automated electron step size optimization in egs5 scott wilderman department of nuclear engineering...
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![Page 1: Automated Electron Step Size Optimization in EGS5 Scott Wilderman Department of Nuclear Engineering and Radiological Sciences, University of Michigan](https://reader036.vdocuments.mx/reader036/viewer/2022062718/56649e7a5503460f94b7a1fe/html5/thumbnails/1.jpg)
Automated Electron Step Size Optimization in EGS5
Scott Wilderman Department of Nuclear Engineering
and Radiological Sciences,
University of Michigan
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Multiple Scattering Step Sizes in Monte Carlo Electron Transport
• Why is there a dependence? Transport mechanics • Optimal step: longest steps that get “right” answer• “Right” answer depends on:
– Particular problem tallies -- “granularity”– Error tolerance
• EGS5 automated method– Broomstick problem– Energy hinge– Initial step size restrictions
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Condensed History Transport Mechanics
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Why?
• Larsen convergence: with small enough steps, should get right answer
• But speed requires long steps, and step lengths limited by accuracy of transport mechanics model
• Anyone can get trick is f(x,y,z), and the best we can do is preserve averages (moments)
• Even with perfect f(x,y,z), there will be a step-size dependence for any tally that is a function of what’s happening along the actual track
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Problem Granularity Dependence of Step Size
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EGS5 Step Size Parameters• Dual Hinge implies two step size controls,
one for multiple scattering, and one for energy loss
• EGS5( used fractional energy loss to set steps:–ESTEPE for energy loss hinge–EFRACH for multiple scattering hinge
• But had both high E and low E values for each hinge variable – 4 different ESTEPES!
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Results: Backscatter and Timing
Run %Backscatter CPU Time
Solid .115842 603
01/01/01/01 .115842 632
01/40/01/01 .1146 244
01/40/01/40 .1135 91
01/40/40/40 .1306 80
40/40/01/40 .1269 38
40/40/40/40 .1529 26
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Central Axis Depth Dose
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How to Proceed?
• Accuracy depends on problem “granularity”– Long steps okay for “bulk” volume tallies– Short steps needed for fine mesh computations
• Speed requires energy dependent step sizes:– Small fractional energy loss at high E for accuracy– Larger fractional loss at low E for speed
• Base step sizes on some measure of problem geometry granularity (“characteristic dimension”) that can be energy dependent -- solve “broomstick problem”
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Broomstick Problem
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Broomstick Problem
• Very sensitive to step size -- infinitesimally small broomstick, step must be 1 elastic mfp
• Determine longest average hinge step which preserves correct average track for given diameter (characteristic dimension)
• Measure tracklength as energy deposition• Measure hinge steps as scattering strength
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Broomstick Methodology
• Run EGS5 on broomstick problem for range of Z, E, hinge sizes vs. broomstick diameters t
• Determine max hinge step (K_1) for 1% energy deposition convergence vs. Z, E, t
• K_1 varies roughly as t Z (Z + 1) / A• Interpolate distance in terms of (t • Interpolate materials in Z (Z + 1) / A
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Broomstick Elements
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Broomstick Parameters
• Energy range: at .1, .2, .3, .5, ..17 in every decade from 2 keV to 1 TeV
• Broomstick space: dimensions in terms of fraction of CSDA range at .1, .2, .3, .5, .7 in every decade from 1E-6 to .50
• Hinge step space: steps in terms of fractional energy loss at .1, .15, .2, .3, .5, .7 in every decade from 1E-4 to .30
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Broomstick Results
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Broomstick Drawbacks
• Broomstick L = CSDA range, so long run times, limiting to 50k histories
• Little scattering at high energies, so significant fraction of energy deposition occurs before step sizes are important
• Net effect: Step size optimization criteria based on 1% converged energy deposition not stringent enough
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Modified Broomstick
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Modified Broomstick
• Set broomstick length = diameter• Look at <r> emerging from end• Shorter volumes permit more histories• 1% convergence in <r> clearly more strict
criteria than 1% convergence in <t>• May be slower than necessary on some
problems, but better accuracy on all problems
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Modified Broomstick Results
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Modified Broomstick Results
• Determine maximum fractional energy loss for convergence to 1% in <r> vs. t for all Z and E
• Convert from EFRACH to K_1• Perform linear fit of log(K_1) vs. log(t), all
Z and E• New EGS5 subroutine RK1 prepares
K_1(E) for all materials, given input t.
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Modified Broomstick Results
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Tutor4 with EGS5
• 2 MeV electrons on 2 mm of Si
Reflected E Transmitted E
EGS4 default 1.3% 49.2%
EGS4 1% ESTEPE 6.4% 61.3%
EGS5 30% EFRACH 8.1% 66.5%
EGS5 1% EFRACH 7.3% 64.4%
EGS5 2 mm charD 7.4% 64.8%
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Energy Hinge
E_0
Energy hinge
ht
E_1
Mono-energetic transport between energy hingesHinges needed only for accuracy of f(E_0) variables
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Energy Hinge
EGS5 integrals: f(E_0) h + f(E_1) (t – h)
h uniformly distributed in E: E / SP(E_0)
All Monte Carlo programs must deal with energydependence over steps. EGS5 relies on average values to be correct.
E (f(E_0) + f(E_1)) / 2Can show EGS5
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Energy Hinge
• PEGS5 compute ESTEPE(E) such that trapezoid rule accurate to within some current default)
• Checks stopping power (for energy loss)• Checks scattering power (for multiple scattering
strength)• Checks on hard collision cross section, mean free
path not yet implemented• Typical values for ESTEPE: between 2% and 8%
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First Step Artifacts
EGS4
EGS5
Gamma angle correlated to electron angle after scatter
Gamma angle correlated to electron angle before scatter
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EGS5 First Step for Primary Electrons
Interface
usual EGS5 first step, as determined from K_1(Z,E,t)
incident electron
incident electron
limited first step, K_f, determined from K_1(Z,E,t_min)
2 K_f 4 K_f 8 K_f min(16 K_f, K_1(Z,E,t))
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Summary
• Optimal step selection will always depend on the problem tally granularity, and in particular, on the importance of events taking place on the first step
• The new method for setting step sizes in EGS5 based on the “characteristic dimension” of the tally regions usually solves this problem for the user