Difference between revisions of "Surface types"
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| ''x<sub>0</sub>, y<sub>0</sub>, z<sub>0</sub>, r, h'' | | ''x<sub>0</sub>, y<sub>0</sub>, z<sub>0</sub>, r, h'' | ||
| <math>(x - x_0)^2 + (y - y_0)^2 - \left(1 - (z - z_0)/h\right)r^2</math> | | <math>(x - x_0)^2 + (y - y_0)^2 - \left(1 - (z - z_0)/h\right)r^2</math> | ||
− | | Half cone | + | | Half cone parallel to z-axis, base at (''x<sub>0</sub>,y<sub>0</sub>,z<sub>0</sub>''), base radius ''r'', height (distance from base to tip) ''h'' |
|- | |- | ||
| <tt>quadratic</tt> | | <tt>quadratic</tt> |
Revision as of 15:57, 24 February 2016
Contents
Elementary surfaces
Notes:
- Elementary surfaces refer here to surfaces that can be represented by a single equation.
Planes
Notes:
- Parametric form of the general plane is assumed if four values are provided in the surface card. With six values the plane is assumed to be defined by three points.
Surface name | Parameters | Surface equation | Description |
---|---|---|---|
py | x_{0} | Plane perpendicular to x-axis at x = x_{0} | |
pz | y_{0} | Plane perpendicular to y-axis at y = y_{0} | |
px | z_{0} | Plane perpendicular to z-axis at z = z_{0} | |
plane | A, B, C, D | General plane in parametric form | |
plane | x_{1}, y_{1}, z_{1}, x_{2}, y_{2}, z_{2}, x_{3}, y_{3}, z_{3} | General plane defined by three points |
Second-order quadratic surfaces
Notes:
- cyl is the same surface as cylz
Surface name | Parameters | Surface equation | Description |
---|---|---|---|
cylx | y_{0}, z_{0}, r | Infinite cylinder parallel to x-axis, centred at (y_{0},z_{0}), radius r | |
cyly | x_{0}, z_{0}, r | Infinite cylinder parallel to y-axis, centred at (x_{0},z_{0}), radius r | |
cylz, cyl | x_{0}, y_{0}, r | Infinite cylinder parallel to z-axis, centred at (x_{0},y_{0}), radius r | |
cylv | x_{0}, y_{0}, z_{0}, u_{0}, v_{0}, w_{0}, r | Infinite cylinder, parallel to (u_{0},v_{0},w_{0}), centred at (x_{0},y_{0},z_{0}), radius r | |
sph | x_{0}, y_{0}, z_{0}, r | Sphere, centred at (x_{0},y_{0},z_{0}), radius r | |
cone | x_{0}, y_{0}, z_{0}, r, h | Half cone parallel to z-axis, base at (x_{0},y_{0},z_{0}), base radius r, height (distance from base to tip) h | |
quadratic | A, B, C, D, E, F, G, H, I, J, K | General quadratic surface in parametric form |
Non-quadratic surfaces
Surface name | Parameters | Surface equation | Description |
---|---|---|---|
inf | - | All space | |
torx | x_{0}, y_{0}, z_{0}, r, R | Circular torus with major radius R perpendicular to x-axis, centred at (x_{0}, y_{0}, z_{0}), minor radius r | |
tory | x_{0}, y_{0}, z_{0}, r, R | Circular torus with major radius R perpendicular to y-axis, centred at (x_{0}, y_{0}, z_{0}), minor radius r | |
torz | x_{0}, y_{0}, z_{0}, r, R | Circular torus with major radius R perpendicular to z-axis, centred at (x_{0}, y_{0}, z_{0}), minor radius r |
MCNP-equivalent surfaces
- Additional surfaces included to simplify input conversion between Serpent and MCNP.
- Includes cones and axisymmetric surfaces defined by points as used by MCNP.
- For description, see Chapter 3 of the MCNP5 User's Guide.^{[1]}
Surface name | Equivalent in MCNP |
---|---|
ckx | K/X |
cky | K/Y |
ckz | K/Z |
x | X |
y | Y |
z | Z |
Derived surface types
Notes:
- Derived surfaces refer here to surfaces composed of two or more elementary types.
Truncated cylinders
Notes:
- Truncated cylinders use the same names as the infinite cylinders above, with two additional values determining the height.
Surface name | Parameters | Composed of | Description |
---|---|---|---|
cylx | y_{0}, z_{0}, r, z_{0}, z_{1} | Infinite cylinder + two planes | Infinite cylinder parallel to x-axis, centred at (y_{0},z_{0}), radius r, truncated between [z_{0}, z_{1}] |
cyly | x_{0}, z_{0}, r, z_{0}, z_{1} | Infinite cylinder + two planes | Infinite cylinder parallel to y-axis, centred at (x_{0},z_{0}), radius r, truncated between [z_{0}, z_{1}] |
cylz, cyl | x_{0}, y_{0}, r, z_{0}, z_{1} | Infinite cylinder + two planes | Infinite cylinder parallel to z-axis, centred at (x_{0},y_{0}), radius r, truncated between [z_{0}, z_{1}] |
Regular prisms
Notes:
- All prisms are parallel to z-axis, and they can be rotated using surface transformations.
Surface name | Parameters | Composed of | Description |
---|---|---|---|
sqc | x_{0}, y_{0}, d | four planes | Infinite square prism parallel to z-axis, centred at (x_{0},y_{0}), half-width d |
rect | x_{0}, x_{1}, y_{0}, y_{1} | four planes | Infinite rectangular prism parallel to z-axis, between [x_{0}, x_{1}] and [y_{0}, y_{1}] |
hexxc | x_{0}, y_{0}, d | six planes | Infinite hexagonal prism parallel to z-axis, centred at (x_{0},y_{0}), flat surface perpendicular to x-axis, half-width d |
hexxy | x_{0}, y_{0}, d | six planes | Infinite hexagonal prism parallel to z-axis, centred at (x_{0},y_{0}), flat surface perpendicular to y-axis, half-width d |
hexxprism | x_{0}, y_{0}, d, z_{0}, z_{1} | eight planes | Truncated hexagonal prism parallel to z-axis, centred at (x_{0},y_{0}), flat surface perpendicular to x-axis, half-width d, truncated between [z_{0}, z_{1}] |
hexyprism | x_{0}, y_{0}, d, z_{0}, z_{1} | eight planes | Truncated hexagonal prism parallel to z-axis, centred at (x_{0},y_{0}), flat surface perpendicular to y-axis, half-width d, truncated between [z_{0}, z_{1}] |
octa | x_{0}, y_{0}, d_{1}, d_{2} | eight planes | Infinite octagonal prism parallel to z-axis, centred at (x_{0},y_{0}), half-widths d_{1} and d_{2} |
dode | x_{0}, y_{0}, d_{1}, d_{2} | twelve planes | Infinite dodecagonal prism parallel to z-axis, centred at (x_{0},y_{0}), half-widths d_{1} and d_{2} |
3D polyhedra
Notes:
- The description of parallelepiped may be wrong.
Surface name | Parameters | Composed of | Description |
---|---|---|---|
cube | x_{0}, y_{0}, z_{0}, d | six planes | Cube, centred at (x_{0},y_{0},z_{0}), half-width d |
cuboid | x_{0}, x_{1}, y_{0}, y_{1}, z_{0}, z_{1} | six planes | Cuboid, between [x_{0}, x_{1}], [y_{0}, y_{1}] and [z_{0}, z_{1}] |
ppd | x_{0}, y_{0}, z_{0}, L_{x}, L_{y}, L_{z}, _{x}, _{y}, _{z} | six planes | Parallelepiped, with corner at (x_{0}, y_{0}, z_{0}) and edges of length L_{x}, L_{y} and L_{z} at angles _{x}, _{y} and _{z} (in degrees) with respect to the coordinate axes |
Other derived surface types
Surface name | Parameters | Description |
---|---|---|
pad | x_{0}, y_{0}, r_{1}, r_{2}, _{1}, _{2} | Sector from _{1} to _{2} (in degrees) of a cylinder parallel to z-axis, centred at (x_{0},y_{0}), between radii r_{1} and r_{2} |
cross | x_{0}, y_{0}, l, d | Cruciform prism parallel to z-axis, centred at (x_{0},y_{0}), half-width l, half-thickness d |
gcross | x_{0}, y_{0}, d_{1}, d_{2}, ... | Prism parallel to z-axis, centred at (x_{0},y_{0}), formed by planes at distances d_{n} from the center (see figure below) |
Rounded corners
User-defined surfaces
References
- ^ X-5 Monte Carlo Team. "MCNP — A General Monte Carlo N-Particle Transport Code, Version 5, Volume II: User’s Guide." LA-CP-03-0245, Los Alamos National Laboratory, 2003.