Universes and Lattices

Why Use Universes?

Nuclear systems contain many identical components. Instead of defining hundreds of fuel pins individually, universes let you create one template and reuse it everywhere.

Creating Your First Universe

A universe is a complete geometry template. Let's build a simple fuel pin universe step by step.

c Fuel pin surfaces
1  cz   0.4096    $ Fuel radius
2  cz   0.4178    $ Gap radius  
3  cz   0.4750    $ Clad radius

c Universe 1: Fuel pin
10  1  -10.4   -1     u=1  imp:n=1    $ UO2 fuel
11  0           1 -2  u=1  imp:n=1    $ Helium gap
12  2  -6.56    2 -3  u=1  imp:n=1    $ Zircaloy clad
13  3  -0.714   3     u=1  imp:n=1    $ Water (infinite)

c Place fuel pin in assembly
20  0  10 -11 12 -13  fill=1  imp:n=1    $ Pin location

c Boundary surfaces
10  px  -0.63    $ Pin boundaries
11  px   0.63    $ (1.26 cm pitch)
12  py  -0.63
13  py   0.63

Multiple Universe Types

Real assemblies need different components. Create separate universes for each type, then mix them as needed.

c Universe 1: Fuel pin (already defined)

c Universe 2: Guide tube  
25  2  -6.56   -4     u=2  imp:n=1    $ Zircaloy tube (solid)
26  3  -0.714   4     u=2  imp:n=1    $ Water outside tube

c Universe 3: Water hole
30  3  -0.714         u=3  imp:n=1    $ Pure water

c Additional surface
4  cz   0.612    $ Guide tube radius

Rectangular Lattices

For regular arrays, lattices automatically place universes in a grid pattern. This is perfect for fuel assemblies.

c 3x3 lattice universe
c The lattice cell defines ONE unit element (one pitch).
c MCNP tiles space by repeating this element.
c lat=1 → rectangular lattice  (lat=2 → hexagonal)
100  0  20 -21 22 -23  lat=1  u=10  imp:n=1
     fill=-1:1 -1:1 0:0    $ ix:jx iy:jy iz:jz index ranges
     1 1 1                 $ Row -1: fuel-fuel-fuel
     1 2 1                 $ Row  0: fuel-guide-fuel  
     1 1 1                 $ Row  1: fuel-fuel-fuel

c Single lattice element boundaries (1.26 cm pitch)
20  px  -0.63    $ Half-pitch left
21  px   0.63    $ Half-pitch right
22  py  -0.63    $ Half-pitch bottom
23  py   0.63    $ Half-pitch top

c Place 3x3 assembly in reactor
200  0  30 -31 32 -33  fill=10  imp:n=1    $ Assembly location

c Assembly boundaries  
30  px  -2.5     $ Assembly box
31  px   2.5
32  py  -2.5
33  py   2.5

Realistic PWR Assembly

Let's create a simplified 5×5 PWR assembly with proper guide tube placement.

c 5x5 PWR assembly
c Again, the lattice cell defines a single pitch element.
300  0  40 -41 42 -43  lat=1  u=20  imp:n=1
     fill=-2:2 -2:2 0:0    $ 5x5 grid (indices -2 to 2)
     1 1 1 1 1             $ Row -2: all fuel
     1 1 2 1 1             $ Row -1: guide tube
     1 2 3 2 1             $ Row  0: guide-instrument-guide
     1 1 2 1 1             $ Row  1: guide tube
     1 1 1 1 1             $ Row  2: all fuel

c Single lattice element (1.26 cm pitch)
40  px  -0.63    $ Half-pitch
41  px   0.63
42  py  -0.63
43  py   0.63

Positioning and Transformations

Universes can be positioned anywhere using translation vectors or transformation cards.

c Place assemblies at different positions
c Each cell defines a box using px/py planes
c (positive sense of lower bound, negative sense of upper)
400  0  50 -51 52 -53  fill=20 (0 0 0)      imp:n=1    $ Assembly 1
401  0  54 -55 56 -57  fill=20 (10 0 0)     imp:n=1    $ Assembly 2
402  0  58 -59 60 -61  fill=20 (0 10 0)     imp:n=1    $ Assembly 3
403  0  62 -63 64 -65  fill=20 (10 10 0)    imp:n=1    $ Assembly 4

Working with universes in practice

One rule about universe design is not a preference but a requirement: the outermost cell of a universe must extend to infinity. A universe is a template, and the cell that fills it gets clipped by the container it is placed into — so if the template's own outer cell stops at a finite boundary, there is a shell of undefined space between where the template ends and where the container's wall is. MCNP reports that as a lost particle, sometimes thousands of cycles in.

Everything else is bookkeeping that pays off later. Keep each universe to one component, number its surfaces in a consistent block so you can tell at a glance which universe a surface belongs to, and say in a comment what the universe is for. On the lattice side, the failure mode is almost always a mismatch: a fill index range that does not match the number of map entries you wrote, or a universe number in the map that does not exist. Neither of these is necessarily an error MCNP catches, which is why building up from a 3×3 case before writing a seventeen-row map is worth the extra run.

Building your first universe model

The order of work follows the structure of the input. Decide first what geometry repeats — for a reactor that is nearly always the fuel pin — and define the surfaces that bound it. Add u=N to each of those cells to assign them to universe N, and make the outermost of them infinite as described above. At that point the universe exists but appears nowhere; it enters the model when some other cell carries fill=N.

Then check it before scaling up. Plot the geometry, and run a short calculation to see whether any particles are lost. A universe model that is subtly wrong tends to run — MCNP will happily track through a geometry with a gap in it until a particle happens to enter the gap — so the absence of an error message on a five-cycle run is not the same as a correct model.