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MCNP CLASS SERIES
(MCNP GEOMETRY)
Jongsoon Kim
Learning Objectives: Geometry
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…
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Understand how to
define all four classes
of surfaces
Understand how to
create cells from
surfaces
Understand the
detailed definition of
macrobodies
Geometry Basics
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…
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The “universe” is divided into regions of different
materials and properties
The entire infinite universe must be included in
geometric model
The basic unit of a geometry is a “cell”
All cells are defined by bounding surfaces
All surfaces divide the universe into two regions
Quick Start:
Surfaces
…
Equation surfaces
† Surfaces
defined by providing the equation of the
surface and the parameters (Table 3.1)
† Examples
„
A sphere located at the origin with radius R
j
„
R
A cylinder parallel to the y-axis at x, z with radius R
j
„
so
c/y X Z R
A plane normal to the z-axis at Z
j
pz
Z
Quick Start:
Combining Surfaces into Cells
…
Interior points of cell are related to a surface by
the “sense” of the cell: ‘t’ or ‘-’
† Surfaces
…
divide universe into 2 half-regions
Boolean operators
† Combine
half-regions to create cells/objects
Intersection
„ Union
„ Complement
„
Quick Start: Combining Surfaces into Cells
Sense
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All the points in a cell are related to the surfaces
that define the cell by the sense – which side of a
surface the points of a cell are on
+ (positive sense):
† For open surfaces (planes), points in positive direction from
surface
† For closed surfaces (spheres, cylinders, etc), outside the
surface
- (negative sense):
† For open surfaces, points in negative direction from surface
† For closed surfaces, inside the surface
Quick Start: Combining Surfaces into Cells
Intersection
…
…
Space where both
senses are true
Input syntax: a
<space> between two
surface numbers
† 2_-1represents
only
the region of space
with sense +2 and
sense -1
Quick Start: Combining Surfaces into Cells
Union
…
…
Space where either
sense is true
Input syntax: a
<colon> ‘:” between
two surface numbers
† 2:-1
represents both
the region of space
with sense +2 and the
region with sense -1
Quick Start: Combining Surfaces into Cells
Complement
…
…
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Space outside another cell
Input syntax: a <pound
symbol> ‘#’ before a cell
number
† #5 represents the region
outside cell 5
This region can then be
intersected or united
with other regions
† -2 #5 represents the only
the region outside cell 5
and inside surface 2
Four Classes of MCNP Surfaces:
Analytic Equations
…
Analytic equations
† Planes,
Spheres, Cylinders, Cones, Tori, Arbitrary
Quadratics
Four Classes of MCNP Surfaces:
Macrobodies
…
…
Combinatorial geometry based on closed primitives
Surfaces of finite “building blocks”
† BOX:
arbitrarily oriented orthogonal box
† RPP: rectangular parallelepiped
„
All surfaces normal to respective axes
† SPH:
„
Identical to “equation” for sphere
† RCC:
„
sphere
right circular cylinder
Axis orthogonal to base, but arbitrarily oriented
Four Classes of MCNP Surfaces:
Axisymmetric sets of points
…
…
Planes & Linear or Quadratic surfaces
Example 1: j Z 7 5 3 2 4 3
†A
surface sysmmetric about z-axis, which passes
through the three (z,r) points, (7,5), (3,2), and 4,3)
Four Classes of MCNP Surfaces:
Three point in a plane
…
…
General Planes
Form: j P X1 Y1 Z1 X2 Y2 Z2 X3 Y3 Z3
† Coordinates
of three points lying in the desired plane
† Convert them to the required surface coefficient to
produce plane
Ax + By + Cz – D = 0
Coordinate Transformation
…
TRn Data Card (see page 3-31)
† TRn
…
Ox Oy Oz Bxx’ Byx’ Bzx’ Bxy’ Byy’ Bzy’ Bxz’ Byz’ Bzz’
n
† Number
…
of transformation
Ox Oy Oz
† Displacement
…
vector of the transformation
Bxx’ . . . Bzz’
† Rotation
matrix of the transformation
† Angles in degrees when *TRn card is used, otherwise in
cosines
Example of Coordinate Transform
(CCW 67.5 for apple simulation for 1.35 MeV electron beam irradiation)
o
Z
Y
Z
Y
xx’ yx’ zx’ xy’ yy’
*TR1 0 0 0 0
90 90
zy’
xz’ yz’
zz’
90 67.5 22.5 90 157.5 67.5
Homework
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Think about your geometry for term project and
make cell and surface cards