Automated Electron Step Size Optimization in EGS5

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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 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 whats 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(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!

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Results Backscatter and Timing
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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 r Z (Z 1) / A
• Interpolate distance in terms of (t r)
• 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 ltrgt emerging from end
• Shorter volumes permit more histories
• 1 convergence in ltrgt clearly more strict
  criteria than 1 convergence in lttgt
• 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 ltrgt 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

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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
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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 DE z DE / SP(E_0)
DE (f(E_0) f(E_1)) / 2
Can show EGS5
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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

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First Step Artifacts
g
EGS4
Gamma angle correlated to electron angle after
scatter
EGS5
g
Gamma angle correlated to electron angle before
scatter
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EGS5 First Step for Primary Electrons
usual EGS5 first step, as determined from
K_1(Z,E,t)
incident electron
limited first step, K_f, determined from
K_1(Z,E,t_min)
incident electron
min(16 K_f, K_1(Z,E,t))
2 K_f
4 K_f
8 K_f
Interface
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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