Electra Foil Heating Analysis

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Electra Foil Heating Analysis

• D. V. Rose,a F. Hegeler,b A. E. Robson,c and J.
  D. Sethianc

• ATK Mission Research, Albuquerque, NM
• Commonwealth Technologies, Alexandria, VA
• Naval Research Laboratory, Washington, DC

High Average Power Laser Meeting PPPL, Princeton,
NJ October 27-28, 2004
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The key components of a Krypton Fluoride (KrF)
Laser
Laser Input
Laser Gas Recirculator
Pulsed Power System
Cathode
Electron Beam
Foil Support(Hibachi)
Laser Cell Kr F2 ( Ar)
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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

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1D Lsp foil runs at 500 keV (flat top) No diode
fields. Average Reflected and Transmitted Energy
and Current Densityas a Function of Foil
Thickness
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A comparison of the backscattered electron energy
distributionfrom the foil only for a 500 keV
electron beam.
1-mil Fe
5-mil Fe
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Power deposition in foil WITHOUT re-injection of
backscattered electrons (and perfect absorber
behind foil)
1D calculations,single-passfor 500
keVelectrons
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Adding backscattering from gas (electrons
scattered into AK gap are lost)
Iron _at_ 500 keV
Aluminum _at_ 500 keV
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Fractional Power Deposition (Pdeposited/Pinjected)
is compared at 500 keV for various thicknesses
of iron and aluminum, isolating the contributions
from the gas-scattered and diode re-injected
electrons.
Iron _at_ 500 keV
Aluminum _at_ 500 keV
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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)

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Voltage scans Deposition in foil is reduced with
increasing voltage, but backscattered electron
quantities only weakly affected
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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).
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Data for aluminum foils available in the
literature
2D LSP simulations
1D LSP simulations (backscattered
electronsremoved from simulation)
R. B. Peterson and D. Podwerbekki, Meas. Sci.
Technol. 3, 533 (1992).
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From these results, the rate at thick the foil
temperature increases as a function of voltage
can be found
The peak in the curve for1-mil iron is an
important transition from the foil being a
thick target electronabsorber to a thin
foil. This transition for 1-mil aluminum occurs
below 100 kV.
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Functional Forms for Foil Heating
For 1-mil Al
For 1mil Fe (or stainless steel)
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2D Simulations

• Detailed model of localized foil heating for
  direct comparison with Electra measurements

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2D LSP simulation geometry Periodic boundaries
alongrib positions for computational speed,
electrostatic solverfor self-consistent diode
current using Electra voltage waveform.
Iron ribs (1.3 cm deep, 0.5 cm wide)
Cathode (30 kV/cm)
Periodic BoundaryConditions
30 cm
Al absorber
Gas
z
4.4 cm
x
B0
foils
f0
f-V(t)
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Typical Electra voltage and current waveforms
used for this analysis
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Power deposition in several foils and electron
beam power in the diodes from 1D LSP simulations.
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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 Solid2D sims
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Simulation results scaled to give approximate
current density of 24 - 25 A/cm2.
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1.5 atm, 60 Argon, 40 Kr
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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.
0.17 atm Helium
(Red curves assume perfect absorption of
electrons transmitted through foil.)
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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.