MCNP Guide

❮ Tutorial: Criticality AnalysisVariance Reduction ❯

Tutorial: Shielding Analysis

Practical radiation shielding calculation with MCNP

Problem Setup

A 14 MeV D-T neutron point source sits at the origin behind a composite shield: 1.5 cm of steel followed by 30 cm of ordinary concrete. Detector points at 50 cm and 100 cm measure the attenuated flux beyond the shield.

Physical Setup

  • 14 MeV neutron point source at origin (D-T fusion)
  • Source sphere: r = 0.5 cm (void)
  • Steel liner: x = 0.5 to 2.0 cm (1.5 cm thick)
  • Concrete shield: x = 2 to 32 cm (30 cm thick)
  • Point detectors at x = 50 and 100 cm

Analysis Goals

  • Calculate neutron flux attenuation through each shield layer
  • Determine flux at detector points beyond the shield
  • Observe spectrum hardening and thermalisation
  • Demonstrate importance-based variance reduction

Complete Input File

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mcnp — hover sections to explore
Neutron Shielding Analysis Example
c Cell Cards
c Geometry: point source -> steel slab -> concrete slab -> air,
c all inside a large bounding sphere.
1  0        -1        imp:n=1    $ Source region (inside small sphere)
2  2  -7.85  1 -2 -5  imp:n=2    $ Steel slab (x = 0.5 to 2 cm)
3  3  -2.3   2 -3 -5  imp:n=4    $ Concrete slab (x = 2 to 32 cm)
4  0         3 -5     imp:n=2    $ Air / detector region
5  0         5        imp:n=0    $ Outside world
 
c Surface Cards
1  so   0.5      $ Source sphere (at origin)
2  px   2.0      $ Steel / concrete interface
3  px   32.0     $ Concrete back face
5  so   200.0    $ Outer boundary sphere
 
c Data Cards
c Materials
m2  26056.70c  -1.0       $ Steel (simplified, single isotope)
m3  1001.70c   -0.01      $ Concrete (NBS ordinary)
    8016.70c   -0.532
    14028.70c  -0.337
    20040.70c  -0.044
    26056.70c  -0.014
    13027.70c  -0.034
    11023.70c  -0.029
 
c Source - 14 MeV neutron point source
sdef  par=n  erg=14  pos=0 0 0   $ par=particle, erg=energy(MeV)
 
c Tallies
f2:n  2 3                   $ Surface flux at surfaces 2 and 3
e2    1e-9 1e-6 1e-3 0.1 1 5 10 15   $ Energy bin upper bounds (MeV)
f5:n  50 0 0  0             $ Point detector at (50,0,0), R=0
      100 0 0  0            $ Point detector at (100,0,0), R=0
e5    1e-9 1e-6 1e-3 0.1 1 5 10 15
f4:n  2 3                   $ Volume-averaged flux in cells 2 and 3
 
c Physics and cutoffs
mode  n                     $ Neutron transport only
cut:n J 1e-8                $ J=default time, 10 keV energy cutoff
nps   1e6                   $ Number of source particles

Annotated MCNP Input

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●Source region (cell 1)
●Steel + concrete cells (2–3)
●Air region + outside void (4–5)
●Geometry surfaces
●Steel material (m2)
●Concrete material (m3)
●SDEF — 14 MeV D-T source
●F2/E2 surface flux tally
●F5/E5 point detectors
●F4 cell flux tally
●MODE / CUT / NPS settings

Variance Reduction

The importance ladder (imp:n=1 → 2 → 4 → 2 → 0) built into the cell cards above is already a basic form of variance reduction. For very deep penetration problems (shield thickness of 10+ mean free paths) you may need additional techniques. A DXTRAN sphere around the detector region forces neutrons to scatter toward the detector.

Enhanced Input: DXTRAN Sphere

mcnp
c Add to the previous input:
c Variance reduction
c DXTRAN sphere around detector region (not at source)
c Syntax: DXT:n x y z ri ro
dxt:n   100 0 0  5.0  40.0  $ At x=100, inner=5 outer=40 cm
cut:n   1e-8
nps     5e5

Running the Calculation

Commands

bash
# Run the shielding calculation
mcnp6 i=shield_input n=shield_output

# Monitor progress
tail -f shield_output

# Check for completion
grep "mcnp     version" shield_output

Key Results to Extract

  • Attenuation factors: compare F2 tally at surfaces 2 and 3
  • Flux at detectors: F5 results at 50 cm and 100 cm
  • Energy spectra: F4 results show how the spectrum changes through the shield
  • Statistical quality: all relative errors should be < 10% and the 10 statistical tests should pass

Typical Results

  • Steel reduces fast neutron flux by ~2× (via inelastic scatter and (n,2n) at 14 MeV)
  • Concrete reduces flux by 100–1000× depending on thickness and energy range
  • Thermal neutron flux increases inside the concrete (moderation effect)
  • Fast neutron flux decreases roughly exponentially with depth (attenuation length ~10–15 cm in concrete)

Shielding Analysis Tips

  • Always use variance reduction for deep-penetration problems
  • Check that all statistical tests pass before trusting tally results
  • Compare to analytical estimates (e.g. removal cross section method) as a sanity check
  • Add photon transport (mode n p) if gamma dose is significant
  • Use ICRP-116 flux-to-dose conversion factors for effective dose from F4/F5 results

Extensions and Variations

Geometry variations

  • Add air gap between steel and concrete
  • Include reinforcing steel bars inside concrete (rebar)
  • Model a streaming path or duct through the shield
  • Use a cylindrical or box-shaped source region

Physics enhancements

  • Enable coupled neutron-gamma transport (mode n p)
  • Add S(α,β) thermal scattering for concrete hydrogen
  • Use a fission neutron spectrum source instead of monoenergetic
  • Add weight window variance reduction for detector accuracy

Learning Objectives

After completing this tutorial, you should understand:

  • How to set up a multi-layer shielding geometry with slab and sphere surfaces
  • Why importance values form a ladder through the shield
  • The difference between F2 (surface), F4 (cell), and F5 (point detector) tallies
  • When to add DXTRAN or weight windows for deep-penetration problems
  • How to convert neutron flux to effective dose using flux-to-dose factors

Related Topics

❮ Tutorial: Criticality AnalysisVariance Reduction ❯