Surface types

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.
• The positive side for a plane defined by three points is determined by the order in which the points are entered (see the right-hand rule).

Surface name	Parameters	Surface equation	Description
px	x0	$S(x) = x - x_0$	Plane perpendicular to x-axis at x = x0
py	y0	$S(y) = y - y_0$	Plane perpendicular to y-axis at y = y0
pz	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
• Infinite cylinders use the same names as the truncated cylinders.
• With three values provided in the surface card for cylx, cyly, cylz or cyl the surface is an infinite cylinder. With five values the surface is an truncated cylinder.

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	$S(x,y,z) = (x - x_0)^2 + (y - y_0)^2 - \left(1 - (z - z_0)/h\right)r^2$	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	$S(x,y,z) = Ax^2 + By^2 + Cz^2 + Dxy + Eyz + Fzx + Gx + Hy + Iz + J$	General quadratic surface in parametric form

Non-quadratic surfaces

Notes:

• Serpent can handle circular and elliptical torii. Radii r₁ and r₂ must be set equal (denoted in the surface equations as r) to describe a circular torus surface.

Surface name	Parameters	Surface equation	Description	Notes
inf	-	$S(y,x,z) = -\infty$	All space	Can not be used in root universe
torx	x0, y0, z0, R, r, r	$S(x,y,z) = \left(R - \sqrt{(y - y_0)^2 + (z - z_0)^2}\right)^2 + (x - x_0)^2 - r^2$	Circular torus with major radius R perpendicular to x-axis (revolving radius), centred at (x0, y0, z0), minor radius r (inner radius).
	x0, y0, z0, R, r1, r2	$S(x,y,z) = \dfrac{\left(R - \sqrt{(y - y_0)^2 + (z - z_0)^2}\right)^2}{r_2^2} + \dfrac{(x - x_0)^2}{r_1^2} - 1$	Elliptic torus with major radius R perpendicular to x-axis (revolving radius) centred at (x0, y0, z0), vertical (x-)semi-axis r1 and horizontal (y-/z-)semi-axis r2.
tory	x0, y0, z0, R, r, r	$S(x,y,z) = \left(R - \sqrt{(x - x_0)^2 + (z - z_0)^2}\right)^2 + (y - y_0)^2 - r^2$	Circular torus with major radius R perpendicular to y-axis (revolving radius), centred at (x0, y0, z0), minor radius r (inner radius).
	x0, y0, z0, R, r1, r2	$S(x,y,z) = \dfrac{\left(R - \sqrt{(x - x_0)^2 + (z - z_0)^2}\right)^2}{r_2^2} + \dfrac{(y - y_0)^2}{r_1^2} - 1$	Elliptic torus with major radius R perpendicular to y-axis (revolving radius) centred at (x0, y0, z0), vertical (y-)semi-axis r1 and horizontal (x-/z-)semi-axis r2.
torz	x0, y0, z0, R, r, r	$S(x,y,z) = \left(R - \sqrt{(x - x_0)^2 + (y - y_0)^2}\right)^2 + (z - z_0)^2 - r^2$	Circular torus with major radius R perpendicular to z-axis (revolving radius), centred at (x0, y0, z0), minor radius r (inner radius).
	x0, y0, z0, R, r1, r2	$S(x,y,z) = \dfrac{\left(R - \sqrt{(x - x_0)^2 + (y - y_0)^2}\right)^2}{r_2^2} + \dfrac{(z - z_0)^2}{r_1^2} - 1$	Elliptic torus with major radius R perpendicular to z-axis (revolving radius) centred at (x0, y0, z0), vertical (z-)semi-axis r1 and horizontal (x-/y-)semi-axis r2.

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.
• With five values provided in the surface card for cylx, cyly, cylz or cyl the surface is an truncated cylinder. With three values the surface is an infinite cylinder.

Surface name	Parameters	Composed of	Description
cylx	y0, z0, r, x0, x1	Infinite cylinder + two planes	Infinite cylinder parallel to x-axis, centred at (y0,z0), radius r, truncated between [x0, x1]
cyly	x0, z0, r, y0, y1	Infinite cylinder + two planes	Infinite cylinder parallel to y-axis, centred at (x0,z0), radius r, truncated between [y0, y1]
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:

• All prisms are parallel to z-axis, and they can be rotated using surface transformations.
• Infinite and truncated triangular prisms use the same name, and are composed by three or five planes, respectively. Infinite prism is assumed if three/four values are provided in the surface card tric. With six values the surface is assumed to be a truncated (equilateral) triangular prism.
• Triangular prisms orientation, ori, corresponds to the cardinal direction of the non-aligned vertex of the triangle. Default orientation is North. It follows the scheme: W-S-E-N (W=1, S=2, E=3, N=4).

Surface name	Parameters	Composed of	Description
tric	x0, y0, r, ori	three planes	Infinite (equilateral) triangular prism parallel to z-axis, centred at (x0,y0), incircle radius r, orientation ori (optional)
	x0, y0, r, ori, z0, z1	five planes	Truncated (equilateral) triangular prism parallel to z-axis, centred at (x0,y0), incircle radius r, orientation ori, truncated between [z0, z1]
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

• 

  X-type hexagonal prism (hexxc)

• 

  Y-type hexagonal prism (hexyc)

• 

  Octagonal prism (octa)

• 

  Dodecagonal prism (dode)

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, αx, αy, αz	six planes	Parallelepiped, with corner at (x0, y0, z0) and edges of length Lx, Ly and Lz at angles αx, αy and αz (in degrees) with respect to the coordinate axes

Other derived surface types

Surface name	Parameters	Description
pad	x0, y0, r1, r2, α1, α2	Sector from α1 to α2 (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, centered 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)
hexxap	x0, y0, wd, dw, a	Surface for simplified modeling of hexagonal fuel assembly angle pieces. Consists of two infinite hexagonal prisms parallel to z-axis, centered at (x0, y0), flat surfaces perpendicular to x-axis, with the outer hexagon having outer half-width of wd, and the surface perpendicular thickness is dw (the inner hexagon half width is wd - dw), and each half-section of each angle piece with width of a, measured from the tip of the angle piece angle to the flat surface of the angle piece.
hexyap	x0, y0, wd, dw, a	Surface for simplified modeling of hexagonal fuel assembly angle pieces. Consists of two infinite hexagonal prisms parallel to z-axis, centered at (x0, y0), flat surfaces perpendicular to y-axis, with the outer hexagon having outer half-width of wd, and the surface perpendicular thickness is dw (the inner hexagon half width is wd - dw), and each half-section of each angle piece with width of a, measured from the tip of the angle piece angle to the flat surface of the angle piece.
involute	x0, y0, r0, θ1, θ2, r1, r2	Involute parallel to z-axis, centred at (x0,y0), involute radii r0, and involute starting angle θ0 (defined by θ1 and θ2, first and second involute angles, respectively), and, limited by an inner and an outer cylinder with radii r1 and r2, respectively.
vessel	x0, y0, r, z1, z2, h1, h2	Vessel-like surface based on a infinite cylinder parallel to z-axis centred at (x0, y0), radii r, truncated between [z1,z2], and two semi-ellipsoids: [bottom] centred at (x0,y0,z1), with semi-axes r, r, h1, truncated at z1; [top] centred at (x0,y0,z2), with semi-axes r, r, h2, truncated at z2. If the last value is omitted: h = h1 = h2.

• 

  Cylinder sector (pad)

• 

  Cruciform prism (cross)

• 

  Generalized cruciform prism (gcross)

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):

• 

  Square prism with rounded corners

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.

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.