1 Electra Foil Heating Analysis D. V. Rose, a F. Hegeler, b A. E. Robson, c and J. D. Sethian c High Average Power Laser Meeting PPPL, Princeton, NJ October 27-28, 2004 a)ATK Mission Research, Albuquerque, NM b)Commonwealth Technologies, Alexandria, VA c)Naval Research Laboratory, Washington, DC 2 The key components of a Krypton Fluoride (KrF) Laser Laser Input Electron Beam Foil Support (Hibachi) Cathode Laser Gas Recirculator Laser Cell Kr + F 2 (+ Ar) Pulsed Power System Amplifier Window BZBZ 3 1D Simulations: Isolate contributions to foil heating from: Primary or first pass electrons electrons back-scattered from the foil Electron scattered back into the foil from the gas. Develop functional forms for easy estimation of foil heating 4 1D Lsp foil runs at 500 keV (flat top) No diode fields. Average Reflected and Transmitted Energy and Current Density as a Function of Foil Thickness 5 1-mil Fe 5-mil Fe A comparison of the backscattered electron energy distribution from the foil only for a 500 keV electron beam. 6 Power deposition in foil WITHOUT re-injection of backscattered electrons (and perfect absorber behind foil) 1D calculations, single-pass for 500 keV electrons 7 Adding backscattering from gas (electrons scattered into AK gap are lost) 500 keV 500 keV 8 Fractional Power Deposition (P deposited /P injected ) is compared at 500 keV for various thicknesses of iron and aluminum, isolating the contributions from the gas-scattered and diode re-injected electrons. 500 keV 500 keV 9 Backscatter and foil deposition are independent of gas pressure assuming that the pressure is high enough to stop most of the beam in the gas cell length: 500 keV e-beam, no diode fields Gas composition fixed at 60% Ar, 40% Kr 1.0 atm case run with and without applied 1.4 kG B-field (no change in results) 10 Voltage scans: Deposition in foil is reduced with increasing voltage, but backscattered electron quantities only weakly affected: 11 Calculated transmitted current fraction for a mono- energetic electron beam in good agreement with data and models: Model and data from E. DAnna et al., J. Vac. Sci. Technol. 17, 838 (1980). 12 Data for aluminum foils available in the literature: R. B. Peterson and D. Podwerbekki, Meas. Sci. Technol. 3, 533 (1992). 1D LSP simulations (backscattered electrons removed from simulation) 2D LSP simulations 13 From these results, the rate at thick the foil temperature increases as a function of voltage can be found: The peak in the curve for 1-mil iron is an important transition from the foil being a thick target electron absorber to a thin foil. This transition for 1-mil aluminum occurs below 100 kV. 14 Functional Forms for Foil Heating: For 1-mil Al: For 1mil Fe (or stainless steel): 15 2D Simulations Detailed model of localized foil heating for direct comparison with Electra measurements 16 Gas 30 cm =-V(t) =0 Iron ribs (1.3 cm deep, 0.5 cm wide) foils Al absorber x z B0B0 Periodic Boundary Conditions Cathode (30 kV/cm) 4.4 cm 2D LSP simulation geometry: Periodic boundaries along rib positions for computational speed, electrostatic solver for self-consistent diode current using Electra voltage waveform. 17 Typical Electra voltage and current waveforms used for this analysis: 18 Power deposition in several foils and electron beam power in the diodes from 1D LSP simulations. 19 Electra measurements are consistent with simple 1D and 2D LSP simulations of energy deposition and heating of various foils: 1.5 atm Argon: Dashed = 1D sims Solid=2D sims 20 Simulation results scaled to give approximate current density of A/cm 2. atm, 60% Argon, 40% Kr 22 Low pressure helium used to minimize electron backscatter from gas cell: Calculations so far suggest that ~0.17 atm of helium is not a perfect absorber and backscattered electrons are adding to the measured foil temperature atm Helium (Red curves assume perfect absorption of electrons transmitted through foil.) 23 Summary: accurate modeling of foil energy deposition is a critical aspect of rep-rated KrF laser system design: Experiments underway now at the Electra facility are providing important data that is benchmarking the computational modeling. Preliminary Electra measurements are consistent with the modeling results of energy deposition and foil temperature rise for single shot diode operation. This analysis impacts foil materials selection, which in turn is part of the energy efficiency calculation for an IFE system.