Thomas M. Antonsen Jr.
Departments of ECE and Physics
University of Maryland
April 13, 2016

Vacuum Tube amplifiers are favored by some audiophiles.
They have a “warm” sound.
Will be the subject of a plenary talk at IVEC 2016
IVEC = International
Vacuum Electronics
Conference

Professor Roy

Used in Military/Commercial/Research Applications
High Power
2 MW 170 GHz CW Gyrotrons for fusion plasma heating
Multi-GW 1 GHz pulsed sources for HPM “effects”
High Frequency
220 GHz folded waveguide travelling wave amplifier
XFEL Stanford LCLS
High Efficiency
C-Band Helix TWT for satelite communications (> 60%)
SLAC Klystron

Electron Beam formation
Driver (Amplifiers only)
Power out
Energy recovery
Static magnetic fields beam-wave interaction

L3 Ka Band
Power Module http://www.link
microtek.com
Monica
Blank
170 GHz CPI Gyrotron
IEEE IVEC http://ieeexplore.ieee.org
Experimental high power set-up showing the CPI
218.4 GHz EIK driving the compact NRL Serpentine
Waveguide (SWG) TWT.


Density modulation gridded tubes inductive output tubes
Velocity modulation (O-Type) klystrons
Traveling wave tubes
Spatial modulation (M-Type)
Magnetrons
Cross field amplifiers
Density modulation effective only for low frequencies due to grid capacitance

power in power out
10
2
Cavity 2
I(t)
0.5
1
1.5
0
0 1 2 3
Time
4 5 6
Cavity 1
Field in cavity 1 gives small time dependent velocity modulation
Cavity 2
8
6
4
Fast electrons catch up to slow electrons giving large current modulation.
2
Cavity 1
0
0 5 10
Time
15 20

Electron
Gun
Helix Traveling Wave Tube (TWT)
RF
In
RF
Out
Sever Sever
Depressed
Collector
Electron Beam
Interaction Circuit
Electron
Gun
Impedance
Electron
Gun
Extended Interaction Amplifier
RF
In
Interaction
Circuit
RF
Out
Depressed
Collector
Electron
Gun
Electron Beam
RF
In
Coupled - Cavity TWT
RF
Out
Interaction
Circuit
Depressed
Collector
Electron Beam
Klystron
RF
In
Interaction
Circuit
RF
Out
Electron Beam
Impedance
Depressed
Collector
Impedance Impedance

E ( x , t ) = Re { E exp [ ik z z – w t ]}
Dispersion curve w (k z
) w
TWT w
= k z v z
BWO
Doppler curve k z v z
p
/d 0 p
/d 2 p
/d k z

Baruch Levush, Alexander Vlasov, Igor Chernyavskiy, Simon Cooke,
John Pasour, George Stantchev ,
Khanh Nguyen 1 , Edward Wright 1 ,
David Chernin 2 , John Petillo 2 and Thomas Antonsen 2
US Naval Research Laboratory, Washington, DC
1 Beam Wave Research, Inc., Bethesda, MD
2 Leidos Inc., Reston, VA
Work supported by the US Office of Naval Research

Why is Modeling and Simulation Important?
• Understanding of basic physical processes
• Understanding and diagnosing particular experiments
• Designing improved experiments
• Optimizing designs for “ first pass success”

Basic Code Types
• Steady State Trajectory Codes
- electron guns
- depressed energy collectors
• Computational Electromagnetics Codes
- cavities
- periodic structures
• Beam-Wave Interaction Codes
-parametric
-PIC
-hybrid

Reality
Parametric Models
• Many approximations
- Synchronous interactions
- Requires subsidiary calculations
- Can Incorporate measured data
• Computationally efficient
Hybrid Models
-Incorporates the
Best features of the other two
First Principles
(PIC)
• few approximations
-high self fields
-one calculation incorporates all physics
• Computationally intensive

3D Time Domain Electromagnetic Modeling
The 3D Finite-Difference Time-Domain (FDTD) Algorithm
Simulation domain is subdivided into a 3D Cartesian grid of cells
Yee grid
Electromagnetic field components are associated with the edges and faces of each cell
Maxwell’s Equations are expressed as centered finite difference equations
(in space and time) – and solved in time using an explicit leapfrog scheme
E x n

1 / 2
H x n

1 

E x n

1 / 2 
H x n 
 t
 x
 t


 x z

 y
H
E y n

1 / 2 z n   z
 
H y n  y
E z n

1 / 2

J x n
 centered difference
• 3D FDTD is widely used for time-domain electromagnetic simulation in research…
– Exploration of new concepts – changes to 3D geometry/topology are easily represented
– Time-domain model can include non-linear physics and transient effects
– Full electromagnetic beam-wave interaction predicts amplifier gain, instabilities
16

Challenges in PIC Simulations of Vacuum
Electronic Devices
17

GPU Accelerated PIC Simulations
FDTD algorithm for electromagnetics
(explicit time step)
NRL Code Neptune was created to target GPU simulation
Based on existing algorithms – adapted for the GPU architecture
Boris algorithm for particle time step, with charge-conserving current deposition
13.7M cells, 1M particles
CPU
Conformal representation of metal surfaces
(accurate geometry discretization)
CPU
GPU
GPU
Simulation speed (normalized to 6-core “Sandy Bridge” CPU)
18

Parametric Models Based on
Multiple Time Scales Analysis
• Separation in length scales l helix
< < L l gyro
= v z
/ W c
< < L l wiggler
< < L w T transit
= w L / v z
> > 1
FEL
• Separation in time scales - gyrotron oscillator
T = 2 w
< <
L v z
< <
Q w
< < t rise
6 n sec < < 250 n sec < < 6 p sec < < 10  sec

Parametric Approach
Amplifier Model
Fields
E rf
( x , t ) = i
B rf
( x , t ) = i
 A ( z , t ) e ( x ) exp [ i y ] + c .
c .
 A ( z , t ) b ( x ) exp [ i y ] + c .
c .
e ( x ) b ( x )
Phase y
= k z z
– w t w ( k z
) w ( k z
) e ( x ) b ( x ) w ( k z
) found in separate calculation
Amplitude d
A ( z )
Determined by
Parametric Code

Parametric Equations
Signal Amplitude

 t
+ v g

 z
+ g ( z )  A ( z , t ) w p i
U d
2 x
^ j ×
* ( x ) exp [ – i y ]
Particle Equations
Ensemble of nonlinear trajectories sampling all phases d g dt
=

 t
+ v z

 z g
= q mc 2 v × E rf
+ E sc beam d y dt
= k z v z
– w

Spatial - Temporal Characteristics for
Different Devices
T t
0 v g
> 0
Electrons t
Radiation amplifier
L
T x w
TWT
0 w
= k z v z
BWO
FEL
p
/d 0 p
/d 2 p
/d k z v g
< 0
Electrons
Radiation oscillator
L z

Saturation by Phase Trapping
Phase
Space

Example of Hybrid Approach: TESLA-CC Code
RF Input
CL
Equivalent
Circuit
Approach:
Solve time dependent circuit equations
RF Output
RF Fields in cavities outside beam tunnel are found as a
Collector solution of equivalent circuit equations
TESLA: Telegraphist’s Equations
Solution for Linear beam Amplifiers
Full solution of Maxwell’s equations rewritten as matrix telegraphist’s equations inside beam tunnel
Electron beam modeling:
• Solve 3D equations of particle motion in symmetric (2D) RF fields
• AC and DC space charge effects are included
• Realistic focusing magnetic fields
• Initial beam particles distribution can be imported from a gun code (including spreads due to thermal effects)
• Extensive diagnostics of beam dynamics
24

Calculate electron beam properties using gun code
Beam properties
Gun-code MICHELLE calculations of beam transport
Use 3D Electromagnetic
(EM) Codes for dispersion and EM field distribution z=-L
Color-coded EM field distribution
V n-1
*http://web.awrcorp.com/Usa/Products
/Analyst-3D-FEM-EM-Technology
TESLA-FW NRL Code (Beam-wave interaction) i

(0)
V n i

(0)
Y s
“Transmission line Model for
Folded Waveguide Circuits”,
T.M. Antonsen, Jr., et al., IEEE
Trans. on Electron Devices , 60
(9), 2013.
1000
500
•
Separation of external structure region from beam tunnel region
•
Solve discretized circuit equations for fields external to beam tunnel
•
Relativistic 3D equations of electron motion
• Reproduce full solution of Maxwell
Equations inside the beam tunnel V n+1 z=0 z=L
Results of dispersion and impedance fitting in
TESLA-FW to match the given ANALYST data
2000
TESLA-FW dispersion
3D EM code ANALYST
TESLA -FW
ANALYST
1500
High accuracy (better than 0.1% in dispersion approximation and ~1% in impedance approximation)
0
Phase Advance [Deg]
Frequency
25

 Circuit model:
• Dispersion and impedance: cos
   cos
   sin

Z
Kino

V s
2
2 P
 
Z
0 sin sin


 
L c w
2
 w c
2 ;
   i
2
Y s
Z
0
; Z
0

Z
1
1
 w c
2
/ w 2
Values for

, L, w c
, and Z
1 cell) must be specified.
(and attenuation per
Y s
I b
Z
0
I b
•
Current induced in circuit by

I t e
 
  bunched beam:
DC
 e
*
  exp

 gap field arrival shape
time of
 i w t
 dz particle
L z
Representation of a bunched beam
 Beam model:
•
Fixed radius disks
─ ~20-30 per wavelength
• Axial ( z) motion only
• AC and DC space charge fields are included.
Iterative Self-Consistent Solution for the Gap Voltages and Particle Trajectories:
Compute
Gap Voltages from
Circuit Eqns
Integrate
Beam Eqns of Motion in
Gap Fields
Compute
Currents
Induced in Gaps
26

Sensitivity Study of G-Band NRL
Serpentine/Folded Waveguide TWT
Extra space due to brazing: extra rectangle of 1.5% of W size of SWS
Top
Trapezoidal shape with
5% difference on the top and on the bottom
Beam tunnel off-set in Y direction
BT alignment:
(+x)
(-x)
Bottom
240
220
280
260
After Brazing
11.7 kV Beam
Before Brazing
200
Include all measured details
180
180 200 220 240 260 280
Phase Advance [deg]
300 320
Ø is 3.7% less a2 x z
N = 64 gaps
“IN” “OUT”
Ideal Ø
W a1
Approx SWG cross sectional profile y x
Shifted by 12.6%
As-Built Ideal
Symmetric
Beam Tunnel Location
27

Modeling of G-Band TWT Using Large Signal
Codes
15
20
Small Signal Gain
Measured+2.9 dB
TESLA
CHRISTINE
CPI 218.4 GHz
EIK, 5W
NRL G-band
SWG TWT
10
5
0
200 205 210 215 220 225 230 f/GHz
235 240
60
Drive Curves
50
40
30
20
10
0
0 2 measured at Flange: 11.70 kV measured at Flange: 11.90 kV
TESLA-FW : 11.70 kV
TESLA-FW : 11.90 kV
12 4 6 8
Pin (at Flange) [W]
10 14
Experimental high power set-up showing the CPI
218.4 GHz EIK driving the compact NRL Serpentine
Waveguide (SWG) TWT.
Beam voltage 11.7 kV
Collector current 104-110 mA
Beam diameter 190 um
Beam transmission >86%
Output Power at flange 33.6 W
Large Sig. Gain flange-toflange
10 dB
Frequency 218.4 GHz
C.D. Joye, et. al.
“ Demonstration of a High
Power, Wideband 220 GHz
Serpentine Waveguide
Amplifier Fabricated by UV-
LIGA”, IVEC 2013 .
28

Neptune Simulations of NRL G-Band SW TWT
NRL 220 GHz Serpentine TWT amplifier
(simulations performed using measured dimensions)
Small Signal Gain
Ckt Small Signal Gain
11.7 kV, 105 mA collected, Raw+2.9dB
Transfer curves
50
15
218.4 GHz
40
10 Data 11.7kV
Neptune 11.7kV
11.9kV
11.7kV
30
5
20
0
10
-5
-10
190 200 210 220
Frequency (GHz)
230 240 250
K. T. Nguyen et al., “Design Methodology and Experimental
Verification of Serpentine/Folded-Waveguide TWTs”
IEEE T-ED Special Issue on Vacuum Electronics, 2014
0
0 2 4 6
Input Power (W)
Good Agreement between Neptune predictions and measurements
8 10
29

FW Booster
~3-5 dB gain @ sat
RF input
70 mW
NRL-CPI Ka-Band Power Booster TWT
CC-TWT Driver + FW-TWT Booster
• Driver (CC-TWT):
– Output power limited by drive-induced oscillation (DIO)
• Booster (FWG-TWT):
– Advantages over CC-TWT
• Easier broadband matching – increased margin of stability
RF In RF Out
20 cm 38 cm
CC-TWT Driver
~40 dB gain @ sat
Goal: Power  Bandwidth
~ 2 kW x 5 GHz
B. Levush, IVEC 2014
30

Conclusions
•
Varity of design codes suitable for accurate prediction of operation of millimeter wave amplifiers has been developed, verified and validated recently in NRL:

Fast parametric 1D code CHRISITINE-FW

Hybrid 2.5D code TESLA-FW

Accelerated GPU based PIC code Neptune
• NRL beam-wave interaction codes together with gun/collector design code MICHELLE (Leidos/NRL) and commercial 3D electromagnetics
(ANALYST, HFSS) and magnetostatic (MAXWELL) codes are providing opportunities for:

Design Improvement

New optimized design

Tolerance analysis

First cut success design
31

History of Parametric Models
• Linear beam devices (TWTs)
-J. R. Pierce, in Traveling Wave Tubes , New York: Van Nostrand,
1950.
-J. E. Rowe, Nonlinear Electron-Wave Interaction Phenomena
(Academic Press, New York, 1965).
-L. A. Vainshtein, "The Nonlinear Theory of Travelling Wave Tubes:
Part I, Equations and Laws of Conservation", Radio Eng. Electron.
(USSR) (Engl. Transl.) 7 , 92-108 (1957).
• Numerical models
- N. J. Dionne, IEEE Trans. Electron Devices , ED 4, p. 365, 1970.
- H.K. Detweiler, JPL Quarterly Technical Review , vol. 1, no. 1, pp.
106-115, 1971.

History (continued)
• Gyro devices
-A. V. Gaponov, M. I. Petelin, and V. K. Yulpatov, Radiophysics and
Quantum Electronics 10 , 794-813 (1967).
-V. L Bratman, M. A. Moisev, M. I. Petelin, and R. E. Erm,
Radiophys. Quantum Electron. 16 , 474-480 (1973).
-P. Sprangle and A. Drobot IEEE Trans Microwave Theory Tech.
MTT 25 , 528 (1977).
K. R. Chu, A. T. Drobot, H. H. Szu and P. Sprangle, IEEE Trans
MTT 313(1980).
-A. W. Fliflet, M. E. Read, K. R. Chu, and R. Seeley, Int. J. Electron.
53 , 505-521 (1982)
-A. K. Ganguly and S. Ahn Int. J Electr 53, 641 (1982)..
• Mode competition
-G. S. Nusinovich (Review) IEEE Trans. Plasma Sci. 27 , (1999).
I. G. Zarnitsyna and G. S. Nusinovich, Radiophys Quantum Electr.
17, 1418 (1974).
-D. Dialetes and K. R. Chu, Infrared and Millimeter Waves 7,
(1983).
-A. Bondeson, W. Manheimer and E. O tt, ibid

History (cont.)
• Free electron lasers
-W. Colson, Phys Lett A 64, 190 (1977).
-A. A. Kolomenskii and A. N. Lebedev Sov. J Quantum Electr.
8,
879 (1978).
- T. Kwan, J. M. Dawson and A. T. Lin, Phys Fluids 20, 581
(1977).
- P. Sprangle, C. M. Tang, and W. Manheimer Phys Rev. A 21,
302 (1980).
- D. Proznitz, A. Szöke, V. K. Niel, Physic of Quantum
Electronics: Free Electron Generators of Coherent radiation 7, 175
(1980).
- Y. Bogomolv, V. bratman, N. S. Ginzburg, M. I. Petelin, A.
Yunakovsky, Opt. Comm. 36, 209 (1981).
- J.C. Goldstein, B. McVey, B. carlsten and L. Thode, Nucl. Instr.
Meth A285, 192 (1989).