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

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

Who is that Audiophile? Professor Roy

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

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

Examples L3 Ka Band Power Module http://www.linkmicrotek.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.

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

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

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

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

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

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

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

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

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

Challenges in PIC Simulations of Vacuum Electronic Devices    

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)

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

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

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

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

Saturation by Phase Trapping Space

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

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) *http://web.awrcorp.com/Usa/Products/Analyst-3D-FEM-EM-Technology

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

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”

Modeling of G-Band TWT Using Large Signal Codes Small Signal Gain CPI 218.4 GHz EIK, 5W NRL G-band SWG TWT Drive Curves 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-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.

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

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 gain @ sat CC-TWT Driver ~40 dB gain @ 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

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

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

History (continued) • Gyro devices • Mode competition

History (cont.) • Free electron lasers