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www.cst.com | CST EuMW 2011 Presentations| October 2011 | 1
Electron Devices Simulation with
CST STUDIO SUITE™ Richard Cousin, CST
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Brief History, principles of Vacuum Tubes
Electron Guns (Generation of electron beam sources)
Amplifiers (TWT)
Oscillators (Magnetron)
Relativistic devices
High Power Microwave tubes
VIRCATOR
MILO
Overview
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Brief History of Vacuum Devices
1883 Thermo-electronicemission (T. A. EDISON) Light emissio
1895X-Rays (W. ROENTGEN) Radiology
1896First Wireless Telegraph (G. MARCONI)
1907TRIODE (Lee DE FOREST)
1939KLYSTRON (VARIAN Brothers)
1940
MAGNETRON (BOOT, RANDALL, WILLSHAW
1942TWT (R. KOMPFNER)
1970HPM (VIRCATORS-BWO
90s-00MILO-RKO-RELRelativistic Devices
ConventionalDevices
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MESFET
10-1
1
10
105
10-2
104
107
106
103
102
.1 1 10 100 1,000 10,000
Frequency (GHz)
A v e r a g e P o w e r ( W )
Klystron
Helix TWT
Gridded Tubes
CFA Gyrotron
BWOFEL
TWT
Vacuum Devic
BJT
SIT
Power Device Technology
FET
HEMT
Solid State Devices
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Classification of Electron Devices
Conventional Devices(Amplifiers – Oscillators) Relativistic Devic(HPM)
Emission process Thermionic Explosive
Pulse duration• Continuous•
Pulse > 100 µs
• Transient•
100s of ns
Output Power < 100 MW 100 MW < P < 10 G
ApplicationsIndustrial, Medical, Space
(embedded devices)Military
Research activiti
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Principle of Vacuum Tubes
• A vacuum tube is an electron device in which an electron beam isinteracting with an electromagnetic wave
• The energy is transferred from the e-beam to the EM-wave
Power Source
E-beam creation
Interaction Process
RF in
(Amplifiers)
RF out
(Amplifiers - Oscillator
DissipatedPower
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Electron Gun: Generation of e-beams
Pierce Gun Magnetron Injection Gun(MIG)
Cold emissiongenerating inten
hollow beams
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Electron Gun: PIERCE
• Thermionic emission (I = µV3/2)• Space charge and Temperature limited• Solid beam formation• Focusing electrodes• Low current emission (< 1A)
Space charge iterations
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Electron Gun: Cold emission
• Space charge limited emission•
Hollow beam formation• Focusing electrodes• High current emission (several kA)
Space charge iterations
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Amplifiers(Traveling Wave Tubes – TWT)
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Amplifiers: Principles
B
• Longitudinal static magnetic field applied (e-beam focusing)•
Interaction into Slow Wave Structures (SWS)• The electron velocity modulation creates bunches• The electron kinetic energy is converted into RF-Energy• The Static B-Field doesn’t contribute to the interaction process
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Slow Wave Structure geometry
• Helical structure of 40 turns
• The first and 4 last turns are embedded in resistive couplers
• Turns 4-36 constitutes the linear gain region
• The RF signal is introduced at turn 4 and analyzed through thedifferent voltage probes
50 mm
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Eigenmode solver @ 5 GHz
• Two different algorithm (AKS, JDM)
• Display the 3D-EM field inside the structu
• Take into account the lossies
• Perform Q-factor calculations
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Study of 1 period of the SWS
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Dispersion Diagram
TW
BW
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Synchronism conditions in the SWS
Evidence of e-beam modulation
• If electron velocity = phase vno global energy transfer occurbecause the energy transferredEM wave amplified is equal thetransferred to the electron beathe EM slow wave.
• If the electron velocity is sligover the phase velocity of the some EM power is transferred m
from the e-beam to the RF-stru
Ve > V
Evidence of the Travelling Wave
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Evidence of the Travelling WaveAmplification process at 5 GHz
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RF In RF OutSlow Wave Structure
Particle Beam
More complex TWT geometry
50 period folded waveguide for broadbandtravelling wave tube application
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Particle Trajectory (hot test)
• Simulation performed with the self-consistent particle incell (PIC) solver of CST PARTICLE STUDIO®
• Interaction of wave and particle beam becomes evidentdue to velocity modulation towards TWT end
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Output signals (hot test)
RF In RF Out
GAIN
Simulated 20.24 dB
Pierce small signal theory 20.9 dB
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Oscillators(Magnetrons)
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Oscillators: Principles
RF Window
B
• Crossed-Field Devices• The External Static B-Field is perpendicuthe E-Field components• The synchronism condition is defined by geometry which fixes the single operatingfrequency• The electron drift velocity (E/B) equals tphase velocity of the slow EM-wave• The static B-field participates to the inteprocess• The interaction is leading to so-called “sformation
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Magnetron Structure
Dimensions:rc=0.57 cm ra=1.92 cm rv=3.42 ch = 7.2 cm
Angle = 20°Number of Vanes = 6
Modified Version of the MIT A6Magnetron Small aspect ratio rc/(ra-rc) = ∏- Mode favourable
[1] J. Benford, J. A. Swegle, E. Schmiloglu, „High Power Microwaves“, 2nd Edition, Taylor & Franc[2] A. Palevsky and G. Bekefi, „Microwave Emission from Pulsed Relativistic Beam Diodes. II. The
multiresonator magnetron.“, Phys. Fluids, 22, 986, 1979.[3] H.W. Chen, C. Chen, „Numerical Studies of Relativistic Magnetrons“, PFC/JA-92-34, 1992.
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Eigenmode Simulation
Cold Test: Interaction prediction
∏-Mode 2∏-Mode
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Applied Voltage & Resulting E-Field
Applied Voltage Potential
E-Static Field
• Voltages are applied as CST EM STUDIO®sources
• Corresponding routines are calledautomatically internally by PIC solver
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• The Static B-Field is calculated to allow magnetic insulation andsynchronism condition in the magnetron structure
• There exists a cutoff condition to allow magnetron oscillation
Predefined B-Field
T r
r
r
V
e
m B
a
c
a
H 17.01
22
1
2
2
H B B leads to the magnetronoscillation
l f l d
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PIC Simulation of Closed Structure
Stabilized Signal
One distinct peak @ ∏–Mode
f hot
= 3.7 GHz
Field recorded with field probe in one position
PIC Si l i f Cl d S
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Particle Trajectory
Spoke Formation according to ∏-Mode Interaction
PIC Simulation of Closed Structure
M t S l L Fil
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Magnetron: Solver LogFile
Number of Meshcells 2
Number of Particlesmax
Number of Particlessteady state
Time CPU 2h 5
Time GPU 4
Speed Up Factor
New Feature V.2012GPU acceleration with PIC solve
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Relativistic Devices(Vircator & MILO)
Relativistic Devices for HPM applications
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Relativistic Devices for HPM applications
• Technologies based on Classical devices with higher output power (range
of GW output power)
• Usually driven by high voltage generator (hundreds of kVs)
• Explosive emission cathode (velvet-like coating)
• Limited microwave pulse (hundreds of ns)
• Operating frequency in GHz frequency range
Vircator structure
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wavegfor
mon
elefp
emission surfaces
Particle Trajectory
Vircator structure
Vircator results
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E - f i
e l d s p e c
t r u m
/ [ k V / c m
]
f/GHz
O u
t p u
t p o w e r /
G W
t/ns
Power>1GW
A. Santos, B.S. Araújo Filho, J. J. Barroso, H. S.Maciel, „Microwave Generation by a VirtualCathode Enclosed in a Circular Cavity PlacedTransversally in a Cylindrical Waveguide“,Proceedings of the 9th IEEE International VaccumElectronics Conference (IVEC), Monterey, USA, 2008
Vircator results
E - f
i e l d
a t
p r o
b e
/ [ k V
/ c m
]
t/ns
Magnetically Insulated Line Oscillator (MILO)
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Collector
Anode SWS(4 coupled cavi
Cathode
Magnetically Insulated Line Oscillator (MILO)
Similar to a linearrelativistic magnetron
[1] R. Cousin et al, „Gigawatt Emission from a 2.4 GHz compact Magnetically InsulatOscillator (MILO)“, IEEE Transactions on Plasma Science, Vol. 35, No. 5, Oct. 20
Slow Wave Structure Eigenmodes
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Er
Ez
Pi-mode configuration at 2.45 GHz
Transverse Magnetic mode (TM01)
Possible interaction with an e-beam propagating along thecathode structure
Slow Wave Structure Eigenmodes
Slow Wave Structure Eigenmodes
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Er
Ez
Pi-mode configuration at 2.68 GHz
Hybrid Electro-Magnetic mode (HEM11)
Possible interaction with an e-beam propagating along thecathode structure in Pi-mode
Slow Wave Structure Eigenmodes
Dispersion Diagram
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Dispersion Diagram
TM01
TM02
HEM11
HEM21
F r e q u e n c y
Phase
• Phase velocity depends only on the geometry parameters.
•
In an oscillator particles have to be in exact synchronism. The main Mointeraction depends on the geometry
Diagnostics and Sources
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Diagnostics and Sources
Voltage sourceexcites a ramped
voltage
Excitation function
Field probesCurrent monitorVoltage
monitor
Waveguidfor abso
MILO Operating Frequency
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MILO Operating Frequency
Signals recordedwith field probes
50 ns needed for stable RF oscillations
2 compeeting modes as predicted inCousin et al
Main interaction in PI-mode of theTM01 mode
Smaller peak belongs to PI-mode
configuration of HEM11 mode
MILO oscillating regime
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MILO oscillating regime
MILO oscillation at 2.48 GHzon first TM mode
First TM mode cutoff at 1.68 GHz
TM extraction through the outputwaveguide
2.6 GW peak output power
Particle Trajectory
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Particle Trajectory
Spoke formationaccording to PI-Mode
Summary/Conclusions
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Summary/Conclusions
CST STUDIO SUITE™ can handle
Electron Devices simulation Amplifiers/Oscillators
Cold and hot test facilities
GPU acceleration with PIC solver (New in V.2012)
Only one model necessary which can be exchanged CST EM STUDIO® for analysis of static EM fields
CST PARTICLE STUDIO® for any kind of particle tracking
CST MICROWAVE STUDIO® for dispersion analysis and S-
parameter simulations of couplers and tubes