相對論效應的一個應用
清華大學物理系
朱國瑞
2006.10.11
Outline
An overview of vacuum electronics
 Principle and significance of the
electron cyclotron maser (ECM)
 ECM-based devices (gyrotrons)
and applications
 Mode competition in ECM-based
devices

電子流如何產生電磁波
-以速調管(klystron)為例
直流電子與電磁波作用: <P>t = <I0E0cosωt>t = 0
交流電子與電磁波作用: <P>t = <I0cosωtE0cosωt>t = ½I0E0
→ 需要一個「群聚」機制,使電子由直流變交流
Vacuum Electronics for the Generation
of Coherent Radiation
Microwave tubes: matured in the 1960s
1. Magnetron
Cornerstones: 2. Klystron
3. Traveling Wave Tube (TWT)
Relativistic electronics: 1970s – present
Cornerstones:
1. Free Electron Laser (FEL)
2. Electron Cyclotron Maser (ECM)
什麼是coherent radiation?
Comparison between Conventional
and Relativistic Electronics
Conventional
Microwave Electronics
Examples
Magnetron, Klystron, TWT
Relativistic
Electronics
ECM, FEL
Frequency
< 1011 Hz
1010 Hz – X-ray
Power
< 106 W
104 W – 1010 W
Electron Energy < 105 V
103 V – 1010 V
Beam Current
Basic
Equations
< 102 A
Circuit equations
+ Fluid equations
1 A – 106 A
Maxwell equations
+ Relativistic kinetic eq.
Basic Model of the
Electron Cyclotron Maser (ECM)*
RF structure
*Discovered independently by:
R. Q. Twiss,
(1958)
classical theory
A. V. Gaponov, classical theory
(1959)
J. Schneider,
(1959)
QM theory
R. H. Pantell,
(1959)
experiment
帶電粒子在均勻靜磁場中的迴旋運動
d
運動方程式:
pF
dt
F  qv  B
1. 牛頓: p  mv
 迴旋角頻率:  c 
qB
m (不隨能量而變)
2. 愛因斯坦: p   mv,  
F  qv  B
F v
(無法作功)
   const
qB
  c   m (隨能量而變)
1
v2
1
c2
Principle of the Electron Cyclotron Maser
– a Relativistic Bunching Mechanism
c 
eB
me
ECM-Based Devices (Gyrotrons)
fusion plasma heating
industrial processing
high-resolution space radar
particle acceleration
space radar
(not yet exploited)
Significance of the ECM
multiple photon
one photon
per electron,
per excitation, large interaction
large interaction space
space
multiple photon
per excitation,
interaction space
~ wavelength
Current and Potential Applications of
High-Power Millimeter/Submillimeter Waves
materials
processing
NTHU High Frequency Electrodynamics Laboratory
The NTHU Experimental
Gyrotron Traveling-Wave Amplifier
Comparison of the NTHU Gyro-TWT with the
state-of-the-art TWT
Planned Applications of the Gyro-TWT
1. Satellite and orbital debris
radar measurements:
W-band upgrade of the
Haystack radar (operated
by MIT Lincoln Laboratory)
2. Missile and space object
tracking:
Ka-band upgrade of the U. S.
Army Kwajalein Atoll radar
complex (operated by MIT
Lincoln Laboratory)
Gyroklystron and Applications
94GHz, 100kW Gyroklystron, W-band Advanced Radar for Low
Observable Control (WARLOC)
Naval Research Laboratory
Radar image of cloud from
the WARLOC
The Gyromonotron Oscillator
165 GHz, TE31,17 mode,
2.2 MW coaxial
gyromonotron for
fusion plasma heating
(Piosczyk et al.,2002)
D-T fusion reaction
Nature’s fusion reactor: Sun
Sea water
Energy
Application of the Gyromonotron:
Fusion plasma heating
ITER Tokamak
Participants: EU, USA,
Russia, Japan,
China, Korea
Cost: US$15 Billion
Completion date: 2015
Plasma temp: 108 K
Output power: 500 MW
ITER Plasma Heating System
R. Vernon et al., in the 16th ANS Meeting on the Technology of Fusion Energy, Madison, Wisconsin, 2004
ITER ECH System
R. Vernon et al., in the 16th ANS Meeting on the Technology of Fusion Energy, Madison, Wisconsin, 2004
Mode Competition in the Gyromonotron
“One should find such a start-up scenario which will provide the
initial excitation of the desired mode, which, being excited, will
suppress all parasites.”
G. S. Nusinovich, IEEE Trans. Plasma Sci. 27, 313 (1998)
K. E. Kreischer and R. J. Temkin, Phys. Rev. Lett. 59, 547 (1987).
operating
mode

2
0
final
voltage
Traces I and II correspond to
different ways to raise the beam
voltage to its final value.
2
parasitic
modes

2
0

  z20 2
Mode Competition in the Gyro-TWT
“Self-consistent beam perturbations associated with one mode
will appear as deleterious momentum/energy spreads to another
mode of different frequency and field structure.”
L. R. Barnett et al., Phys. Rev. Lett. 63, 1062-1065 (1989)
K. R. Chu et al., Phys. Fluid B. 3, 2403-2408 (1991)
TE11 output power and TE21 oscillation power versus the TE11 drive.
TE11
TE11
TE21
TE21
Mode Competition in the Gyro-BWO
Particle simulation (Ib = 4.8 A)
160
(a)
Pout (kW)
Pout (kW)
160
120
80
40
Experiment (Ib = 4.88 A)
(a)
120
80
40
0
0
0
1
2
0
3
1
(b)
(b)
l=2
l=3
l=2
36
(G
ency
u
q
e
r
F
Hz)
ncy (G
e
u
q
e
Fr
Hz)
l=3
35
35
l=1
34
3
33
32
2
1
0
s)
Time (
3
Time (s)
Time (s)
36
2
l=1
34
3
33
32
2
1
0
Time (
s)
K. F. Pao, T. H. Chang, C. T. Fan, S. H. Chen, C. F. Yu, and K. R. Chu,
Phys. Rev. Lett. 95, 185101 (2005).

The latest-starting, lowest-order l = 1 mode eventually
dominates.