Surface types

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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 x0 S(x) = x - x_0 Plane perpendicular to x-axis at x = x0
pz y0 S(y) = y - y_0 Plane perpendicular to y-axis at y = y0
px z0 S(z) = z - z_0 Plane perpendicular to z-axis at z = z0
plane A, B, C, D S(x,y,z) = Ax+ By + Cz - D General plane in parametric form
plane x1, y1, z1, x2, y2, z2, x3, y3, z3 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 y0, z0, r S(y,z) = (y - y_0)^2 + (z - z_0)^2 - r^2 Infinite cylinder parallel to x-axis, centred at (y0,z0), radius r
cyly x0, z0, r S(x,z) = (x - x_0)^2 + (z - z_0)^2 - r^2 Infinite cylinder parallel to y-axis, centred at (x0,z0), radius r
cylz, cyl x0, y0, r S(x,y) = (x - x_0)^2 + (y - y_0)^2 - r^2 Infinite cylinder parallel to z-axis, centred at (x0,y0), radius r
cylv x0, y0, z0, u0, v0, w0, r S(x,y,z) = (1-u_0^2)(x - x_0)^2 + (1-v_0^2)(y - y_0)^2 + (1-w_0^2)(z - z_0)-r^2 Infinite cylinder, parallel to (u0,v0,w0), centred at (x0,y0,z0), radius r
sph x0, y0, z0, r S(x,y,z) = (x - x_0)^2 + (y - y_0)^2 + (z - z_0)^2 - r^2 Sphere, centred at (x0,y0,z0), radius r
cone x0, y0, z0, r, h (x - x_0)^2 + (y - y_0)^2 - \left(1 - (z - z_0)/h\right)r^2 Half cone parallel to z-axis, base at (x0,y0,z0), base radius r, height h (distance from base to vertex)
quadratic A, B, C, D, E, F, G, H, I, J, K S(x,y,z) = Ax^2 + By^2 + Cz^2 + Dxy + Eyz + Fzx + Gx + Hy + Jz + K General quadratic surface in parametric form

Non-quadratic surfaces

Notes:

  • Serpent can currently handle only circular torii. Radii R1 and R2 must be set equal (denoted in the surface equations as R).
Surface name Parameters Surface equation Description
inf - S(y,x,z) = -\infty All space
torx x0, y0, z0, r, R1, R2  S(x,y,z) = \left(R - \sqrt{(y - y_0)^2 + (z - z_0)^2}\right)^2 + (x - x_0)^2 - r^2 Circular torus with major radius R perpendicular to x-axis, centred at (x0, y0, z0), minor radius r
tory x0, y0, z0, r, R1, R2  S(x,y,z) = \left(R - \sqrt{(x - x_0)^2 + (z - z_0)^2}\right)^2 + (y - y_0)^2 - r^2 Circular torus with major radius R perpendicular to y-axis, centred at (x0, y0, z0), minor radius r
torz x0, y0, z0, r, R1, R2  S(x,y,z) = \left(R - \sqrt{(x - x_0)^2 + (y - y_0)^2}\right)^2 + (z - z_0)^2 - r^2 Circular torus with major radius R perpendicular to z-axis, centred at (x0, y0, z0), minor radius r

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 y0, z0, r, z0, z1 Infinite cylinder + two planes Infinite cylinder parallel to x-axis, centred at (y0,z0), radius r, truncated between [z0, z1]
cyly x0, z0, r, z0, z1 Infinite cylinder + two planes Infinite cylinder parallel to y-axis, centred at (x0,z0), radius r, truncated between [z0, z1]
cylz, cyl x0, y0, r, z0, z1 Infinite cylinder + two planes Infinite cylinder parallel to z-axis, centred at (x0,y0), radius r, truncated between [z0, z1]

Regular prisms

Notes:

Surface name Parameters Composed of Description
sqc x0, y0, d four planes Infinite square prism parallel to z-axis, centred at (x0,y0), half-width d
rect x0, x1, y0, y1 four planes Infinite rectangular prism parallel to z-axis, between [x0, x1] and [y0, y1]
hexxc x0, y0, d six planes Infinite hexagonal prism parallel to z-axis, centred at (x0,y0), flat surface perpendicular to x-axis, half-width d
hexyc x0, y0, d six planes Infinite hexagonal prism parallel to z-axis, centred at (x0,y0), flat surface perpendicular to y-axis, half-width d
hexxprism x0, y0, d, z0, z1 eight planes Truncated hexagonal prism parallel to z-axis, centred at (x0,y0), flat surface perpendicular to x-axis, half-width d, truncated between [z0, z1]
hexyprism x0, y0, d, z0, z1 eight planes Truncated hexagonal prism parallel to z-axis, centred at (x0,y0), flat surface perpendicular to y-axis, half-width d, truncated between [z0, z1]
octa x0, y0, d1, d2 eight planes Infinite octagonal prism parallel to z-axis, centred at (x0,y0), half-widths d1 and d2
dode x0, y0, d1, d2 twelve planes Infinite dodecagonal prism parallel to z-axis, centred at (x0,y0), half-widths d1 and d2

3D polyhedra

Notes:

  • The description of parallelepiped may be wrong.
Surface name Parameters Composed of Description
cube x0, y0, z0, d six planes Cube, centred at (x0,y0,z0), half-width d
cuboid x0, x1, y0, y1, z0, z1 six planes Cuboid, between [x0, x1], [y0, y1] and [z0, z1]
ppd x0, y0, z0, Lx, Ly, Lz, \alphax, \alphay, \alphaz six planes Parallelepiped, with corner at (x0, y0, z0) and edges of length Lx, Ly and Lz at angles \alphax, \alphay and \alphaz (in degrees) with respect to the coordinate axes

Other derived surface types

Surface name Parameters Description
pad x0, y0, r1, r2, \alpha1, \alpha2 Sector from \alpha1 to \alpha2 (in degrees) of a cylinder parallel to z-axis, centred at (x0,y0), between radii r1 and r2
cross x0, y0, l, d Cruciform prism parallel to z-axis, centred at (x0,y0), half-width l, half-thickness d
gcross x0, y0, d1, d2, ... Prism parallel to z-axis, centred at (x0,y0), formed by planes at distances dn from the center ("generalized cruciform prism", see figure below)

Rounded corners

Infinite prisms:

  • sqc
  • hexxc
  • hexyc
  • cross

Allow defining rounded corners. The radius is then provided as the last surface parameter (s in figure below):

MCNP-equivalent surfaces

Notes:

  • Additional surfaces included to simplify input conversion between Serpent and MCNP.
  • For description, see Chapter 3 of the MCNP5 User's Guide.[1]
Surface name Equivalent surface in MCNP
box BOX
ckx K/X
cky K/Y
ckz K/Z
mplane P (form defined by three points)
rcc RCC
x X
y Y
z Z

User-defined surfaces

Notes:

  • Remember to make a backup of your subroutine before installing new updates.
  • If you have a working surface routine that might be useful for other users as well, contact the Serpent team and we'll include it in the next update as a built-in type.
Surface name Parameters Description
usr p1, p2, ... User-defined surface, implemented in source file "usersurf.c". The subroutine receives the number and list of surface parameters as input. Instructions are included as comments in the source file.

References

  1. ^ 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.