IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 22, NO. 5, OCTOBER 1994
87 1
Influence of Sideband Oscillations
on Gyrotron Efficiency
W. C. Guss, M. A. Basten, K. E. Kreischer, Member, IEEE, R. J. Temkin, Fellow, IEEE,
T. M. Antonsen, Jr., S . Y. Cai, G. Saraph, and B. Levush
Abstract-We report the observation of sideband mode effects
on the efficiency of overmoded gyrotron operation. Two cavities
were designed and operated which differed in the presence of
sideband modes. In one version of the cavity, parasitic backward
waves modes were observed and efficiencies were approximately
22% at 40 A beam current. With the use of a multi-mode selfconsistent nonlinear code, a modified design was generated which
eliminated the sideband modes. Experimentswere conducted with
this new cavity which produced efficienciesof approximately33%
at 30 A and 27% at 40 A beam current, but with a slightly higher
velocity ratio than seen with the earlier cavity. An additional
cavity, also with no sideband modes but with a longer cavity
length and therefore higher Q obtained powers up to 1.3 MW
with an efficiency of 39% at a 40 A beam current.
I. INTRODUCTION
H
IGH power gyrotron oscillators are proposed [ 11-[3] as
plasma heating sources at frequencies near the fundamental electron cyclotron resonance and its second harmonic.
Increased microwave generation efficiency is an important
consideration in the implementation of gyrotrons as microwave
sources.
In a previous experimental investigation [4] of the efficiency
of a high-frequency, high-power gyrotron oscillator, experimental results were compared to the computational efficiency
estimates from a single-mode, nonlinear, self-consistent computer code [ 5 ] . At low beam currents (Ib < 20 A), good
agreement existed between the experimental and computational efficiencies. At higher beam currents (20 < 16 < 50
A), discrepancies of varying amounts were noted.
Multiple modes have been observed to have a significant
effect on gyrotron efficiency. Standard gyrotron operation is
in a single mode far from boundaries with neighboring modes.
However, operation near those boundaries can result in the
presence of several modes. When these multiple modes are
observed, a significant reduction in efficiency is also observed.
Manuscript received September 24, 1993; revised August 23, 1994. This
research is supported by the Department of Energy Contracts DE-AC0278ET5 1013 and DE-FG05-87ER52147, and under appointment to the Magnetic Fusion Science Fellowship program administered by Oak Ridge Associated Universities for the U.S. Department of Energy.
W. C. Guss, K. E. Kreischer, and R. J. Temkin are with the Plasma Fusion
Center, Massachusetts Institute of Technology, Cambridge, MA 02 139 USA.
M. A. Basten, was with M.I.T., Cambridge, MA. He is now with the
Electrical Engineering Department., University of Wisconsin, Madison, WI
53706 USA.
T. M. Antonsen, Jr., S. Y. Cai, G . Saraph, and B. Levush are with the
Laboratory for Plasma Research, University of Maryland, College Park, MD
20742 USA.
IEEE Log Number 9406110.
Typically, two modes were observed with approximately equal
amplitudes and resulting overall efficiency reduced by a factor
of two. Operation in this unusual regime suggests the possibility of low amplitude multimode operation under standard
operation conditions. Standard gyrotron operation has been
studied [ 6 ] ,[7] using a multimode, nonlinear, time-dependent
code with a fixed-field approximation. The modes considered
for these studies were the CO-and counter-rotating modes of
the main and nearest modes with differing azimuthal indices,
and as a result the frequencies were given by the cold-cavity
frequencies for that cavity. Recently measurements were made
of the power levels and frequencies of sideband oscillations
[8] under normal operation in high power gyrotron operation
containing a short weakly-tapered cavity. Power levels of the
observed sideband modes were approximately 30 dB down
from the main mode and the frequencies were separated by
frequency differences much larger than w / Q from the cold
cavity frequencies.
To further study this type of gyrotron operation computationally, a multi-mode, nonlinear, self-consistent theory [9]
and computer code (MAGY) were developed. Backward as
well as forward modes with several azimuthal mode indices
were included. Standard gyrotron operation far from mode
boundaries was analyzed to determine whether low amplitude
multi-mode sideband operation might be present which would
similarly decrease the efficiency. The resulting relative power
and frequencies of the sideband modes were in good agreement
with experiment.
Using the multi-mode code, cavity design changes were
made which produced a design which successfully eliminated
the sidebands. Several cavities were designed for operation
without sidebands. We report here observations of the sideband
modes and our study of their influence on the efficiency of
gyrotron operation. And although much of the current gyrotron
research is conducted at 110-140 GHz, gyrotron oscillators
operating in high order modes are under investigation for
higher frequency (230-280 GHz) gyrotrons. The problem
of sideband mode excitation in such oscillators will be far
more severe than in the present generation of gyrotrons.
The present results will be useful in carrying out those
experiments.
The following section outlines the theory of sideband
mode generation through a four-wave mixing process. In
Section 111, the experiment and diagnostics are described,
and in Section IV, the results are reported. Conclusions
are contained in Section V.
0093-3813/94$04.00 0 1994 IEEE
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872
IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 22, NO. 5, OCTOBER 1994
11. THEORY
170
The modes of a weakly tapered gyrotron cavity can be
approximated as TE,,,
modes of a circular cylinder cavity
where m , p , and y are the azimuthal, radial and axial mode
indices, respectively. The oscillation frequency w is given
approximately by
W”C2
= IC2 = IC;
+ k;
(1)
where k l = .;,/a
(the cutoff frequency is k l c ) , a is the
cavity radius, and U;, is the p t h zero of J k ( z ) . The axial
wavenumber, kll, is given by y r / L for a uniform closed
cylinder of length L. In the present theory, the axial mode
structure will be determined self-consistently for an open
resonator in the presence of an electron beam. The condition
for excitation of the cyclotron maser instability is
where q ,2
1
1 are the axial and transverse electron velocity
components,,BII = q / c , , B l = . u ~ / c , y ; =
~ l-/?;-/?;,B is
the axial magnetic field, Re is the electron cyclotron frequency
and e , m are the electron charge and mass respectively. The
linear theory of the gyrotron indicates that (1) and (2) apply
exactly in the limit of vanishingly small electron beam density.
Equations (1) and (2) are plotted in Fig. 1 for a particular
q and the case of the TE16,2 mode, which was studied
experimentally, and the nearby TE15,2 and TE17,2 modes.
Values of key parameters in Fig. 1 are a = 0.764 cm, B = 5.73
T, ,BII = 0.255 and y = 1.157 (80 kV). For other values of P I I ,
or equivalently a(= pl/,Bll),beam lines of varying slope are
defined. Fig. 1 indicates that excitation of the desired mode,
TE16,2, can lead to simultaneous excitation of an unwanted
mode such as TE15,2 since the beam line (2) intersects the
waveguide curve (1) for both the TE16,z at kll > 0 and TE15,2
modes at kll < 0. The beam line does not intersect the TE17,2
mode curve. Nevertheless, the TE17,z can still be excited via a
nonlinear, four-wave mixing process [lo]-[ 121 at a frequency
w+1 where
160
5
N
150
g
a
140
U.
130
120
-2000
-lo00
0
1000
2000
Fig. 1. Oscillations are possible at intersections of the cavity dispersion
line (parabola) and the Doppler shifted beam line. The assumed physical
parameters are those of the cavity proper.
cavity. We have also included the effects of space charge, and
the electron velocity spreads using a triangular distribution
for the perpendicular velocity. The width of the distribution
was adjusted so the computational efficiency agreed with the
experimental efficiency.
Fig. 2 shows typical electric field amplitude profiles for the
TE15,2,TE16,z and TE17,2 mode triplet for the short weaklytapered cavity. The TE15,Z backward wave mode is excited
in the downtaper that leads to the beam tunnel. Because the
taper cuts off this mode, backward wave power is reflected
toward the gyrotron output window where it may be observed.
The forward wave move (TE17,z) is cutoff in the gyrotron
cavity and must be excited at a larger radius corresponding to
a location in the uptaper, and propagates directly to the output
window. The axial locations for the maximum electric field
for the two modes do not coincide. For typical beam voltages
(80 kV) and currents (40 A), a velocity ratio a of 1.64 and a
2w0 - w+1- w-1
S W Fz 0.
(3) magnetic field of 5.73 T, the theoretical frequency separation
Here, WO and w-1 are the frequencies of the TE16,2 and TE15,2 [SI of the TE16,2 mode and the sideband TE15,2 and TE17,2
modes respectively and Sw is the four-wave beat frequency modes is about 5 GHz and is roughly independent of a.
mismatch. In addition, the azimuthal mode numbers must For modes excited individually in a cylindrical cavity .without
satisfy a similar matching condition, viz. m+l = 2m, - m P l , tapered walls, the expected separation would be about 7 GHz.
where m+l = 17,mo = 16, and m-1 = 15. The frequency The detected sideband output powers 181 relative to the TE16,2
w+1 may be displaced somewhat from the normal frequency mode were both x -30 dB. While this may appear to be a very
of the TE17,2 mode. For a high Q cavity, this displacement small output power, the amplitude of the computed electric
should be less than the resonance width w+1/Q. In the fields in the cavity as shown in Fig. 2, can be substantial. In
relatively low Q cavity under consideration, the beam is able the computational model, these spurious electric fields cause a
to significantly alter the axial structure of the modes, such that significantspread of the electron energies and interfere with the
electron bunching process. From the numerical model, reduced
the four-wave resonance condition can be satisfied.
The multi-mode, multifrequency, time dependent code used efficiency is observed which is attributable to energy spread
for these calculations has been described in detail elsewhere induced by the TE15,2 backward wave. The magnitude of the
191. In this code, the transverse dependence of the radiation predicted efficiency decrease was sensitive to the quality of the
field is expanded as a set of waveguide modes. Each of the injected beam. With a cold beam the decrease was too large. It
modes has a time dependent axial profile which is determined was somewhat mitigated by the addition of ~ 2 0 %
pitch angle
self-consistently by the response of the electrons and which spread ( ~ 5 %
perpendicular velocity spread) which reduced
satisfies appropriate boundary conditions at both ends of the the amplitude of the sideband modes. Further degrading the
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GUSS et al.: INFLUENCE OF SIDEBAND OSClLLATlONS ON GYROTRON EFFICIENCY
'
n
-
TE15.2
0.20
- TE1 6.2
- - TE17,2
0.15
-
0.10
-
0.05
-
m
873
0
W
Q)
7J
3
r
.e
Q
E
cr:
L
I
/
-
///\
x - .
/
\
/
>
=
'
-2.0 -1.5 -1.0 -0.5 0.0 0.5
1.0
1.5
2.0
Fig. 2. Electric field amplitude as a function of axial distance for the
TE15.2,TE16,2 and TE17.2 mode triplet. The beam enters from the left and
exits toward the gyrotron window on the right, The middle of the 0.5 cm cavity
is located at z = 0. The initial non-linear uptaper length is approximated by
a linear 6' taper.
TABLE I
short
weaklytapered
tapered angle (")
cavity radius (cm)
cavity length (cm)
Leff/A
Qcoid
1
0.76
0.50
4.96
310
short
stronglytapered
4
0.76
0.70
4.4
430
long
stronglytapered
4
0.76
1.10
5.56
800
(b)
beam by the addition of ~ 5 %
energy spread could bring
the computational and observed efficiencies into agreement.
However, the possible origin of such a spread is not known.
Additionally, the relative power in the sidebands was sensitive
to the shape of the pitch angle distribution. Clearly, the role
of beam quality on sideband excitation merits further study.
111. EXPERIMENT
The experiment was conducted in a manner similar to our
previous studies [4]. The electron beam was produced from a
thermionic cathode in a magnetron injection gun (MIG) and
accelerated to 80 kV. The control-anode voltage was 24.5 25.0 kV. Beam currents could be varied up to 50 A. The pulse
length was about 3ps. The magnetic field was approximately
5.72 T, with no magnetic tapering, producing in the cavity, a
beam with radius Tb = 0.53 cm. The average velocity ratio
( a ) of the beam electrons was measured using a capacitive
probe [13] and typically varied between 0.5 and 2.5. Gyrotron
operation was optimized for the TEl6,2 mode at 146 GHz.
Fig. 3. Cavity profiles and cold cavity electric fields of the short
weakly-tapered (a) and short strongly-tapered (b) cavities.
Power and efficiency measurements were made using a
Scientech Model 372 calorimeter. Two other diagnostics, a
wire-mesh Fabry-Perot interferometer and a power-calibrated
single ended mixer and (yttrium-iron-garnet)YIG-tuned filter,
were used to detect the sideband modes. The Fabry-Perot
etalon was 5 cm in diameter using 50 linekm wire mesh.
The reflectance at x140 GHz was measured [14] to be 0.966
and the resulting theoretical intensity resolution Imax/Imin
"N
3.3 x lo4 or about 35 dB. Frequency measurements were
made using a calibrated wavemeter at the output of the FabryPerot. The output of the etalon was sent through a calibrated
attenuator to a detector diode. The attenuator setting was
adjusted to maintain a constant diode voltage to minimize
effects of possible diode nonlinearities. This system gave
relative intensity measurements to within 3 dB and frequency
measurements to within 0.1 GHz. In the mixer plus YIG filter
diagnostic, the sideband modes were beat against the TE16,2
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IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 22, NO. 5, OCTOBER 1994
814
155
I
n
N
I
c3
W
0
a00
0
145
L
2
2
U
a
L
G
t
135
1.50
1.75
2.00
01
2.25
AYG
Fig. 4. Observed (open symbols) and computed (solid symbols) frequency
for the TE15.2,TE16.2, and TE17.2 modes as a function of velocity ratio
for the short weakly-tapered cavity at low beam current, I b = 15 A.
m
-10
-
-20
-
1
1
'17.2 I'l6.2
0 F-P
U
W
L
2z
primary mode in the single ended mixer and the difference
.-al
frequency was sent through the YIG filter. After calibration,
0
relative powers of about 45 dB were detectable. This system
al
-30 0
gave frequency separations to an accuracy of about 0.05
GHz. Intensity and frequency measurements from these two
independent systems were generally in very good agreement.
I
The cavities tested in this study are characterized in Table I.
-40
1.50
1.75
2.00
2.25
The weakly-tapered cavity is similar to the design previously
(a)
studied [4], except it had a slightly larger radius and employed
a nonlinear rather than linear uptaper. The measured efficiency
(b)
as a function of beam current was very close to that of
Fig. 5. Observed (open symbols) and computed (solid symbols) power
the earlier cavity. The multi-mode code used to predict the relative to the TE16,2 mode as a function of velocity ratio for the short
multi-mode behavior of the short weakly-tapered cavity was weakly-tapered cavity at low beam current, I b = 15 A.
used to design a cavity that would not produce any spurious
modes, and would yield higher efficiencies. Elimination of
IV. RESULTS
the sideband modes was accomplished by increasing the
Sideband mode operation was studied [4] in detail for
downtaper angle from the 1' of the weakly-tapered cavity
to 4" for the strongly-tapered cavity. This modification had current values of 15 A and 40 A in the short weakly-tapered
the effect of moving the axial location of the backward wave cavity. At the 15 A level, the agreement between the singleresonance much closer to that of the TE16,2 mode which then mode code efficiency and the short weakly-tapered cavity
suppressed it. The two cavities had approximately the same experiment is good. At 40 A, the agreement is not as good,
effective cavity length (L/X x 5), and approximately the same and sideband modes might be expected to be important in
Q(x400). The short weakly-tapered and the short strongly- explaining the disagreement. Fig. 4 and Fig. 5 show the
tapered cavities are compared in Fig. 3. The values of L , f f are backward wave frequency and relative power for the short
twice the root-mean-square (RMS) widths of the cavity electric weakly-tapered cavity at low beam current Ib = 15 A as
field from cold-cavity code modeling of the respective cavities. a function of the velocity ratio, ( a ) as measured by the
For the short weakly-tapered cavity, the cutoff frequencies of capacitive probe. Most of the data for this beam current was
the lowest order axial modes are 138.28 GHz for the TE15,2 taken with only the Fabry-Perot interferometer. Similar data
mode, 145.29 GHz for the TE16,2 mode and 152.27 GHz for for the high beam current case are shown in Fig. 6 and Fig. 7.
the TE17,2 mode, approximately 7 GHz apart.
Data from the Fabry-Perot and YIG-tuned filter are shown
Y
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GUSS et al.: INFLUENCE OF SIDEBAND OSCILLATIONS ON GYROTRON EFFICIENCY
155
875
0
3
1
1
TE17,2
h
9
-10
W
I
1
1
ti
5 -20
.-aJ
4-
L
Q,
-30
a,
3
A
A
A
-40
135
0.
1.5
1.6
1.7
1.8
1.9
2.0
(a)
Fig. 6 . Observed (open symbols) and computed (solid symbols) frequency
for the T E ~ ~ , ~ , T Eand
I ~TEli.2
. Z . modes as a function of velocity ratio
for the short weakly-tapered cavity at high beam current, I b = 40 A.
m
-10
'17.2 "18.2
0 F-P
A nG
-
mbory
U
v
0
L
2s -20 and are in good agreement. The frequency separation ( x 5
GHz) and relative powers ( Z -30 dB) are comparable for
both the low and high beam current cases. The magnitude
of the frequency separation is significantly smaller than the
separation of the lowest order forward modes, and is one of
the indicators that a backward wave mode was observed, and
that a nonlinear four-wave mixing process was operative.
The optimized T E I ~ efficiency
,~
as a function of beam
current was measured and is shown in Fig. 8 along with the
computational efficiencies. The cathode and cavity magnetic
field were optimized for each current value. The present
experimental results with the weakly-tapered cavity as well
as our previous results [4], show efficiency decreasing at
beam currents above about 20 A. The highest efficiency was
observed at low current and was about 27% for ( a ) z 2.0.
At the high current level, the efficiency was about 22% for
( a ) = 1.45.
Similar studies were made for the short strongly-tapered
cavity. A wide range of cathode and cavity magnetic fields, and
( a ) were explored to determine whether the spurious modes
might be present for optimal as well as nonoptimal operating
conditions. For beam current levels of 15 A and 40 A, no
spurious modes were observed to the signal-to-noise limit of
the diagnostics. The multimode code also indicated that only
single mode emission should be present. The efficiency as a
function of beam current (Fig. 8) has a behavior similar to
that of the weakly-tapered cavity. With this cavity, the beam
current corresponding to the peak efficiency increased from the
earlier x 1 5 A to ~ 2 A.5 The largest efficiency was measured
at this new low current and was 32% at ( a )= 2.5, and at high
-4n
.- I
1.5
1.6
1.7
1.8
1.9
2.0
(a)
(b)
Fig. 7. Observed (open symbols) and computed (solid symbols) power
relative to the TE16.2 mode as a function of velocity ratio for the short
weakly-tapered cavity at high beam current, I b = 40 A.
current the efficiency decreased to about 27% at ( a )= 1.7 In
general, the short strongly-tapered cavity had its best operation
at higher velocity ratios than the short weakly-tapered cavity,
which contributed to its slightly higher efficiencies.
A long strongly-tapered cavity was also tested. It also
showed no indication of the spurious modes to the limits
of our diagnostic detectability which was consistent with the
computational model. Its best operation was at velocity ratios
lower than those for the short weakly-tapered cavity. The long
strongly-tapered cavity has a monotonically rising efficiency
with beam current as shown in Fig. 9. At a current corresponding to our previous low current (15 A), the efficiency was 30%
at ( a ) = 1.4, and at high current, the highest efficiency was
observed at about 39% with ( a ) = 1.3 for a peak power of
1.3 MW.
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IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 22, NO. 5, OCTOBER 1994
876
60
m
50
40
m
r-----l
5
0
0
O0
i
h
s
m
0
U
0
o o
0
0
a
.
30
U
c
0
.-a,
0
0
0
O
2
U
0
0
20
Lu
8
0
10
0
n
U
0
10
20
30
40
50
Beam Current (A)
Fig. 8. Optimized output microwave efficiency as a function of electron
beam current at a constant beam voltage v b = 80 kV for the short
weakly-tapered cavity (circles) and strongly-tapered cavities (squares). Solid
symbols are calculated efficiencies from the multi-mode code.
v.
0
10
20
30
40
50
Beam Current (A)
Fig. 9. Optimized output microwave efficiency as a function of electron
beam cumnt at a constant beam voltage vb = 80 kV for the long
strongly-tapered cavity. Solid symbols are calculated efficiencies from the
multi-mode code.
DISCUSSION
AND CONCLUSIONS
reduced beam quality and cavity Q, may be more important
in
determining the efficiency.
We have developed a multi-mode, nonlinear, self-consistent
A second, longer strongly-tapered cavity, was constructed
theory and computer code which predicts the frequency and
relative power of several sideband modes with differing az- which did produce much higher efficiency at high beam current
imuthal mode numbers. Measurements of the spurious mode (Ib = 40 A). In contrast to the short cavities, the efficiency
frequency and relative power in the short weakly-tapered monotonically increased as a function of beam current up to
cavity at a beam current of 40 A agree well with those Ib = 40 A. We attribute this to ( a ) remaining approximately
predictions. Using the multi-mode code, it was possible to constant with beam current unlike the short cavities which
design a cavity which did not, to the detection limits of our showed a much larger ( a ) range. At the maximum current
diagnostics, support the sideband modes, also in agreement studied, 40 A, a power of 1.3 MW was obtained for an peak
.
Q of this cavity was about twice
with the theoretical and computational predictions. Because the efficiency of ~ 3 9 %The
cavity sthght section and uptaper were the same for the short that of either of the shorter cavities and maybe responsible,
weakly-tapered and strongly-taperedcavities, we conclude that in some as yet unexplained manor, for the higher efficiency.
the downtaper angle determined whether the backward-wave Unfortunately, the ohmic wall loading of the longer cavity is
too high for it to be CW relevant. In order to utilize a high
mode can be excited and generate the forward T E I ~mode
,~
Q cavity in a CW gyrotron, operation in a higher order mode
in the uptaper via the four-wave mixing process.
We now compare the two short cavities, which have similar would be necessary.
Q values and similar expected performance with regard to efACKNOWLEDGMENT
ficiency and RF field profile. In the case of the weakly-tapered
Parts of this experimental program were conducted using
cavity both simulation and experiment show the presence of
sideband modes, and for the strongly-tapered cavity, both the facilities at the Francis Bitter National Magnet Laboratory,
simulation and experiment show the absence of sideband Cambridge, MA. We also gratefully acknowledge helpful dismodes. The simulated efficiency for the strongly-taperedcavity cussions with T. Grimm and M. Blank and the computational
is much higher than for the weakly-tapered cavity due to the assistance of W. Menninger. W. Mulligan and G . Yarworth
absence of these sideband modes. However, in the experiment assisted in fabrication of the experiment.
the performance of the strongly tapered cavity, while better
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CUSS et al.: INFLUENCE OF SIDEBAND OSCILLATIONS ON GYROTRON EFFICIENCY
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811
K. E. Kreischer, photograph and biography unavailable at time of publication.
R. J. Temkin, photograph and biography unavailable at time of publication.
T. M. Antonsen, Jr., photograph and biography unavailable at time of
publication.
S. Y. Cai, photograph and biography unavailable at time of publication.
G. Saraph, photograph and biography unavailable at time of publication.
W.C. Guss, photograph and biography unavailable at time of publication.
M. A. Basten, photograph and biography unavailable at time of publication,
B. Levush, photograph and biography unavailable at time of publication.
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