MCNP Guide

❮ Tutorial: Shielding AnalysisParallel Computing ❯

Variance Reduction Techniques

Making Monte Carlo simulations more efficient

Why Variance Reduction?

Standard Monte Carlo can be inefficient when few particles reach regions of interest. Variance reduction techniques guide more particles to important areas without biasing results.

Common Problem Types

Deep penetration

Radiation through thick shields

Small detectors

Few particles naturally reach target

Rare events

Low probability interactions

Distant regions

Far from source location

Cell Importances: Start Here

Cell importances are the simplest and most widely used variance reduction technique. They tell MCNP which regions are more important to your problem.

Basic Concept

When a particle moves from low to high importance, MCNP splits it into multiple particles. When moving from high to low importance, particles may be killed (Russian roulette).

mcnp
c Shielding problem - importance increases toward detector
1  1  -1.0   -1        imp:n=1     $ Source region
2  2  -7.8    1 -2     imp:n=2     $ First shield layer
3  2  -7.8    2 -3     imp:n=4     $ Second shield layer
4  2  -7.8    3 -4     imp:n=8     $ Third shield layer  
5  0          4 -5     imp:n=16    $ Detector region
6  0          5        imp:n=0     $ Outside (kill particles)

Importance Guidelines

  • • Increase toward regions of interest: Higher importance = more particles
  • • Use ratios of 2-4: Avoid large jumps between adjacent cells
  • • Set boundary to zero: imp:n=0 kills particles leaving the problem
  • • Start simple: Begin with powers of 2 (1, 2, 4, 8, 16)

Practical Example: Shielding

Let's set up importance for a typical shielding problem where we want to calculate dose rates behind a concrete wall.

mcnp
c Co-60 source behind concrete wall
1  1  -8.9    -1        imp:n=1 imp:p=1     $ Cobalt source
2  2  -2.3     1 -2     imp:n=2 imp:p=2     $ Concrete (0-30 cm)
3  2  -2.3     2 -3     imp:n=4 imp:p=4     $ Concrete (30-60 cm)
4  2  -2.3     3 -4     imp:n=8 imp:p=8     $ Concrete (60-90 cm)
5  0           4 -5     imp:n=16 imp:p=16   $ Air behind wall
6  0           5        imp:n=0 imp:p=0     $ Outside world

c Surfaces
1  so  2.5     $ Source sphere
2  px  30      $ 30 cm concrete
3  px  60      $ 60 cm concrete  
4  px  90      $ 90 cm concrete
5  px  200     $ Problem boundary

c Tallies
f4:p  5        $ Photon flux in air
de4   0.01 0.1 1.0 10.0    $ Energy bins
df4   3.6e-6 3.6e-6 3.6e-6 3.6e-6    $ Dose conversion

Notice that both neutron and photon importances increase toward the detector. This ensures adequate sampling of both particle types.

Source Biasing

Source biasing samples particles from distributions that favor important directions or energies. This helps when only a fraction of source particles contribute to your tallies.

Directional Biasing

mcnp
c Bias source toward detector
sdef  pos=0 0 0  par=2  erg=1.25  dir=d1
si1   H  -1 0.8 1         $ Cosine bins
sp1   D  0.1 0.2 0.7      $ Original probabilities  
sb1   D  0.05 0.15 0.8    $ Biased probabilities (favor forward)

This biases photons toward the forward direction (cosine > 0.8), increasing the fraction that reach a forward detector.

Energy Biasing

mcnp
c Bias toward high-energy neutrons
sdef  pos=0 0 0  par=1  erg=d2
si2   H  0.1 1.0 10.0     $ Energy bins (MeV)
sp2   D  0.6 0.3 0.1      $ Fission spectrum
sb2   D  0.2 0.3 0.5      $ Biased (favor high energy)

This example biases the source toward high-energy neutrons, useful for fast neutron dose calculations.

Weight Windows (Advanced)

Weight windows provide automatic population control throughout the geometry. They're more sophisticated than simple importances but require more setup.

Two-Step Process

Step 1: Generate Windows

mcnp
c Generate weight windows from flux tally
f4:n  (1 2 3 4 5)    $ Flux in all cells
wwg   4              $ Generate from tally 4
nps   1e5            $ Preliminary run

Step 2: Use Windows

mcnp
c Use generated windows (remove wwg card)
wwn:n  1e-6 2e-6 4e-6 8e-6 1e-5    $ Windows from step 1
nps    1e6                          $ Main calculation

Choosing the Right Technique

Start Simple

  • • Cell importances first
  • • Directional source biasing
  • • Energy source biasing
  • • Test one technique at a time

Advanced Options

  • • Weight windows for complex geometry
  • • Forced collisions in thin regions
  • • Point detectors for specific locations
  • • Combine multiple techniques carefully

Checking Your Results

Variance reduction should improve precision without changing results. Always verify your techniques are working correctly.

Quality Checks

  • • Compare with analog: Run same problem without variance reduction
  • • Check relative errors: Should decrease with variance reduction
  • • Monitor figure of merit: Should increase (FOM = 1/(R²×T))
  • • Watch for bias: Results should be statistically consistent

Common Pitfalls

  • • Using too large importance ratios (causes inefficiency)
  • • Forgetting to set boundary importance to zero
  • • Over-biasing source distributions
  • • Not testing variance reduction effectiveness
  • • Combining too many techniques at once

Quick Start Guide

Follow this systematic approach to implement variance reduction:

  1. Run analog first: Establish baseline results and identify problems
  2. Add cell importances: Increase toward regions of interest
  3. Test and compare: Verify results match and efficiency improves
  4. Consider source biasing: If source direction/energy matters
  5. Advanced techniques: Weight windows for complex problems
  6. Always validate: Check results against known solutions

Related Topics

❮ Tutorial: Shielding AnalysisParallel Computing ❯