Numerical Modeling of the Electra Electron-Beam Diode* D. V. Rose1, D. R. Welch1, S. B. Swanekamp2, M. Friedman3, M. C. Myers3, J. D. Sethian3, and F. Hegeler4. 1Mission Research Corp., Albuquerque, NM 87110 2TITAN/JAYCOR, McLean, VA 22102 3Naval Research Laboratory, Washington, DC 20375 4Commmonwealth Technology Inc., Alexandria, VA 22315 High Average Power Laser Program Workshop Naval Research Laboratory Washington, DC December 5 – 6, 2002 *Work supported by U.S. DOE through the Naval Research Laboratory.

Goal is to minimize electron energy losses in order to maximize energy deposition in the KrF gas on Electra. Detailed comparisons between measurements and numerical simulations provide a benchmark and develop confidence in the simulations as a design tool. Electra Facility Diodes and Laser Cell Applied B=1.4 kG Anode Anode Electron Emitter Hibachi Cathode Cathode Laser Cell The goal of this research project is to understand where the electron-beam deposits its energy in hopes that extraneous loss mechanisms can be identified and reduced. To date we have identified an instability in the diode that can lead to enhanced energy deposition in the foils and hibachi. We have developed a model for the instability which suggests a possible way to eliminate it. We have also characterized the electron beam energy deposition in the foils, hibachi, and KrF gas using a 3D single particle, coupled electron/photon transport code. In the next several years we hope to verify this instability on Electra and test the slotted cathode design as a way to eliminate it. We also will design and field new Hibachi/foils to reduce losses and improve energy transfer efficiency to the KrF gas. We will improve our modeling so that we can self-consistently simulate electron beam generation and acceleration in the diode, energy loss processes in the Hibachi and foils, and transport in the KrF laser cell. This work will then be coupled to laser kinetics and amplified stimulated emission (ASE) models being developed by Giuliani and Lemberg. X-ray generation and their effects on the laser optics and other critical components will also be investigated. Laser Window Anode Foil Anode Foil Pressure Foils 12/5/02 D. V. Rose, MRC Laser Beam

Basic Diode Physics Static field solutions using LSP in 1-D, 2-D, and 3-D simplified geometries. No beam rotation or shearing accounted for Scattering and energy loss of beam in foil and gas using ITS [1] Monte Carlo algorithms incorporated into LSP. Study role of backscatter on diode operation, especially losses to hibachi and foil. 12/5/02 D. V. Rose, MRC

Sample trajectory from 1-D diode simulation illustrates multiple passes through a 2-mil Ti pressure foil. Eo = 500 keV 1.2 atm Kr 2-mil Ti pressure foil 1-D LSP simulations of a parallel plate diode operated at 500 kV with backscattering from foil/gas define an upper limit on energy deposited into the foil: Energy fraction deposited in foil for case with perfect absorber behind foil: 11% Energy fraction deposited in foil for case with 30-cm KrF gas cell: 27% 12/5/02 D. V. Rose, MRC

1-D diode simulations show optimal energy deposition in gas cell for 500 keV operation at 1.2 atm of Kr. 1.2 atm Kr 2-mil pressure foils on both sides of gas cell Gas pressure not high enough to stop all of the beam for 600 keV operation 12/5/02 D. V. Rose, MRC

2-D periodic simulations illustrate the role of the floating field shapers (FFS) in reducing losses to the ribs. Eo = 500 keV 1.2 atm Kr 2-mil Ti pressure foil Slotted cathode 2.5 cm wide 12/5/02 D. V. Rose, MRC

Three cathode configurations considered, along with Hibachi ribs: 12/5/02 D. V. Rose, MRC

Current density across a single beam is more uniform with the floating field shapers. 12/5/02 D. V. Rose, MRC

Experimental Configuration With an anode Front view Without an anode 12/5/02 D. V. Rose, MRC

Good Agreement with Measured Current Density Found in LSP Simulations Flat Cathode w/Mark I hibachi 2-mil Ti Pressure Foil 1.2 atm Kr Faraday cups filtered with 1-mil Ti foil 12/5/02 D. V. Rose, MRC

Full 3-D EM Simulations Detailed simulations of the Electra diode including the Mark I hibachi and newly designed “cooled” hibachi. Comparisons with measured data highlighted for both flat and slotted cathodes. 12/5/02 D. V. Rose, MRC

Sample 3-D LSP Simulation with a slotted cathode: Cathode face, emission surfaces are 2-cm wide, with 4-cm center-to-center spacing, 7 deg. “tilt” (SCL emission from shaded regions only) Ribs (0.5 cm wide, 4-cm apart) (y=0) 12/5/02 D. V. Rose, MRC

Electron Beam Density Patterns Show Illustrate Beam Rotation in AK Gap ~ 550 keV operation Entering Ribs: Inside Ribs: 12/5/02 D. V. Rose, MRC

Electron beamlets are merged within 1-2 cm after entering gas Just After Foil: 1 cm Past Foil: 12/5/02 D. V. Rose, MRC ~ 550 keV, 1,3 atm Kr

No Rib Shadowing After ~2-cm of Gas Transport 12/5/02 D. V. Rose, MRC

3-D LSP simulations use a drive pulse that approximates the Electra voltage and current waveforms. 12/5/02 D. V. Rose, MRC

3-D LSP simulations of the full Electra pulse in good agreement with measured energy deposition efficiencies. Solid Cathode Strip Cathode 12/5/02 D. V. Rose, MRC Experiment: 47% (entire pulse) Experiment: 62% (entire pulse)

Summary: Detailed comparisons of Electra diode data in good agreement with LSP simulations. Benchmarked LSP code a powerful design tool for large-area electron beam diode/hibachi designs for ICF systems. Ongoing Work: Adding conductivity evolution model to laser gas Exporting 3-D energy electron energy deposition profiles from LSP to Guiliani et al. laser kinetics model 12/5/02 D. V. Rose, MRC