1. Advances in Vacuum Electronic Sources of Coherent Radiation Thomas M
Advances in Vacuum Electronic Sources of Coherent Radiation Thomas M. Antonsen Jr. Departments of ECE and Physics University of Maryland April 13, 2016

2. Vacuum Electronic Device (VED) a.k.a. a Tube
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

3. Who is that Audiophile?
Professor Roy

4. Vacuum Electronic Devices Strong Suit
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

5. Generic VED Source Energy recovery Power out beam-wave interaction
Driver (Amplifiers only)
Energy recovery
Electron Beam formation
Power out
Static magnetic fields
beam-wave interaction

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

7. Current Modulation: DC  AC
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

8. Velocity Modulation O-Type bunching
power in
power
out
Cavity 2
I(t)
Cavity 1
Cavity 2
Field in cavity 1 gives small time dependent velocity modulation
Fast electrons catch up to slow electrons giving large current modulation.
Cavity 1

9. Different Classes of O-Type Devices
Electron
Gun
Interaction Circuit RF In
Out
Depressed
Collector
Sever
Electron Beam
Impedance
Helix Traveling Wave Tube (TWT)
Interaction
Circuit
Coupled - Cavity TWT
Extended Interaction Amplifier
Klystron

10. Synchronism in a Linear Beam Device
Dispersion curve
w (kz)
Doppler curve
kz vz

11. Beam Wave Interaction Simulations
Baruch Levush, Alexander Vlasov, Igor Chernyavskiy, Simon Cooke, John Pasour, George Stantchev,
Khanh Nguyen1, Edward Wright1 ,
David Chernin2, John Petillo2 and Thomas Antonsen2
US Naval Research Laboratory, Washington, DC
1Beam Wave Research, Inc., Bethesda, MD
2 Leidos Inc., Reston, VA
Work supported by the US Office of Naval Research

12. Apology: I am not really a computer expert.
Computation
Apology: I am not really a computer expert.

13. 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”

14. 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

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

16. 3D Time Domain Electromagnetic Modeling
The 3D Finite-Difference Time-Domain (FDTD) Algorithm
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
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
centered difference

17. Challenges in PIC Simulations of Vacuum Electronic Devices

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

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

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

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

22. Spatial - Temporal Characteristics for Different DevicesL t
Electrons
Radiation T v g
> t v g
<
Electrons
oscillator
amplifier T
Radiation x z L
FEL

23. Saturation by Phase Trapping
Space

24. Example of Hybrid Approach: TESLA-CC Code
RF Fields in cavities outside beam tunnel are found as a solution of equivalent circuit equations
Gun
RF Input
RF Output
Collector
TESLA: Telegraphist’s Equations Solution for Linear beam Amplifiers
Full solution of Maxwell’s equations rewritten as matrix telegraphist’s equations inside beam tunnel CL
Equivalent Circuit Approach:
Solve time dependent circuit equations
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

25. TESLA-FW Large Signal Code
Calculate electron beam properties using gun code
Gun-code MICHELLE calculations of beam transport
Beam properties
TESLA-FW NRL Code (Beam-wave interaction)
“Transmission line Model for Folded Waveguide Circuits”, T.M. Antonsen, Jr., et al., IEEE Trans. on Electron Devices, 60 (9), 2013.
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
Use 3D Electromagnetic (EM) Codes for dispersion and EM field distribution
Color-coded EM field distribution
Results of dispersion and impedance fitting in TESLA-FW to match the given ANALYST data
High accuracy (better than 0.1% in dispersion approximation and ~1% in impedance approximation) *

26. Parametric Approach: CHRISTINE-FW
Circuit model:
Dispersion and impedance:
Current induced in circuit by bunched beam:
Beam model:
Fixed radius disks
~20-30 per wavelength
Axial (z-) motion only
AC and DC space charge fields are included.
Values for , L, c, and Z1 (and attenuation per cell) must be specified. Ys Ib Z0 L
Representation of a bunched beam z
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
Currents Induced in Gaps

27. 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
Trapezoidal shape with 5% difference on the top and on the bottom
Top
Beam tunnel off-set in Y direction
Bottom
Include all measured details
BT alignment:
(+x)
(-x)
Ø is 3.7% less
Ideal Ø a2 z x
N = 64 gaps W x y
Shifted by 12.6% a1
As-Built
Ideal Symmetric
Approx SWG cross
sectional profile
Beam Tunnel Location
“IN”
“OUT”

28. Modeling of G-Band TWT Using Large Signal Codes
Small Signal Gain
CPI GHz EIK, 5W
NRL G-band SWG TWT
Drive Curves
Experimental high power set-up showing the CPI GHz EIK driving the compact NRL Serpentine Waveguide (SWG) TWT.
Beam voltage
11.7 kV
Collector current mA
Beam diameter
190 um
Beam transmission
>86%
Output Power at flange
33.6 W
Large Sig. Gain flange-to-flange
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.

29. Neptune Simulations of NRL G-Band SW TWT
NRL 220 GHz Serpentine TWT amplifier (simulations performed using measured dimensions)
Transfer curves
Small Signal Gain
Data 11.7kV
Neptune 11.7kV
11.9kV
11.7kV
K. T. Nguyen et al., “Design Methodology and Experimental Verification of Serpentine/Folded-Waveguide TWTs” IEEE T-ED Special Issue on Vacuum Electronics, 2014
Good Agreement between Neptune predictions and measurements

30. NRL-CPI Ka-Band Power Booster TWT
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
FW Booster
~3-5 dB sat
CC-TWT Driver
~40 dB sat
38 cm
20 cm
Goal: Power  Bandwidth
~ 2 kW x 5 GHz
CC-TWT Driver + FW-TWT Booster
RF input
70 mW
RF Out
RF In
B. Levush, IVEC 2014

31. 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

32. History of Parametric Models
• Linear beam devices (TWTs)
• Numerical models

33. History (continued)
• Gyro devices
• Mode competition

34. History (cont.)
• Free electron lasers