Complex Geometries

Boolean Operations

Real nuclear systems require combining basic shapes using Boolean logic. MCNP uses three operations to create complex geometries from simple surfaces.

Intersection: Bounded Regions

Intersection creates regions that satisfy multiple conditions simultaneously. This is how you build finite volumes from infinite surfaces.

c Basic cylindrical pellet
1  cz   0.4096    $ Pellet radius
2  pz   0.0       $ Bottom face
3  pz   1.0       $ Top face

c Fuel pellet cell  
10  1  -10.4  -1 2 -3    imp:n=1    $ UO2 pellet

c PWR fuel pin surfaces
1  cz   0.4096    $ Fuel radius
2  cz   0.4178    $ Gap radius
3  cz   0.4750    $ Clad radius
4  pz   0.0       $ Pin bottom
5  pz   366.0     $ Pin top

c Pin regions
10  1  -10.4   -1 4 -5        $ UO2 fuel
11  0           1 -2 4 -5     $ Helium gap
12  2  -6.56    2 -3 4 -5     $ Zircaloy clad
13  3  -0.714   3 4 -5        $ Water around pin

Union: Multiple Regions

Union operations (using colons) combine separate regions into single cells. This simplifies input files for discontinuous structures.

c Four guide tubes in assembly
1  c/z  5.4 5.4   0.612     $ Guide tube 1
2  c/z  5.4 16.2  0.612     $ Guide tube 2  
3  c/z  16.2 5.4  0.612     $ Guide tube 3
4  c/z  16.2 16.2 0.612     $ Guide tube 4
5  pz   0.0                 $ Assembly bottom
6  pz   366.0               $ Assembly top

c Guide tube steel (single cell for all four)
20  1  -7.8  (-1:-2:-3:-4) 5 -6    $ Steel tubes (solid cylinders)
21  2  -0.7  (1 2 3 4) 5 -6         $ Water outside all tubes

c 2x2 detector crystals
1  rcc  0 0 0    0 0 5  2.5     $ Crystal 1
2  rcc  6 0 0    0 0 5  2.5     $ Crystal 2
3  rcc  0 6 0    0 0 5  2.5     $ Crystal 3
4  rcc  6 6 0    0 0 5  2.5     $ Crystal 4
5  rpp  -3 9  -3 9  -1 6       $ Housing box

c Detector assembly
30  1  -3.67  (-1:-2:-3:-4)          $ NaI crystals
31  2  -2.7   -5 1 2 3 4             $ Aluminum housing
32  0          5                     $ Outside air

Complement: Excluding Regions

Complement operations use the # symbol to exclude specific cells. This is useful for defining void spaces around complex objects.

c Room and equipment
1  so   2.0       $ Source sphere
2  so   12.0      $ Shield sphere
3  rpp  -50 50  -50 50  -30 30    $ Room boundary

c Definitions
10  1  -19.3   -1              $ Source
20  2  -11.3   -2 1            $ Lead shield
30  0          -3 2 #40 #50    $ Air (excluding equipment)
40  3  -7.8    -4              $ Steel table
50  4  -2.7    -5              $ Detector

c Equipment surfaces
4  rpp  -10 10  -5 5  -25 -20  $ Table
5  rcc   30 0 0   0 0 10  5    $ Detector

Practical Assembly Example

Let's build a realistic fuel assembly step by step, showing how to combine operations systematically.

c Assembly components
1  cz   0.4096    $ Fuel radius
2  cz   0.4178    $ Gap radius  
3  cz   0.4750    $ Clad radius
4  cz   0.561     $ Guide tube inner radius
11 cz   0.612     $ Guide tube outer radius
5  px  -10.71     $ Assembly boundaries
6  px   10.71
7  py  -10.71
8  py   10.71
9  pz   0.0       $ Bottom
10 pz   366.0     $ Top

c Fuel pin at origin
20  1  -10.4   -1 9 -10        $ UO2 fuel
21  0           1 -2 9 -10     $ Helium gap
22  2  -6.56    2 -3 9 -10     $ Zircaloy clad

c Guide tube at (5.4, 5.4)
23  2  -6.56    4 -11 9 -10  trcl=1  $ Guide tube wall (Zircaloy)
24  3  -0.714  -4 9 -10      trcl=1  $ Water inside guide tube

c Transformation
tr1  5.4 5.4 0    $ Translation to position

c Water around all pins
25  3  -0.714  5 -6 7 -8 9 -10 #20 #21 #22 #23 #24    $ Water
26  0          -5:6:-7:8:-9:10                          $ Outside

Advanced Techniques

c Complex grouping
1  1  -2.7  (-1 2):(-3 4)  $ Two separate regions

c Rotated component
c Full rotation matrix for 90° about z-axis:
c   x'=y, y'=-x, z'=z
c (* prefix = angles in degrees, not cosines)
*tr1  0 0 0  90 0 90  180 90 90  90 90 0

Geometry Checking

Check a complicated geometry before you spend transport time on it, because a geometry error found after a four-hour run costs four hours. The void card strips all materials from the problem, which lets particles stream through and expose gaps and overlaps far faster than a transport run would. Plotting is the other half of that check: MCNP's own plotter, or an external viewer, will show you a slice through the model and make an overlap visible in a way no output listing does.

Then run something short and read the output rather than the answer. Lost particles are listed explicitly, with the coordinates where tracking failed, and those coordinates point straight at the offending surface. If any tally divides by a volume that MCNP cannot compute — which is the normal situation for cells in a lattice or a filled universe — supply it on a vol card, or the run is a fatal error rather than an approximation.

Keeping it manageable

Build up rather than out. A complicated region assembled from simple shapes, checked at each step, is far easier to debug than the same region written in one go — and the intermediate checks are cheap. Number surfaces and cells in blocks that mean something, so that surface 200 through 210 belongs to one component and you can tell that from the number alone.

Comment the Boolean logic, not the syntax. Nobody needs to be told that : is a union, but everybody benefits from a note saying which physical region a five-term expression is meant to describe. And keep asking whether a universe would be simpler: repeated structures are what universes exist for, and Boolean expressions that describe the same shape four times are four chances to make a typo.