MCNP Guide
MCNP Tallies
Extracting meaningful results from your simulation
What Tallies Measure
Tallies extract physical quantities from your Monte Carlo simulation. Without tallies, MCNP would simply track particles without recording useful information. Each tally type uses different mathematical approaches to estimate quantities like neutron flux, particle current, or energy deposition.
The Five Standard Tally Types
F1 - Surface Current
Particles crossing a surface
F2 - Surface Flux
Flux across a surface
F4 - Cell Flux
Average flux in a volume
F5 - Point Detector
Flux at a specific location
F6 and F8 tallies measure energy deposition and pulse height, respectively. FMESH tallies overlay spatial grids for detailed mapping.
F4 Tally: Your Primary Tool
The F4 tally estimates average neutron flux in a cell using track-length estimation. This makes it ideal for most reactor physics calculations, including reaction rates and flux distributions.
Basic Flux Measurement
c Simple flux tally in fuel cell
F4:n 10 $ Neutron flux in cell 10
E4 1e-11 1e-6 20 $ Thermal, epithermal, fast groups
c Multiple cells with total
F14:n (10 20 30) T $ Individual cells plus total
E14 1e-11 1e-6 20 $ Same energy structureThe F4 tally automatically accounts for cell volume, giving you flux per unit volume. The E4 card defines energy bins - here we have thermal (below 1 eV), epithermal (1 eV to 1 MeV), and fast (above 1 MeV) groups.
Reaction Rate Calculations
c Fission rate in fuel
F24:n 10 $ Flux in fuel cell
FM24 (-1 1 -6) $ Fission cross-section multiplier
E24 1e-11 1e-6 20 $ Energy groups
c Absorption rate
F34:n 10
FM34 (-1 1 -2) $ Absorption cross-section
E34 1e-11 1e-6 20
c Multiple reactions
F44:n 10
FM44 (-1 1 (102) (16) (17)) $ Capture, (n,2n), (n,3n)
E44 1e-11 1e-6 20The FM card converts flux to reaction rates. The format is (multiplier, material, reaction). Common reactions include -6 (fission), -2 (absorption), and 102 (capture). The -1 multiplier normalizes by atom density, giving reactions per atom.
F5 Tally: Point Detectors
Point detectors use next-event estimation to calculate flux at specific locations. They excel at deep penetration problems where few particles would naturally reach the detector location.
c Dose rate detector outside shield
F5:n 200 0 0 0 $ Point at (200,0,0), zero radius
DE5 1e-9 1e-8 1e-7 1e-6 1e-5 1e-4 1e-3 1e-2 1e-1 1 10 20
DF5 2.78e-6 3.48e-6 2.47e-6 2.47e-6 2.78e-6 3.79e-6
4.49e-6 4.73e-6 4.56e-6 4.55e-6 4.55e-6 4.49e-6
c Multiple detector positions
F15:n 100 0 0 0 $ First detector
150 0 0 0 $ Second detector
200 0 0 0 $ Third detectorThe DE/DF cards convert neutron flux to dose rate using flux-to-dose conversion factors. Point detectors work best when placed away from surfaces and in regions with reasonable particle density.
Surface Tallies: F1 and F2
Surface tallies measure particle flow across boundaries. F1 counts actual crossings (current), while F2 estimates flux using angular weighting. Both are essential for understanding particle leakage and boundary conditions.
c Current leaking from reactor core
F1:n 100 $ Current across surface 100
E1 1e-11 1e-6 20 $ Energy groups
c Flux at detector surface
F2:n 200 $ Flux across surface 200
E2 1e-11 1e-6 20
C2 -1 -0.5 0 0.5 1 $ Angular bins (cosine)
c Time-dependent leakage
F11:n 100
T11 0 1e-6 1e-5 1e-4 1e-3 $ Time bins (seconds)
E11 1e-11 1e-6 20Surface tallies help verify boundary conditions and measure leakage rates. The C2 card adds angular binning, while T11 provides time dependence. These features are crucial for transient analysis and detailed flux characterization.
Mesh Tallies: Spatial Mapping
Mesh tallies overlay geometric grids on your problem, providing detailed spatial distributions independent of your cell structure. They're invaluable for visualization and identifying hotspots.
c Cartesian mesh for dose mapping
FMESH14:n GEOM=xyz $ Rectangular mesh
ORIGIN=-50 -50 0 $ Starting corner
IMESH=50 $ X boundary
IINTS=50 $ X divisions (2cm each)
JMESH=50 $ Y boundary
JINTS=50 $ Y divisions
KMESH=100 $ Z boundary
KINTS=50 $ Z divisions
OUT=cf $ Column format output
c Cylindrical mesh for reactor
FMESH24:n GEOM=cyl $ Cylindrical mesh
ORIGIN=0 0 0 $ Center
AXS=0 0 1 $ Z-axis
RMESH=150 $ Radial boundary
RINT=30 $ 5cm radial divisions
ZMESH=400 $ Axial boundary
ZINT=80 $ 5cm axial divisionsMesh tallies provide comprehensive spatial mapping. Cartesian meshes work well for general geometries, while cylindrical meshes suit reactor problems. Balance mesh resolution with statistical requirements - finer meshes need more particles for good statistics.
Practical Guidelines
Choosing the Right Tally
Start with F4 tallies for general flux and reaction rate calculations. They're robust and provide volume-averaged results that are easy to interpret. Use F5 tallies for shielding problems where you need flux at specific locations far from sources.
Surface tallies (F1/F2) are essential for boundary analysis and leakage calculations. Choose F1 for particle counting and F2 for flux estimation. Mesh tallies provide detailed spatial information but require more computational resources.
Always verify that your tally locations make physical sense. Check cell volumes for F4 tallies, ensure point detectors aren't too close to surfaces, and verify that surface orientations are correct for F1/F2 tallies.
Statistical Considerations
Good tally statistics require adequate particle sampling. Aim for relative errors below 10% for most applications, and below 5% for critical safety calculations. Use variance reduction techniques when tallies have poor statistics.
Monitor the figure of merit (FOM) to optimize your calculations. The FOM combines tally precision with computation time, helping you balance accuracy with efficiency.