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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

[email protected]

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




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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


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

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