Transcript EGS5 Transport Mechanics and Step Size Optimization
Automated Electron Step Size Optimization in EGS5 Scott Wilderman Department of Nuclear Engineering and Radiological Sciences, University of Michigan
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
Condensed History Transport Mechanics
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 q, 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
Problem Granularity Dependence of Step Size
EGS5 Step Size Parameters • Dual Hinge implies two step size controls, one for multiple scattering, and one for energy loss • EGS5( a) 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 !
Results: Backscatter and Timing Run Solid 01/01/01/01 01/40/01/01 01/40/01/40 01/40/40/40 40/40/01/40 40/40/40/40 %Backscatter CPU Time .115842
.115842
.1146
.1135
.1306
.1269
.1529
603 632 244 91 80 38 26
Central Axis Depth Dose
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”
Broomstick Problem
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
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 r Z (Z + 1) / A • Interpolate distance in terms of (t r) • Interpolate materials in Z (Z + 1) / A
Broomstick Elements
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
Broomstick Results
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
Modified Broomstick
Modified Broomstick • Set broomstick length = diameter • Look at
Modified Broomstick Results
Modified Broomstick Results • Determine maximum fractional energy loss for convergence to 1% in
Modified Broomstick Results
Tutor4 with EGS5 • 2 MeV electrons on 2 mm of Si EGS4 default EGS4 1% ESTEPE EGS5 30% EFRACH EGS5 1% EFRACH EGS5 2 mm charD Reflected E 1.3% 6.4% 8.1% 7.3% 7.4% Transmitted E 49.2% 61.3% 66.5% 64.4% 64.8%
Energy Hinge Energy hinge t h E_0 E_1 Mono-energetic transport between energy hinges Hinges needed only for accuracy of f(E_0) variables
Energy Hinge All Monte Carlo programs must deal with energy dependence over steps. EGS5 relies on average values to be correct. EGS5 integrals: f(E_0) h + f(E_1) (t – h) h uniformly distributed in D E: z D E / SP(E_0) Can show EGS5 D E (f(E_0) + f(E_1)) / 2
Energy Hinge • PEGS5 compute ESTEPE (E) such that trapezoid rule accurate to within some e (.001 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%
EGS4 First Step Artifacts g Gamma angle correlated to electron angle after scatter EGS5 g Gamma angle correlated to electron angle before scatter
EGS5 First Step for Primary Electrons 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) Interface 2 K_f 4 K_f 8 K_f min(16 K_f, K_1(Z,E,t))
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