Download Determining R/Q Using SUPERFISH

SLAC KLYSTRON LECTURES
Lecture 9
March 31, 2004
Other Microwave Amplifiers
TWT, CFA, Gyro-amplifier, SSA
Robert Phillips, [email protected]
Glenn Scheitrum, [email protected]
Stanford Linear Accelerator Center
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Suggested Resources:
Movie viewer: Quicktime, RealPlayer, etc.
References:
Traveling Wave Tubes, J. Pierce,
Principles of Traveling Wave Tubes, A.S. Gilmour, 1994
The electron cyclotron maser, K.R. Chu, Review of Modern Physics, 2004
Microwave Power Engineering, Vol. 1, E. Okress editor, Academic Press, 1968
Microwave Magnetrons, Collins, MIT Radiation Laboratory Series, V6, 1947
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TWT – THE OTHER LINEAR BEAM TUBE
• Brief History – Development and application
• How TWT’s differ from klystrons
• Why TWT’s, not klystrons
• Characteristics of two basic types:
Transmission line circuit
Waveguide circuit
• Operating principles and characteristics summarized
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Pioneers
1933 Haeff
TW deflection devices
1940 Lundenblad
TW amplifier
1943 Kompfner
Early amplifiers
1946 Pierce
Early work at Bell Labs.
Published complete theory.
“Traveling Wave Tubes,” 1950.
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TWT vs. Klystron
Similarities:
• Beam formation, focusing and collection are the same
• Input and output rf coupling are similar
• TWT uses a traveling wave version of the discreet cavity interaction of
•
the klystron
Large overlays in beam voltage, current and rf power output
Differences:
•
•
•
•
Bandwidth
Klystron ≈ 1%
Waveguide TWT ≈ 10%
Transmission Line (Helix) TWT ≈ 1 - 3 octaves
• Form factor more amenable to low-cost, light-weight PPM focusing
Market Impact of Difference
• A single ECM TWT tube type produced by Varian for ECM produced in
greater numbers than all of the klystron amplifier tubes ever built.
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Basic Helix TWT
If this were a coax line in TEM mode (not coiled), vp/c = 1, independent of
frequency, with unlimited bandwidth and no axial E.
By coiling the conductor, axial velocity is reduced by the amount of the
increase in path length, a substantial Ez is created, and vz remains largely
independent of frequency. Gain is obtained by synchronizing the beam
velocity with the axial wave velocity
(from Principles of Traveling Wave Tubes, A. S. Gilmour)
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ω-β diagram showing -1 space harmonic
(from Principles of Traveling Wave Tubes by A. S. Gilmour)
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Helix and contra-wound helix derived circuits
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9”
Photograph of ring-loop circuits, L-band through Ku-band
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ω-β diagram for connected ring circuit showing -1 space harmonic suppressed
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ω-β diagram for TE10 waveguide (from A. S. Gilmour)
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ω-β diagram for periodically-loaded waveguide (from A. S. Gilmour)
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Folded waveguide (from A. S. Gilmour)
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Coupled-cavity circuit – a practical embodiment of a folded waveguide
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Cloverleaf fundamental forward wave circuit produced 5 MW peak power at 10% BW
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Gyro-amplifiers
•Gyro-TWT – medium power, high gain, moderate bandwidth, 15%-30% efficiency
•Gyro-klystron – high power, high gain, low bandwidth, 20%-40% efficiency
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Gyro-amplifiers – electron cyclotron maser interaction devices
Basic interaction physics:
In a magnetic field, electrons orbit flux lines at the cyclotron frequency
eB0
c 
 m0
V0
V0
1

 1
 1
2
2
v
mc
511000
1 2
c
e
where e is the electron mass, m0 is the electron mass and B0 is the
magnetic field in Tesla
If an RF electric field is applied in the orbit plane, the momentum of the
orbiting electrons will be modulated.
Negative mass effect: Electrons which gain energy have increased
mass, larger orbit radius, and reduced angular velocity.
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Available beam power is
proportional to beam area.
Compare beam area of helix,
coupled cavity (similar to
klystron), and cutoff
overmoded waveguide of
gyro-amplifier.
Tunnel size in TWTs and
klystrons limited by a, gyroamplifiers use overmoded
waveguide sections. For a
gyroklystron, rb is limited by
need to have drift tubes cut
off to operating mode
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Gyrodevices interact with the transverse momentum of the beam
Parameter a = v / v║ is the ratio of transverse to parallel velocity
Normal range of a is 1 – 2 making the rotational energy 50% to 80% of
total beam energy
At an a of 1, a total efficiency of 30% implies a rotational efficiency of 60%
It is important to minimize energy spread in the beam as the efficiency
drops dramatically with increased axial velocity spread.
This is especially important in gyro-amplifiers where axial velocity spread
smears the bunch longitudinally as it drifts between cavities.
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CPI-Northrop-NRL
94 GHz Gyroklystron
100 kW peak power
10 kW average power
0.7% bandwidth
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Crossed field amplifiers
• High peak and average power, high efficiency, 10% bandwidth devices
• Low gain ~10 dB, needs multi-device amplifier chain
• Noise due to cycloidal electron trajectories
• Current produced by secondary emission, no heater required
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Equations of motion for an electron in crossed electrostatic and magnetostatic fields
Non relativistic Lorentz force equation F = ma = q ( E + v x B )
For planar magnetron this separates into three orthogonal components
d 2x
e
dy
dz 


E

B

B
z
y
 x

d 2t
m
dt
dt 
z
Ez
By
Assume constant Ez
d2y
e
dz
dx 


E

B

B
x
z
 y

d 2t
m
dt
dt 
and By
Ex=Ey=Bx=Bz=0
d 2z
e
dx
dy 


E

B

B
y
x
 z

d 2t
m
dt
dt 
d 2x e
dz

B
y
d 2t m
dt
x
d 2z
e
dx  Integrating d2x/dt2, defining initial
   Ez  By 
d 2t
m
dt  conditions and substituting into d2z/dt2
yields
2
d 2 z  eB 
e

z


Ez
 
2
d t m
m
Solving for z (and x) gives
z
m Ez 
 eB  
1

cos
 t 
e B 2 
 m 
x
m Ez  eB
 eB  
t

sin
 t 
e B 2  m
 m 
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Block diagram of CFA amplifier chain at 11 GHz for multi-megawatt system
Solid state
Driver 10 W
TWT or klystron
Intermediate amp
30 dB 10 kW
CFA
+10 dB
100 kW
CFA
+10 dB
1 MW
CFA
+10 dB
10 MW
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Solid State Amplifiers (SSAs)
•Broad bandwidth, low power, moderate gain, low noise, low efficiency devices
•Small size, low cost manufacturing process
•Ideal for use as drivers for high power sources
•Two basic transistor types BJTs and FETs
•Both are used at 3 GHz for power amplifiers but FETs dominate at higher
frequencies
•Both are limited in frequency by transit time effects that are similar to those
encountered by vacuum triodes
•New materials GaAs and GaN produce higher mobility carriers and higher
breakdown voltage to extend the performance envelop of solid state amplifiers
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Summary
The discussion has covered solid state amplifiers, traveling wave tubes,
crossed field amplifiers, and gyro-amplifiers.
Obviously solid state amplifiers and traveling wave tubes do not produce the
high peak power required for accelerator sources. They function well as drivers
and as low power, wide bandwidth sources.
CFA’s and gyroklystrons can produce the required power but each has
significant handicaps in comparison to a high power klystron.
The CFA can produce efficiencies in excess of 70% but has very low gain and
requires a multi device amplifier chain to drive the final output CFA.
The gyroklystron has a problem with device efficiency, increasing a to minimize
the energy in axial velocity causes increased axial velocity spread in the beam.
Gyro-amplifiers use overmoded RF circuits and therefore have a heat transfer
advantage as the frequency increases.
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