages.
each
The output files
stage serve as the input files of the next stage.
of
The
first stage is the computation of the launched wave spectrum
(sub-section [13.3]).
used
to
follow
passage
of
spread
a large number of
each
of
In the second stage,
rays
ray tracing is
and
ray across the scattering
rays
is launched,
with 2
record
plane.
dimensions
spatial location and the 3rd dimension for Nil.
each
A
for
the
traced
plane
ray's spatial location and Nil.
one by one;
(450
record
is
wavevector,
The
each time a ray crosses the
spatial
(2) it
power,
location,
A ray is
its
initial
8000 integration steps or
(3) it
either (1) it damps to 1%
exceeds
output
some starting coordinate tags
power and phase,
until
are
scattering
to identify the ray, and the toroidal pass number.
followed
into
rays
toroidally from the waveguide grill) an
written containing the ray's
the
The starting
power and phase of each ray are suitably chosen taking
account
3-D
of
undergoes 20 radial reflections. In practice 84% of the rays
terminate due to damping, with most of the rest executing 20
radial reflections.
In order to obtain smooth graphs, it is
necessary to have several thousand rays.
however,
runs
at
Computation
about 100 rays per minute on
a
time,
Cray-1.
Consequently, the approach taken is to follow about 300 rays
directly,
set.
Also,
containing
and
the
use
Nil
linear interpolation to expand the
range is broken into several
significant
power;
-
99
-
each
interval
ray
intervals
is
run
separately.
This
avoids
wasting
computer
time
on
i
intervals containing little power. Thus the 3rd stage of the
computation
and
is the interpolation to a 'complete'
ray
set,
the 4th stage is the merge of the output files from the
different Nil intervals.
The
fifth
analysis
and last stage of computation consists
and
graphics.
The
graphics
capabilities for generating radial power
maps,
Nil
spectra,
plots
of
of
data
program
has
profiles,
wavevector
contour
orientation
and
puncture plots (one dot for each ray crossing the scattering
plane).
Many
selectivity.
of the plots may be done with either Nil or N,
Some
statistical
performed.
-
100-
analysis
may
also
be
Section [14]
Results
COMPARISON
from
been
experiments
presented
the
of
the
power
a
r
which
and
are
second
not
rays
of
may
measured
be
the
The
partial
agreement
resonance
The
with
is
2
cm
to
(1)
Perhaps
the
a
both
horizontal;
by
the
a
computation
(Fig
-
13.4.6).
101
-
12.2.1):
the
(r/a=0.65
at
the
are
as
center.
at
least
The
were
(1
theory
and
(Fig
experiment
a
cm
volume).
scattering
between
with
in
is
picture
scan.
features
least
13.4.8)
profile
agreement
these
at
the
orientation
fine-grained
spread
NH
--
wider
measured
than
not
positive
experiment
is
smaller
narrow
of
the
more
orientation
very
a
(Fig
computed
a
dramatic
the
showed
in
does
edge
(Fig
power
the
much
most
is
experiment
12.4.1)
less
being
size;
cell
has
rays
11
center
the
profile
in
of
it
at
experiment
farther
features
due
power
radial
and
sharper
partly
well
available
r/a=0.8),
against
than
NU
N
14.01)
the
at
negative
the
reach
The
region
negative
used;
to
lower
computed
cone
The
in
in.
pass
(Fig
seen
being
because
spread.
is
further
first
volumes
what
amplitude
partly
by
scattering
limited
bright
orientation
large
the
edge,
power
rays.
NU
and
demonstrate
the
be
have
By
predicted
to
their
the
well
a
positive
because
that
shows
at
less
determined
pass
seen
match
was
sections.
cone
EXPERIMENT
modelling
Both
and
13.4.1
AND
theoretical
consistent.
directions,
Fig
THEORY
two
resonance
e
of
center
rays
strong
from
previous
are
and
map
the
the
features
presence
both
and
in
gross
BETWEEN
small
matched
offset
from
extremely
1.0
9
20
-
'
nanr0n,
.
Angle of k, (degrees)-e
Fig 14.01
ORIENTATION SPECTRUM NEAR CENTER
Plot of power vs orientation angle for the
through the region of interest (shown in the
-
102 -
rays passing
inset).
Another
lies
point
in
of agreement between experiment
and
theory
the frequency spectrum of the lower hybrid
waves.
Andrews
and
spectral
broadening of lower hybrid waves in a tokamak
to
Perkins
scattering
[Andrews.83
from low
frequency
radiative
transport
diffusion.
They obtain a formula
equation
N11 c Wpe (r=0)
2
-
a
W
have
calculated
fluctuations,
incorporating
2 T. (r=a)
VT for T<<1
2
T for T>1
ce
m-c
using
the
due
a
frequency
14.01
-
for the half-width (HWHM) Aw,
where Ni , c, me, wpe, Wce and
Ti have their usual meanings,
a is the tokamak minor radius
and T is the optical depth given by
w
2
-
Using
110 kHz
(r=0) m c
2T.
2
2
X2
1
c
Vce ci
the parameters in Table 14.1,
we obtain a
or 220 kHz FWHM.
for the half-width,
14.02
value
-
of
This agrees
Table 14.1 PLASMA PARAMETERS USED FOR CALCULATING FREQUENCY
BROADENING DUE TO SCATTERING OF LOWER HYBRID WAVES FROM LOW
FREQUENCY FLUCTUATIONS
Symbol
Value
Minor Radius
a
13 cm
Central Density
neO
Edge Ion Temperature
Tia
Toroidal Field
BT
1 T
Wave Frequency
f
0.8 GHz
Parallel Refractive Index
Nil
3
Quantity
-
103 -
5x 10 1 2 cm-3
10 eV
as
well as one might expect with the experimental value
400 kHz,
considering
Versator
is
theory
that
(1) edge
not well known,
ion
temperature
and (2) assumptions
of
in
in
the
regarding edge conditions and fluctuation level
may
or may not be valid for Versator plasmas.
We also notice from Figs 13.4.4 and 13.4.5 that the computed
Nil
spectrum
at
the
edge
falls
off
more
increasing Ni than the spectrum at the center,
same
with
which is the
result as obtained in the experiment (Figs 12.3.1
12.3.2).
all
steeply
and
these computed spectra include rays with
However
possible orientations.
Fig 14.02 shows
1.0
the
computed
1.0
1.8
4J
.H .46
S-4
0
.0
~2
.0
(b))
(d)
top
S
top
outside
side
(::7
Fig 14.02 COMPARISON OF Nil SPECTRA AT CENTER AND EDGE, WITH
RESTRICTED ORIENTATIONS
(a) and (c) show the Nil spectra of the rays passing through
The plots are
the regions of interest shgwn in (b) and (d).
restricted
to
rays with k,- orientations within 50
horizontal.
-
104
-
of
the
of
including only rays with orientations within 50
spectra
It is apparent that the shape of the center
the horizontal.
between
agreement
and
altered,
somewhat
is
spectrum
experiment and theory on this point is tenuous at best.
are also two notable discrepancies between theory and
There
First, the measured signals are low by at least
experiment.
A
Recall that I(Nil)
one and a half orders of magnitude.
must
satisfy Eqn 11.06
AW
-
-
-
-
-
-
-
- -
-
-
-
-
-
-
-
-
114.03
-
-
-
-
-
be
may
area
beam
the
shows,
14.2
Table
As
=
INgN
-
-
(11.06) - - - - -2
-
m
0.03
between
2
of
a
magnetic
surface).
integral
in
the
small
and
not
10~1,
terms.
Second,
strictly
1.
Table
14.2
GHz
0.8
the
all
TERMS
OF
ESTIMATE
-
105
-
IN
Eqn
for
10-3
here.
both
is
14.03
goes
power
graph
for
Eqn
of
m-2
mention
reasonable
more
side
hand
right
the
Not
is
value
0.03
between
is
terms
deserve
points
of
number
estimated
lower
the
First,
A
1.
two
the
of
product
the
Thus
Nil.
the
extrapolates
one
how
on
depending
,
m-
0.1
between
to
that
shows
12.3.1
Fig
evaluate
may
14.03
Eqn
2
and
of
Inspection
area
(the
m
1.0
and
mouth)
grill
waveguide
the
of
area
(the
14.03
into
not
the
detected
resonance
cone.
Imperfect
coupling
between
waveguide and plasma, waveguide transmission losses, and the
fact
that about 30% of the power is launched in waves
negative
with
N11 are all reasons that the right hand side should
be more like 0.5 than 1.
Third,
the calculation of I(N 1 )
required assumptions about the distribution of power flow as
To calculate I(N11 ) (see Section
a function of orientation.
11) we assumed the power flow to be isotropic for all inward
directions,
however
orientation
The
two
experiment
distribution
clearly
shows
is sharply peaked
that
(Fig
12.4.1).
issues here are (1) is our measured value
peak of the orientation distribution ?
the orientation distribution ?
distribution
assumption
is
less
than
at
the
and (2) how wide
is
The width of the orientation
100,
whereas
an effective width of 900.
has
the
our
isotropic
the
On
other
hand, judging from the offset of the peak in Fig 12.4.1, our
value may be down a factor of 2 or 3 from the peak
measured
value.
In sum,
however, the true value of I(N11 ) is likely
to be lower (by perhaps a factor of 3) than our calculation.
There
is
signal
most definitely a
discrepancy
between
measured
the best estimate is perhaps 2.5
levels and theory;
orders of magnitude.
Assuming
for
the time being that there is
no
fundamental
mistake in the experiment or analysis, there are a number of
possible
explanations
however,
are
for
the low
signal
particularly convincing.
-
106
-
levels;
(1) The
none,
receiving
scattered
antenna may not be properly positioned to see the
It is possible that,
radiation.
despite the CW alignment,
scattered radiation is shifted toroidally away from the
the
receiving horn.
Some toroidal deflection is anticipated due
however,
to the wave's k11 ,
(half-width
of 0.9 cm'1),
power
tilt
Ak1
so that this cannot account
for
Other causes of toroidally
much signal reduction.
scattered
resolution
the
is smaller than
0.7 cm'1)
(typically
as shown in Appendix [17.2], k11
shifted
or
could be a mis-aligned mirror pivot
of the scattering plane out of the vertical.
The
so
and a scattered beam spot size of 3 cm (full-width),
hard to see how toroidal misalignment could account
more than one order of magnitude signal reduction.
power
scattered
either
power,
k,,
above corresponds to an angular half-width of 2
resolution
is
a
may
due
or
to plasma instability
cyclotron absorption [Mazzucato.84).
for
(2) The
beam
incident
be low due to loss of
it
relativistic
We have, however, used
the 2 mm system as an interferometer in similar plasmas, and
transmitted signal may drop to about 30% of
the
while
vacuum
observed
value (probably due to refraction),
worse transmission than this.
is unlikely to be a severe problem.
we
have
the
never
Loss of beam power
(3) Since scattering is
stronger from coherent waves, loss of coherence would appear
to
be
a
likely
reason
for
Unfortunately Parseval's relation
-
107
-
reduced
scattered
power.
dk-
~2 (
d
2
-
f
14.04
that loss of coherence redistributes scattered
shows
in
(2)
but
k-space,
does not reduce the
power
measured
(4) We may not be looking in the right place for the
power.
hybrid waves.
lower
integrated
-
Lower hybrid waves at a spatial
point
exist with two degrees of freedom: magnitude of the k-vector
and the orientation of k,,
whereas our spectral scan is one-
dimensional (N
11 from ~3 to ~8, with a single orientation for
Given the narrow measured orientation width and
t% ).
each
our restricted scan,
But
waves.
we have been quite generous in our assumptions
of k-space width of the power flow,
isotropic in orientation.
power
total
substantially
we
measured,
resonance
cone
(5) Possibly
structure
to
large k 1 or k,,
flow,
we
assuming it to be semi-
In order to raise our estimate of
would
require
therefore
that
more power exists at orientations other
than
first
pass
and this is not likely since the
appears to have been found
turbulence
destroys the
satisfactorily.
hybrid
lower
exists
the point where much of the power
and so escapes detection,
consistent with the narrow orientation width
summary,
strongest
we may just have missed the
but
wave
at
this is not
measured.
In
while some of the shortfall in scattered power may
be explainable, this issue is as yet unresolved.
The
second unresolved discrepancy concerns the Nil
-
108
-
spectrum
for the case of 180* waveguide phasing.
+90*
spectrum
for
launched
spectrum,
on the first pass,
downshifted
phasing
(2) spectrum
strongly
(3) systematic experimental
errors
or
unequal
the
in
drive
checked,
powers
are
are not aware of any serious problems.
The
phasing.
Forward
monitored;
we
second possibility,
possibility,
by
also
waveguide
relatively insensitive to small errors in
supported
4
spectrum
[Luckhardt.85] has shown the launched
calculation
be
launched
are
The waveguide phasing has been
waveguides.
(Fig
off
way
The first possibility could be due to
bias towards low NH.
waveguide
is
computed
the
with
(1)
possiblities
the
different from calculated,
spectrum
to
1800 case
the
but
Briefly,
12.3.5).
quite well
agrees
edge
The measured
reflected
and
waveguide
namely strong downshift,
results.
ray-tracing
And
systematic bias towards low N1 ,
is simply not
third
the
for
whatever
reason (broadening due to loss of coherence, for example, or
a
geometric effect due to the smaller scattering angle
cannot explain why there is good
larger scattering volume),
agreement for the +900
case.
-
and
109
-
CONCLUSION
Section [15]
A
at
A
measured.
in
We
and
is
case)
than
wave
absorption
+900
case
+90*
the
for
center
for
during
are
drive.
current
decreasing
exponentially
-
110
-
is
as
Nil
and
power
density
seen
at
of
evidence
for
spectra
fit
the
drive
current
(the
interpreted
be
may
which
-900,
phasing
waveguide
central
power
lower
Consistently
high.)
quite
the
that
how
tell
to
difficult
it
makes
space
suggests
tracing
(Ray
much.
k
in
and
spatially
both
broadening
though
plasma,
the
of
center
the
reach
to
found
is
Power
computation.
the
in
well
very
reproduced
were
features
which
of
both
4*,
about
by
horizontal
from
offset
and
100)
than
(less
narrow
very
be
to
found
was
spectrum
kLorientation
The
directions.
poloidal
radial
the
in
both
extent
spatial
in
limited
edge,
plasma
the
towards
cone
resonance
a
detecting
in
succeeded
have
done.
been
has
code
tracing
ray
a
using
modelling
theoretical
addition,
In
drive.
current
during
absorption
wave
for
look
to
performed
was
experiment
comparison
phase
specific
A
made.
been
also
has
direction
poloidal
the
scan
spatial
A
performed.
been
has
scan
power
been
have
spectra
orientation
and
spectra
Frequency
density
drive
current
the
below
measured
been
have
spectra
Nil
and
above
both
densities
limit.
and
profiles
Radial
regime.
drive
current
the
in
waves
hybrid
lower
of
propagation
the
study
to
performed
been
has
experiments
of
series
the
computed
the
Brambilla
spectrum
quite well.
Measured spectra
at
the
center are noticeably flatter than at the edge,
although in
the
Nil
outer
regions
penetrate
case
as well.
of
180*
computed
the plasma the
is
between
The
other
theory
significant
and experiment
the
short by about 2 to 3 orders
reasons
not
spectrum
is
do
not
for
the
from
the
source
of
waveguide phasing differ markedly
level of measured power;
absolute
higher
Unfortunately the Nil spectra
spectrum.
disagreement
level
of
well
understood.
The
lies
in
experimental
of
power
magnitude,
measured
consistent with the broadening
the
for
frequency
calculated
by
waves
Andrews and Perkins due to scattering of lower hybrid
by density fluctuations.
this last issue,
Regarding
ray
we note that agreement
between
tracing computation and experiment is reasonable,
though
very narrow.
from
Also the orientation spectrum
fluctuations.
frequency
scattering
ray tracing code ignores
the
even
low
is
Thus we conclude that scattering in k-space is
unimportant at these (relatively low) densities.
Comparison
density
the
ray
of
available
data between
the
cases shows no dramatic differences
tracing
computation.)
low
and
high
(neither
does
Differences
in
wave
propagation characteristics are therefore unlikely to be the
cause of the observed current drive density limit.
-
111
-
The two limitations of our setup that most seriously limited
the
scope
of the measurements were
resolution,
and
(2)
incomplete
(1) marginal
access
for
spatial
scattering
geometries.
Regarding
potential
usefulness
of
microwave
experiments, two comments may be made.
that
very
little
distribution.
Since
measurement
plane
exists
there
are
Our results indicate
in
4
the
wave
parameters
(2 spatial degrees of freedom in the
2
and
symmetry
scattering
components
of k
in
the
power
to
any
poloidal
plane),
same
any
reasonably
complete scan over all 4 parameters in order
to
produce
power
of
a
measurements,
Further
may
not
even
there
wave power,
map would require a
very
large
for a single set of plasma
parameters.
is the frequency spread of the lower
hybrid
and also the fact that a power map in one plane
be indicative of other toroidal locations
tokamak,
set
so
that
global
power
mapping
prohibitive at least very expensive.
seems
in
if
the
not
The second comment is
that the microwave scattering experiment measures intensity,
or
power
per
unit
area,
and beam
area
is
not
easily
measurable.
On the other hand, microwave scattering is a unique tool for
probing waves inside the plasma, and a number of interesting
and
useful measurements can be made.
It is hoped that the
present work is perceived as a small but useful step in that
-
112
-
direction.
-
113
-
Section
[161
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Phys
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115
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(1) 58
Appendix [17]
The
SCATTERING
scattering
CALCULATION
formula derived here relates the
scattered
power to the density amplitude of the waves responsible
the
scattering.
account.
The
scattering
geometry
is
for
taken
into
The calculation is similar to that of Bekefi[.66]
or Slusher[.80].
[17.1]
We
[17.1]
Main Scattering Calculation
[17.2]
k Resolution of Scattering Geometry
Main Scattering Calculation
are
in
interested
frequency w
-I-
>> W
-pe
a
,o
electromagnetic
wave
of
incident on a plasma in the 0-mode
_ce
E = E0 f(r)
plane
cos(k -r-wIt)
17.1.01-
-A
quantities are real.
all
where
is a constant and
F
f(Z')
accounts for the radiation pattern of the transmitting horn.
f(Y)
is
|IE=RX,
defined
where
so
as to have a maximum value
and the scattering volume.
the
relatively
e j(W~t-
)
(The 1/r
scattering
small
2
variation
volume
1
on
transmitting
RX is the distance between the
horn
of
is
over
ignored.)
is more convenient to work with, so write
----- --- j ( t-k
E0f()cos(k-oWt) = 2 o f()e
f - ak
1
r)
=-E
-j(0
+__ f(r)
t-kIr)
e
Then for the time being consider an incident wave
-
116
-
17.1.02-
j( I t-k- r)
-
At
E'
high
f (r)
= E
-
e17.1.03
frequency the electrons may be treated
particles
and
the ions may be ignored.
accelerated and consequently radiate.
may
as
single
The electrons
are
The radiation
fields
be computed from the Lienard-Wiechert formulae.
In the
non-relativistic
limit,
a single electron at
r
generates
A
fields at R = R R in the far field given by
j(w 1 t-k-r)
r
E'(Rt)
_
e
=
RX (RXE)
H ,(R,t) = c 0 c RXEi
17.1.04-
17.1.05-
where
e
=
-r0
-
- -
4-rE
c
0m
-
-
-4T- 0
2
2.82
-
-
fm
-
-
-c
17.1.06-
is the classical electron radius and
-
T
=
t
-
--
--
-
c
17.1.07-
is the retarded time. Writing
A
-
IR-r(T)I ~ R - R-r(T)
17.1.08-
which is good for k1 -r2 << R and
r(T)
~ r
c(t--)
c
17.1.09-
which is good for (v/c).k 1 -r << 1, we can simplify
-
117
-
+ k-r(t 1 )
wI t
T-k - r(T)
WI
-
-
17.1.10-
where we have defined
-t
=t
R
-
-
- tkR - k
c
is
(w
of
frequency
the
=
--
e
Then
wave.)
scattered
the
-ir(ti))
ti
j(W
r9
A
-
17.1.12-
I
-E-R,t)
)
RX(RxE
f(r)
17.1.13-
fields
radiated
scattered
be
may
I
r
OA
-
_rt
For
--
0
Rx(RxE
e
A(k)
k
A()
n
dr
)
t
e
1
r7,,r4
r~
jk
17.1.15-
-1(2Tr)
the
_
-
dr
a
dk
jk-r
l
270
=
e
A(W)B(Z)
obtained
readily
is
formula
convolution
3
A(k
1
(27)
which
may
be
applied
k
t
f(r)g(r)
convention
transform
Fourier
-
0J(o
Rf
=
our
by
found
electrons
over
summing
function
total
receiver
the
into
coupled
field
electric
couple
weight
a
the
Then
)).
f($)
to
not
do
is
there
rather,
analogous
(exactly
g(E)
electrons
various
antenna;
the
into
equally
the
from
the
pattern,
radiation
antenna's
receiving
the
of
Because
-
1
_0l
to
-
118
1
)
17.1.16-
17.1.14
Eqn
)B(k-k
-
to
-r)-
get
-
and
dk 1
re
E (R,t) =
-
the
time
R'Rx(RxE0 )f (2)
Fourier
'(RJA)
ne (k
C(k-k
t
e
3W I
nt
-
17.1.17-
transform
RX%(EXE~wr
Rx(RxE
-
dk
e
e
1
)
i
,f2
w-I
)C(k-k
1
)
r17.1.18-
-(
where
C(K)
=fdr
e
f(r)
g(r)
17.1.19-
But
this
calculation
is
field
electric
of
the
Eqn
component
we
17.1.02,
of
the
incident
For
17.1.03.
Eqn
in
written
field
electric
for
total
the
obtain
-A
r
-
E
S
(R,w)
=
AA
dk
)
2R
1
+
.&
-
CCAf
0^
H S(R,w)
(k
oRE0f 2r 3[e
e
2R
=-
ne
o
,%-
1 rW
1)]
-A
T
n
3 [e
(k
+
(k
n
2
-
))C(k
I )Ckk1
,O+w)C(-k-k
(k
dk2
RxEo
2
1
17.1.20-
I
2
,1o-o )C(k-k)I2
,W+W
)C(-k-k
)
2
17.1.21-
-
P
=
A
-
where
area
P
AR.
intensity
spectral
a
Define
$(w)
by
seen
by
$()
217.1.22-
is
the
We
have
total
for
power
$(w)
-
119
-
a
receiver
of
effective
-
-
-
-
$ (W) =
where
T
-
- -*
-
-2
2
-
-
-
-
-
-
-
-
Re E(w)XH ()
is
the
measures power;
17.1.23-
time interval
over
which
the
receiver
the scattered fields are assumed to be zero
outside this interval. Putting 17.1.20-21 into 17.1.23,
e
-
cdk
0
$ (w) = Re..40T.RxEo2
133f
2
dk22
C(k-k 1)C*(k-_k2
x
where
the
because
cross-terms
and w+w1 terms
1)
ne(kc3)
is
non-zero
Z << w,;
2)
w, > 0;
bandwidth
at
interest
(see
<brackets>
<n e (k,w-w )n*(ky,o-o>)
is
Eqn 17.1.22).
non-zero
17-1-24-
have
only
-
been
over
3) only
dropped
a
is
of
Now the expectation value
in
k1 = k2
k,
only
if
1)
w > 0
narrow
and
2)
satisfies the dispersion relation, which we shall denote by
-
kgl
= H (k
-
)
)17.1.25-
in terms of the components of k
~
k =kaz + k
17.1.26k
-1
= k
z + k
lIt
-L
17.1.27-
Then we may write
-
n
(k ,o-W)n*(k2 WWI)
=<In (kl,ow-w)
x
The
6(k 2 -k)
6(k1 11 -H(k11))
dimensions of the bracketed term on the RHS are
Introduce the incident Poynting flux
-
120
-
_
17.1.28L~ 4 T 2.
S
~
-
2
1
=-esc E
2 0
0
I
17.1.29-
and use for our geometry
^
-2
2
X
=
0
17.1.30-
obtain
to
=
$(-)
Re
2
6
dk1d
X
We
and
ki
see
shall
C
that
relatively
it~
and
0
= S
)
nFe(ki
1
-H(k
1
the
in
k
)
ne(ki
we
))
17.1.31-
the
k
direction
directions.
Using
finally
obtain
-
-1
n(JrWW1
r
(R
-
1
broad
in
-2
-I $(W)
6(k
relatively
narrow
=
ki
is
2
n
(2
)6
-
Q17.1.32-
where
-~ ~
2 -
-
1=dk1L
C
-
(k]-k)
17.1.33-
is
below.
computed
In
of
radiation
quantity
geometry.
this
the
we
section
overlap
will
The
the
the
Fourier
is
the
J
(Eqn
calculated.
-
121
-
17.1.33)
beams'
how
17.1.31
of
k-resolution
integral
scattered
Eqn
from
clear
C(K)
transform
and
incident
It
to
Volume
Scattering
compute
of
patterns.
relates
the
of
k-Resolution
[17.2]
the
will
this
scattering
also
be
and
in the scattering plane x,
17.2.1)
beams
respectively,
angle
OS.
scattered
and
incident
the
along
xg
(Fig
non-orthogonal coordinates
Define
scattering
with
/incident
we
Assuming Gaussian beams,
Tokamak
X-Section
Beam
can
write
and
the gain functions f(")
Fig 17.2.1 NONORTHOGONAL
IN
COORDINATES
SCATTERING PLANE
receiving
g(Y) for the transmitting and
horns respectively:
f(r) = exp[-(zb) 21
-
~ ~
-~~~~~~~~
~
exp[-(x d) 2
-
g(r) = exp(-(za) ] exp[-(x c) 2"
-
17.2.01-
-
17.2.02-
1
where
Vln 2
Vin2 sinG
R RE
R
6
R
sin 6 8
- -
/n2
b =R
R
RX X - - - - - - -d -= -X-.,
-
-
RH-
eXH -
- - 17-2.03-06- --------
-
RR is the distance from the nominal center of the scattering
to the receiving antenna,
volume
y
X
and eRH are the
half-widths
angular
/x
0RE
and
antenna,
of
the
3 dB
receiving
the suffix X denotes
the
e
same
quantities
Measured
antenna.
INFig 17.2.2
OF
TRODUCTION
ORTHOGONAL
COIN
ORDINATES
SCATTERING PLANE
for
the
transmitting
values
[19.3])
are used.
Define
orthogonal coordinates
-
122
-
(Appendix
x,y,
as
shown in Fig 17.2.2, with
S
7T
-0
4
2
17.2.07The
transformation
matrix
is
x S)
sin 63
-sin
a
cos
l
x(
-sin a
x
a
Cos a )
Y)
17.2.08With
introduction
C(K)
of
(Eqn
17.1.19)
orthogonal
is
evaluation
coordinates,
straightforward;
we
of
get
2
3/2
-
C(K)
K 2
K
K2
K
4CX
4B
K
D]
ABCXxp
whee4A
4B
X
CX
17.2.09-
where
2
2
A
X
1/2
+
6
2
ln2(R2
=
XE
R
17.2.10-
RE
2
c-s
B
Cos
ln2
=
.2
2
a
+
12
a
sin
R 2 e2
2
X
sin a
Cos a
(peRH
eXH
2 2
D
1n2 (R1 2
(
X-
17.2.11-
XH
17.2.12-
2 2
RX
2
+
2
R
l
XeH
Cos
c
17.2.13-
RH )
D2/(4B 2C2
17.2.14-
This function has elliptical contours in the poloidal plane.
Calculate the k-resolution terms
Ak
-
=
1
Ak
=
dK1
C 2 (K=0)
= /2TA
17.2.151
dK
C
2-
(K =0)
C (K=0))
= 27BCX
17.2.16-
and then J (Eqn 17.1.33)
-
123
-
(Ak)k
-
To
we
feel for these quantities,
a
get
17.2.17-
in
put
parameters for our experiment: RR = RX = 0.4 m,
FWHM ~ 4.5*.
beams'
Akil = 1.87 cm~1
We
a
obtain
we
need not
typically
about
worry
k,,
system is aligned ( kj = 0 ),
the
for
0.7 cm~.
the
locating
receiving antenna at the correct k,, orientation.
the
and
resolution
which is large compared to
(FWHM)
that
means
63= 200
parallel
lower-hybrid waves in our experiment,
This
typical
As long as
lower hybrid
waves
will be detected.
poloidal
the
In
1.85 cm-1
plane Lk
between
varies
(the extreme values lie along xy
consistently
0.33 cm-1
),
which
and
is
smaller than kg ~ 10 cm~1 of the waves we seek
to detect. This means that the
I1
S
S
receiver really is looking
k
a narrow spread of wavenumbers
k7
(a)
at
Further
scattering
(b)
we note that for
angles
es< 900,
k-RSOLUION
Fig 7.2.
k-RESOLUTION
Fig 17.2.3
OF SCATTERING VOLUME
which is usually the case, the
The spatial extent of a
typical scattering volume
is shown in (a).
(b)
shows the corresponding
spread in kW'
mostly
-
k1
124
-
spread
(see Fig 17.2.3)
in wavenumber and
is
not
The
LOWER
[18]
Appendix
quantity
CALCULATION
In Appendix [17]
is
the
lower
the scattered power was
to the density amplitude of the lower hybrid waves.
the density amplitude will be related
this section,
In
WAVE
of interest in our experiment
hybrid wave power.
related
HYBRID
to
the lower hybrid wave power.
[18.1]
The
[18.1]
Single Wave Analysis
[18.2]
Total Wave Power
Single Wave Analysis
starting
point
equations
comprising
collisionless
jmovj
=
1
equations
set
and
0
=
of
the
a
18.1.01-
% -
1
.
-
the
jk-r) dependence
jk-n 0
jn- -
-
Maxwell's
is
cold plasma fluid equations linearized for
wave with exp(jwt -
for this calculation
(El + vjxB)
n0 q
18.1.02Use
a
slab
wavevector
B = B z
model plasma with magnetic field
k
with
ky = 0.
component
The
cold
and
plasma
electromagnetic tensor relation is obtained
-
jD
S-N2
It2
jD
-
-
-
Na N
where
N,,,
N = c k / w.
P-N2
are
P,
S
0-
Ey
0
S-NL0
N,
E
N,, N.
2
S-N,,-N2
Ezz
(
components
of
18.1.03-
the
refractive
index
and D are in the standard notation
-
125
-
of
Stix[.621.
In the lower hybrid regime
2
2 ~2
2
2
Wci <Wpi ZW<Wpe 1Wce
they
may
be
approximated
2
2
-
P
~-w
/o
pe
-
S
18.1.04-
~1
218.1.05-
+ W
o
-eW .j/o
/W
-
ce
18.1.06-
2
-
D
W
e
/WW
-
pe
The
ce18.1.07-
dispersion
relation
determinant
of
bN
-
aN
-
the
matrix
in
obtained
Eqn
by
18.1.03
to
setting
the
zero
0
c=
+
is
18.1.08-
-
where
-
a=
-
b
S
18.1.092
=
-(P+S)N2
+
2
P(S
+
PS
S
-
(1
D-
18.1.10-
2
-D
)
-
2PSN2
+
PN1
18.1.11-
-
This
can
equation
plasma
be
parameters.
equations
solved
Once
to
N1
for
N
is
known,
given
1
N,,,
we
can
w
and
solve
the
local
the
fluid
obtain
in
nle
0
cB
ExF2
2
W
2
N_-P
F2
F
-
=
2
To
compute
in
terms
Eqn
18.1.03
-
w
N
ce
N
W
of
11
2_
ce
the
N
-.
18.1.13-
NP
N
wave
Ex.
The
and
those
power,
we
need
components
of
of
B
-
from
126
-
the
E
components
are
easily
of
obtained
E
and
from
B
~18.1.14-
-
Then for a single wave we obtain the Poynting flux
3K..
-
2
ExB* + 2EowE
S = -Re
0
90
-
A
-x
=
-
2
0
c( 1E
2
F3
"
~
7
-E*~
i18.1.15-
3
+
zS
18.1.16-
2
PN
2
-
i 3
A
3
-P
-
13
'
-
N
2
2_
18.1.17This
power
plasma,
for
contribute.
been
flux has been computed for a cold
which
18.1.15
For
typical
Versator
parameters
correction is the drift contribution to
term, <10%.
does
not
The thermal and electron drift corrections have
estimated.
dominant
the 2nd term in Eqn
non-drifting
the
the
Ex B
All other corrections are at the <1% level.
[18.2] Total Wave Power
For a spectrum of waves,
the component of the Poynting flux
in the e direction, measured over a time T is
S
e
=
- fE(rt)xB(r.t)
dt
T1po
18.2.01-
Introducing the Fourier transforms, we have
S
2
=P T'Re
e.
3
(do
2 k dk
1
/k
B
(k"o)B*k)e
j(k-k
1
r
-)(18.2.02Use the following
(1)
e = -r,
we are intrested in radial power flow
-
127 -
--
lb
A(
(2) let at be the angle between -r and k
(3) the
expectation value in
<brackets>
is
non-zero
only for k = k
(4) as in Appendix (18.1], E x B*=
-
j1ExF
3
to obtain
-
(
T
3
a
-
do
dw dk
Se = 2E: c F Cosa Re
2
3dk<E(k ,w)I /,6(k-k1 )
f (2T )
18.2.03Now only waves satisfying the dispersion relation exist,
so
that we can write
1E (kw)12 > =<IE
where
the
2 (-,'.L
quantity
to (jn (kw)1>
W) > 6 (k,, -
on
the
RHS
Th
is
18.2.04exactly
analogous
defined in Eqn 17.1.28. In fact
E(kw)>=
>,2
(0 22)n
18.2.05-
Then
-
-
e
e
3
(2Tr)
(n2 (k
c B 2(
2o c
,w) >
3 f27T
n0 F 2
may
k
d
nac
COS<ine(k.,w))
T
27
be related to the scattering
$(w)
via Eqn 17.1.32. Write dkL = k. dk. da and use
-
dk
=
(dk.L/dk
c
dN 1
18.2.06intensity
18.2.07-
to obtain
-
128
-
e
2Eocfc B 21F cosa da (dw
27
2r
(21) 1\no F2)J
0**
dk
-
< n 2(kL,
w)
>
18.2.08-
x JdNk-
Ideally
one
would measure the scattered
n(k,o)I> for many values of w,
a, and N,,,
Eqn 18.2.08 to calculate the total power.
is
not feasible,
power,
and
thus
and then use
In practice
this
and if an estimate of total power flux is
desired, some modelling may be necessary.
-
129 -
Appendix [19]
MICROWAVE MEASUREMENTS
[19.1]
Outline
In
appendix
this
four
different
microwave
measurements
are presented, all of which are necessary for calibration of
our
experiment.
and
conversion
The measurement of mixer noise temperature
loss
in
presented
is
[19.2].
Antenna
radiation pattern measurements are presented in [19.3].
CW
calibration of the transmission system is
And
[19.41.
lastly,
in
[19.5]
the
The
in
discussed
preamplifier
gain
maeasurement is discussed.
using
Outline
[19.2]
Mixer Measurements
[19.3]
Antenna Patterns
[19.4]
Transmission System
[19.5]
Preamplifier Gain
Mixer Measurements
[19.2]
The
[19.1]
mixer was calibrated
and
the hot
cold
load technique. The setup
is shown in Fig 19.2.1. A
tap
off the EIO was used
to
provide
the
nalze
local
-
Boxcar-
Fluke
DVM
power
oscillator
(measured
reHorn
by
a
diode
Eccosorb
at
--
294K
--
77K
biased
Fig 19.2.1
Schottky
Mixer
detector
-
130
-
MIXER TEST SETUP
[Alpha/TRG F965D]) to the Alpha/TRG F9100 mixer. A blackbody
noise
source
gain
for the RF input was simulated by mounting
standard horn on the RF input and putting a
Eccosorb
dipped
foam
in
in
front of it.
A piece of
liquid nitrogen served as a 77
[Weinreb.73];
it
noise power.
stayed
piece
of
Eccosorb
K
noise
cold long enough to
a
foam
source
measure
the
Another piece of the same material served as a
room temperature noise source. The noise power output of the
mixer was amplified by its attached MITEQ preamplifier (gain
36
dB,
analyzer.
below)
[19.5]
see
The
measured
and
detected
by
a
spectrum
noise power P in a bandwidth B
is
given by
P = -G k(T +2T ) B
L
R
N
TR
where
is
temperature
the
the receiver noise
temperature,
TN
is
the
of the RF input signal (blackbody noise),
G is the preamplifier gain and
conversion loss,
Boltzmann's
19.2.1
constant.
The
L is
k
factor of 2 arises because
+/-
is
the
GHz).
By
making power measurements at two different temperatures,
we
receiver
detects
both IF sidebands (at
0.8
have two equations in two unknowns (namely TR and L )
are
even
easily solved.
determined
if G is not known.) In practice TR is much higher than
room temperature,
77 K
(Notice that TR may be thus
which
so that the change in noise power between
quite
and room temperature is
precise
measurement
small.
However,
of P turns out not to be necessary
very
if
the difference in power can be reasonably measured. In fact
-
131
-
2P
where
(T
P2~Pl
2R
subscripts
)
-T
N2
_
T
1,2
Nl
2T
denote
Nl
the
19.2.2
measurements
at
-
two
different noise source temperatures.
With
our
analyzer
setup P 1 was measured directly off
scope
display,
and
the
the difference
spectrum
P2
P1
-
was
with
measured by looking at the scope's vertical signal out
a digital voltmeter, with the help of a boxcar integrator in
between
filter the signal and compensate its DC
to
experimental
The
results
temperature
and
conversion loss as a function of LO power are shown in
Figs
19.2.2
and
for
19.2.3 respectively.
noise
level.
A noise
temperature
of
6600 K is obtained with less than 2 mW of LO drive.
Similar
the
results were obtained in another
where
noise power was measured with broadband diode detectors
(Hewlett
third
experiment
Packard 423A) instead of a
spectrum
analyzer.
experiment using a spectrum analyzer and a
A
different
preamplifier (Watkins Johnson 269) was performed to
measure
mixer characteristics at an IF of 2.45 GHz. Results obtained
were
shown
these
substantially worse than at 0.8 GHz;
19.2.2
Figs
possible
to
use
and 19.2.3.
this mixer to detect
launched by our 2.45 GHz S-Band system.
auxiliary
directional
performed
were
measurements
couplers,
attenuators,
-
132
-
it
As a result
are
waves
a number
Also,
and
not
was
lower-hybrid
to
also
calibrate
139
GHz
of
our
diode
MIXER
19.2.2
Fig
NOISE TEMPERATURE
n
Noise temperature is
shown as a function
power for
of L.O.
and
0.8 GHz
both
2.45 GHz intermediate
frequencies.
1
2
3
Local Oscillator
(L.O.) Power
4
5
(mW)
0
0. 8 GHz
-10
0
K-
x
g
4
2.45 G1z
-20
0
I
I
I
Local Oscillator
(L.O.) Power (mW)
MIXER CONVERSION LOSS
Fig 19.2.3
Conversion loss is shown as a function of L.O. power
both 0.8 GHz and 2.45 GHz intermediate frequencies.
-
133
-
for
A Hughes thermistor (Model 45777H) for a Hewlett
detectors.
these
432A power meter was used as a reference for
Packard
measurements.
Antenna Patterns
[19.31
The
shown
used
setup
directly
determined
plane
The beam
from the test antenna.
horizontally
was
power
EIO
The
19.3.1.
Fig
in
to measure antenna radiation
by measuring power across
patterns
beamed
out
pattern
was
a
approximately normal to the direction of
at a distance of about one meter.
waveguide
open-ended
suitable
for
pattern.
To
receiver,
vertical
propagation
The receiver used was
an
which
is
detector,
diode
a
with
this purpose because of its
broad
radiation
improve coupling of plane wave power into
the
edges
of
the
is
open-ended
waveguide
the
were
Y
.
'Movable
'Diode Detector
4 cm
119 cm
Measurement
P lane
laX
00S.Horn+Lens
Antenna
Power from
EIO
Fig 19.3.1
SETUP FOR ANTENNA PATTERN MEASUREMENT
The dots in the measurement plane correspond to the
at which measurement was made.
-
134
-
points
sharpened. The detail is shown
Fig
in
19.3.2.
dynamic
The
range of this setup was
25 dB.
Diode Detector
Measurements were made
a rectangular lattice with
on
point-to-point spacing varying
Pin Contact
Sharpened
Waveguide Mouth
between 2 and 4
were
Fig 19.3.2
DETAIL OF DETECTOR
program.
Results
about
cm.
plotted with the aid
unsophisticated
an
Contours
of
computer
of a sample measurement are shown in
Fig
19.3.3. From this measurement, the 3 dB FWHM of the horn and
lens configuration was found to be approximately 5* in
both
planes.
Y
x
Fig 19.3.3
-
SAMPLE HORN PATTERN
Contour
Radiation pattern for setup of Fig 19.3.1.
lines
darker
are plotted at 2 dB intervals, with
10 dB.
-
135
-
lines
every
[19.4]
Transmission System
To analyze the measured scattered power, we need to know (1)
the
transmission
Poynting
volume)
flux
loss CL in the receiving
S, in the incident beam (at
and
(3)
the effective area AR
of
line,
the
(2)
the
scattering
the
receiving
antenna. When the system is aligned, a single measurement of
the
maximum
power as shown in Fig
CW
19.4.1
the
yields
quantity PC = SR AR CL, where SR is the Poynting flux at the
receiving antenna.
Defining RX and RR as the distances from
the scattering volume to the transmitting antenna and to the
receiving antenna respectively, we can write
R
S
Fig 19.4.1
CW
POWER
MEASUREMENT
R
=S
2
X
I RX+RR
GEOMETRY
19.4.1
FOR
LO
TRANSMISSION
Flux
S1 and SR are the
Poynting flux at the scattering volume and at the
antenna
receiving
respectively.
RR
Poyntin
Flux S
Power from
EIO
-
136
-
RX
which is the required quantity, is easily
so that SI AR CL,
determined. In one such calibration experiment, PC was found
to
19.3
be
coupler
involved
and
a
a
measured with
mW,
An
detector.
calibrated diode
in this technique is that plasma
assumption
refraction
not significantly change the Poynting flux.
that
directional
calibrated
does
Our estimate is
Poynting
beam broadening due to refraction causes the
flux to drop by less than 20%, a relatively small systematic
error in this experiment.
Preamplifier Gain
[19.5]
The preamplifier gain was measured using a low-power 0.8 GHz
from
source
analyzer.
battery
the
RF
and
system
supply
used,
from
the
Owing to
the
to
the
the sensitivity of the gain
The gain dropped 4 dB upon
supply voltage from 15 V to 11 V,
15 V to 8 V.
spectrum
calibrated
The gain was measured to be 36 dB.
supply voltage was also checked.
lowering
a
The gain change was
15 V and about 13.5 V.
-
137
-
and 10
negligible
dB
between
Appendix [20]
This
HIGH
appendix
filter
VOLTAGE
FILTER
FEEDTHROUGHS
describes the development
of
high
feedthroughs for the EIO power lines.
voltage
These devices
are easy to make and perform very well.
RF-tight
high voltage feedthroughs
provide
high
voltage
power
in
the
EIO
inside
The option of including
experiment's shielded cabinet.
power
to
(10 kV) are necessary to
supplies within the shielded volume is
view of the size of the power supplies;
attenuation
the
tackled,
they occupy two
[At the time this
or by filtering.
possibility
of
doing
an
the
impracticable
RF at 0.8 GHz must be kept out,
full-size racks.
the
either by
issue
experiment
was
with
2.45 GHz lower-hybrid waves was also a consideration.]
Several options are available.
down the center of a copper tube
interspace
Inner
Wrap
[Richards.81]
of a wire with series inductors and ferrite chokes
consists
running
The old scheme
[Fig
20.1].
The
is filled with a cement + graphite dust mixture.
Cement + Graphite
Composite
Outer
Conductor
Fig 20.1
FILTER/ABSORBER
RICHARDS'
-
138
-
FEEDTHROUGH
A
The principle is
few layers of mylar provide insulation.
ferrite beads and graphite all help
that the inductors,
problems:
These devices suffered a few
the TEM RF waves.
attenuating
(1)
RF
high
voltage
(2) the devices were not
leaking
(3) at least one was found to be
to reproduce
(possibly
suitable
the small inductors are not really
for the 1.0 A drawn by the filament
easy
one that had been replaced earlier due
motivation
this was the direct
fault);
in
a
to
for
tackling this problem.
Another
material
scheme is to use a commercial
microwave
that is rated for high voltage to fill a
absorbing
co-axial
Attempts were made using EMAiron 7190 and
line
(Fig 20.2).
8190
(magnetically
loaded
materials
made
Communications' Electronautics Division),
by
Dielectric
but the materials
failed miserably to meet their high voltage specifications.
Outer Co ductor
Inner
uctor
EMA-Iron
Microwave Absorber
Fig 20.2
ABSORBER-FILLED FEEDTHROUGH
-
139
-
The
third
scheme is to use a lumped
implemented
sections
as
with
conductors,
thin
shown in Fig 20.3.
component
The
C's
LC
are
very small spacing between inner
filter
co-axial
and
outer
and the L's are co-axial sections with a coiled
wire for the center conductor.
provide insulation.
A few layers of
mylar
Various configurations were tested and
worked well.
The
final adopted design has 6-1/2 sections in a 1/2"
diameter
gauge
and
5/8" long and the L sections are made
tinned
longitudinal
of
22
in
a
the nominal length of an L section
is
copper
plane;
Two
5/8".
also
0.478"
The (brass) C sections are
long brass tube.
8-5/8"
I.D.
wire
with
a
single
loop
insulation
wraps of 1.5 mil mylar provide
good to over 11 kV.
The
filters
measuring
were
tested
transmission
for
RF
tightness
by
of an 0.8 GHz signal and
directly
comparing
8
Inductive Half-Section
Inner
ctor
5Cond
.5"
Capacitive
Half-Section
Air
0.478"
Outer
Conductor
B
Mylar Wrap
0.500"
Fig 20.3
6-1/2 STAGE LC FILTER FEEDTHROUGH
-
140
-
RF Shielded Cabinet
Test Filter
RF Signal
Generator
Fig 20.4
FILTER TRANSMISSION
SETUP
TEST
Spectrum
Analyzer
with
the transmission of a simple
co-axial
wire-in-a-tube
(so as to account for mismatches and radiative power loss at
input
and
difference
in
the
output of the device;
transmission
The
attenuation.
is
see Fig
quoted
as
20.4.)
the
The
filter
test results are shown in Table 20.1
for
all six devices, measured after installation at both 0.8 and
2.45 GHz.
The
worst attenuations are 72 dB at 0.8 GHz
56 dB at the higher frequency.
Table 20.1
OF 6-1/2
Filter #
MEASURED TRANSMISSION
STAGE LC FILTER
Transmission (dB)
@ 2.45 GHz
@ 0.8 GHz
1
2
3
4
5
6
-78
-72
-72
-76
-76
-78
-
141
-57
-68
-65
-56
-61
-60
and
PROGRAMS
COMPUTER
Appendix [21]
Outline
[21.1]
this
in
described
are
data
analyze
to
(2)
and
geometries
scattering
determine
to
(1)
used
programs
computer
The
section.
The
codes
They
are
SBATPREP2
[21.3]
SCATBACL
[21.4]
2MM4016
Versator.
at
file
on
and
IV.
Nova
General
Data
the
for
FORTRAN
in
documented
r/a
and
N
1 1
solving
the
computes
the
of
sketch
used
to
product
the
calculates
convert
may
geometry
scattering
the
(normalized)
measured
-
142
scattering
angle
relation,
and
As
positions.
mirror
appropriate
also
program
dispersion
lower-hybrid
-
over
looping
for
made
the
determines
program
The
.
is
orientation
poloidal
and
1 1
Provision
interest.
of
waves
the
N
the
(4)
and
volume,
scattering
made
be
CPL,
the
of
location
the
(3)
horns,
receiving
and
incident
the
of
orientation
and
location
the
(2)
parameters,
plasma
the
(1)
provides
user
The
measurements.
scattering
particular
for
required
geometry
the
determine
to
performs
It
SCATPREP.
of
version
current
the
is
calculations
factor
[21.2]
SBATPREP2
This
The
Outline
all
are
[21.2]
of
[21.1]
an
(Fig
where
scattered
by
then
a
option,
21.2.1).
C
the
is
power
central
density
magnetic
field
program version
serial#
N:
SoATLEPX
8.0
r/a
NEO 0.67SE 19
RA
0.s0e
Nz 3.0 f---
nominal
r
Ni j
horn
coordinates
.10
XMIt -260S.5 660. 176.5 3.5
RECV 364.5 645.0 183.0 3.6
~
X
MIRR-I
6.00
49.0
0.44
MIRR-S
5.00
49.0
0.32
TV 352. 0
TPK
F2 -3.6394
F3
AREA 0.003931 M2
f
mirror
c
Jcoordinates
0.2
scattering
0.01393
volume
parameters
Fig 21.2.1
PS
into
SCATTERING GEOMETRY PLOT FROM SBATPL2
lower-hybrid wave spectral intensity
I(Nfl)
=
C PS
(PL is the launched lower hybrid wave power).
The
plasma parameters to be specified are the
line-average
electron density and the toroidal field. The program assumes
the following:
on axis.
centered
With this simplified
calculates the local plasma
SCATANG
(2) no poloidal
(4) plasma position
model,
parameters,
the cold plasma electromagnetic dispersion
solves
(see
parabolic density profile,
(3)
field,
(1) uniform toroidal field,
Appendix
angle
scattering
relation
is
to
[18.1])
used
e3.
determine
and
electromagnetic
The
because
N11
the
electrostatic
relation was found to be typically off by 10%.
-
143
-
subroutine
and
then
relation
then
the
dispersion
dispersion
The
scattering plane,
with the origin at the tokamak center (ie
range,
[0,360)
Angles are specified in a
at a major radius of 0).
degree
the
used are 2-D Cartesian coordinates in
coordinates
90*
with 0* being horizontally outwards and
vertically up.
geometry calculations are performed by
Coordinate
and SBATM2.
SCAT1 identifies the scattering
SCAT1,
SBATRS
volume
location and the incident and scattered
are specified by a point and a direction).
(rays
rays
SBATRS finds the
and
which the rays are reflected by the mirrors
at
points
routines
identifies the ports out of which the incident and scattered
rays
the
finds
SBATM2
emerge.
mirror
which
locations
appropriately reflect the rays.
Subroutine SBATPL2 makes the scattering volume sketch, which
the tokamak cross-section
includes
horns
(routine PHORN) and mirrors (PMIRR),
through
the
system,
3dB
points
The sketch is annotated
identify
values of numerous quantities that
the
the
the central rays
and the side rays at the
which define the scattering volume.
with
CROSEC),
(routine
the
particular case.
The
terms
places;
that
go into C are
calculated
in
appropriate
the factor containing plasma and wave quantities is
calculated
and the geometry factor is computed
in SCATANG,
in SBATPL2.
-
144
-
SCATBACL
[21.31
of
version
current
complements
SCATBACK,
SCATBACL,
the
SBATPREP2
by
returning
positions.
The
problem
positioned
in 1/2" steps and rotated to 1/20 accuracy,
NH
and
r/a
only
may
is that the mirrors
some fine-tuning is necessary to get mirror
be
and
accuracy.
SBATPREP2 returns mirror coordinates of arbitrary
So
mirror
given
for
coordinates
that may actually be set and yet have the right (or at least
With SCATBACL,
close enough) position and scattering angle.
this fine-tuning may easily be done.
The
structure
of
SCATBACL
similar
is very
that
to
of
SBATPREP2.
The
user inputs the plasma parameters and
horn
positions.
The
program then sits in a loop where the
user
enters
the
mirror
positions and the program
returns
the
location of the scattering volume and the particulars of the
detected wave.
Subroutine
SCAT2 traces the (central) rays to
the
nominal
center of the scattering volume. Subroutine SCAT3 determines
the
local
relation
plasma
for N11 .
parameters
and
solves
dispersion
the
Subroutine SBATPL2 is used to prepare the
optional sketches of the scattering geometry.
[21.4]
This
2MM4016
program
is used to analyze shot
-
145
data:
it
computes
scattered
power
multiplies
by
spectral
lower-hybrid
factor C to get
the
also
and
signal,
measured
the
from
intensity I(Nil).
The experimental data files contain electronically processed
of
(described in Section 9.8) proportional to the log
data
measured
the
to
log
from
power.
Program 2MM4016 converts the
signal
the
plasma
'real' units and
out
subtracts
Let VN be the
emission
and noise from the measured signal.
datafile
voltage corresponding to the receiver noise
(measured,
level
Let F be the
for example, on a no-plasma shot).
Then if VE is
electronics calibration factor (in dB/Volt).
the datafile voltage before the lower hybrid pulse is turned
on (this corresponds to plasma emission and noise) and VS is
A
pulse
hybrid
lower
the
the
power plus emission plus noi-se),
(scattered
scattered
noise
may be calculated (in units of the receiver
P
power
during
voltage
datafile
the
power).
F
F_
P
N
E
10
(Vs-VN)
10
- 10
=10
21.4.01
S
The
quantities
unchanged
when
the
within
noise
ms
intervals
assumes
calculation
to
and
1/2
typically
power
the
plasma
unit,
RF
5
that
the
power
is
turned
can
emission
acceptable
entirely
-
146
-
on.
RF
be
remains
emission
plasma
after
This
points).
7
or
over
averaging
by
taken
are
(6
millisecond
first
changing
V
VE
By
measuring
the
turn-on,
less
to
held
when
P
-
is
V
error
due
than
one
typically
5
in the 10 to 1000 range. VE is measured just before RF turnon.
The
enters (1) data array indices for
user
units,
computer
(=
power)
in
(3) the electronics calibration factor
in
(2) the
intervals,
time
two
the
level
baseline
noise
dB/Volt, (4) the scattering channel on the A-to-D converter,
(5) the run number,
PL.
program then sits in an outer loop where the
The
enters
(7) Nil,
calculated
the
outer
and (6) the injected lower-hybrid power
user
loop
(8) r/a and (9) the correction
by either SCATBACL or SBATPREP2.
factor
Within
is an inner loop where the user enters
shot number, which is analyzed by the program.
-
147
-
CPL
level
At this
may change data directories or stop.
user
(10)
the
a