MCNP Guide
MCNP Example: PWR Fuel Pin Model
What you'll learn
- Build a four-region pin cell — fuel, gap, cladding, moderator — from four concentric cylinders and two axial planes.
- Apply boundary conditions with the surface prefixes:
+for a white boundary and*for a reflecting plane. - Define the four materials the model needs, including
mt4 lwtr.10tfor thermal scattering in water. - Score a flux spectrum with
f4:nplus ane4energy grid, and fission heating withf7:n. - Say why these boundary conditions give k∞ rather than keff, and what k∞ to expect for fresh 4.5% fuel.
Before you start
Problem Description
This example models a typical PWR fuel pin cell: a UO₂ fuel pellet, helium-filled gap, Zircaloy-4 cladding, and water moderator — enclosed by a white cylindrical boundary and two reflecting planes, which together stand in for an infinite lattice.
The four radii below are the ones every card on this page refers to, and they are the dimensions of a real 17×17 pressurized water reactor pin rather than round numbers. The equivalent cell radius is the one that is not a physical measurement: it is chosen to give a circle of the same area as the square 1.26 cm pitch cell, which is what makes a cylindrical outer boundary a fair stand-in for a square lattice.
| Region | Outer radius (cm) | Material | Density (g/cm³) |
|---|---|---|---|
| Fuel pellet | 0.4096 | UO₂, 4.5% | 10.4 |
| Gap | 0.4178 | Helium | 0.0001 |
| Cladding | 0.4750 | Zircaloy-4 | 6.56 |
| Moderator | 0.7108 | Light water | 0.998 |
Complete Input File
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PWR Fuel Pin Cell Modelc ---- Cell Cards ----c cell mat density surfaces params1 1 -10.4 -1 5 -6 imp:n=1 $ UO2 Fuel2 2 -0.0001 1 -2 5 -6 imp:n=1 $ Helium Gap3 3 -6.56 2 -3 5 -6 imp:n=1 $ Zircaloy-4 Cladding4 4 -0.998 3 -4 5 -6 imp:n=1 $ Water Moderator5 0 (4 : -5 : 6) imp:n=0 $ Outside the cellc ---- Surface Cards ----1 cz 0.4096 $ Fuel Radius2 cz 0.4178 $ Gap Outer Radius3 cz 0.4750 $ Clad Outer Radius+4 cz 0.7108 $ Cell boundary (+ = white, see notes)*5 pz 0.0 $ Bottom of the slice (* = reflecting)*6 pz 1.0 $ Top of the slice, 1 cm tallc ---- Data Cards ----c Materials (positive fractions = atom, negative = weight)m1 92235.70c 0.045 $ 4.5% enriched UO2 (atom fractions)92238.70c 0.9558016.70c 2.0m2 2004.70c 1.0 $ Helium fill gasm3 40090.70c 0.5145 $ Zirconium, natural (atom fractions)40091.70c 0.112240092.70c 0.171540094.70c 0.173840096.70c 0.0280m4 1001.70c 2.0 $ Light water (atom ratios)8016.70c 1.0mt4 lwtr.10t $ S(a,b) thermal scatteringc kcode: neutrons/cycle k-guess skip totalkcode 5000 1.0 50 250ksrc 0 0 0.5 $ Mid-slice, not on a boundaryc Talliesf4:n 1 $ Track-length flux in fuel celle4 1e-9 1e-8 1e-7 1e-6 1e-5 1e-4 1e-3 1e-20.1 1 2 3 4 5 6 7 8 9 10 $ Energy bin upper bounds (MeV)f7:n 1 $ Fission energy deposition in fuelc Output controlprdmp j 300 1 2
Annotated MCNP Input
Hover over any highlighted section to see a detailed explanation. Tap on mobile.
What to expect
Fresh 4.5% fuel at this hydrogen-to-heavy-metal ratio gives a k∞ in the range 1.3 to 1.5. If your answer lands there, the deck is behaving. If it lands near 1.0, look first at the thermal scattering card, because a pin cell without mt4 loses a large part of the moderation that makes the lattice work — and it runs without complaint.
The flux spectrum from f4:n should show the thermal peak highest in the water and depressed inside the pellet. That dip is self-shielding, and it is physical rather than a modeling artifact: the outer layers of the pellet absorb the thermal neutrons before they reach the center, which is why a fuel pin burns from the outside in. The f7:n fission heating should be confined almost entirely to the fuel, since the fissions are there and F7 scores the recoverable energy at the fission site rather than following the gammas.
With 200 active cycles the standard deviation on k lands around 0.0003 to 0.0006, and all ten statistical checks should pass. The thermal and epithermal flux bins converge easily here because the pin cell is small and every history visits every region; that comfortable situation does not survive the move to a full core.
Three approximations in this deck are worth naming, because each is a deliberate trade rather than an oversight. The cylindrical outer boundary replaces the true square cell — a Wigner–Seitz equivalence that preserves the moderator volume but not the corner geometry, and which four reflecting planes at the real pitch would avoid at the cost of three more surfaces. The boundary conditions make the model infinite, so what comes out is k∞, and a finite reactor built from this lattice would sit lower by its leakage.
And the cross sections are room-temperature .70c data, which describes a cold shutdown core rather than an operating one. Moving to hot conditions means both a higher fuel temperature and a lower water density — and the two push k in the same direction, downward, by several thousand pcm together.
Where to take it next
This deck is a good platform for reactivity coefficients precisely because it is small enough to run repeatedly. Sweeping enrichment from 2 to 5 % traces out how k∞ saturates — the returns diminish, because at some point you are adding U-235 to a lattice that has already thermalized everything it can. Changing the pitch varies the hydrogen-to-heavy-metal ratio and finds the moderation optimum, which is the calculation that shows why a pressurized water reactor is deliberately built on the under-moderated side of that peak. And reducing the water density models voiding, giving the sign and magnitude of the void coefficient directly.
Beyond that, the interesting additions each bring in new physics rather than new geometry. A burnable absorber layer on the pellet surface changes the reactivity history. The tmp card sets a temperature per cell so that Doppler broadening can be resolved. And the burn card turns a single k into a depletion history, at which point the run stops being a few minutes of work.
Card semantics on this page follow MCNP6.3.1 Theory & User Manual (LA-UR-24-24602 Rev. 1), §5.5.1 VOL: Cell Volume, §5.8.10 KCODE: Criticality Source and §5.8.11 KSRC: Criticality Source Points.
Full reference list on the attribution page.
Check yourself
- Build a four-region pin cell from concentric cylinders and two axial planes?
- Say why the curved outer boundary takes
+and the axial planes take*? - Define the four materials, including
mt4for thermal scattering in water? - Score a flux spectrum with
f4:nand fission heating withf7:n? - Explain why this model reports k∞ rather than keff?