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 cylinder is assumed if three values are provided in the surface card for cylx, cyly, cylz or cyl. With five values the surface is assumed to be a 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	$(x - x_0)^2 + (y - y_0)^2 - \left(1 - (z - z_0)/h\right)r^2$	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	Notes
inf	-	$S(y,x,z) = -\infty$	All space	Can not be used in root universe
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.
• Infinite cylinder is assumed if three values are provided in the surface card for cylx, cyly, cylz or cyl. With five values the surface is assumed to be a truncated 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.

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

• 

  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, $\alpha$x, $\alpha$y, $\alpha$z	six planes	Parallelepiped, with corner at (x0, y0, z0) and edges of length Lx, Ly and Lz at angles $\alpha$x, $\alpha$y and $\alpha$z (in degrees) with respect to the coordinate axes

Other derived surface types

Surface name	Parameters	Description
pad	x0, y0, r1, r2, $\alpha$1, $\alpha$2	Sector from $\alpha$1 to $\alpha$2 (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 middle 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 middle tip of the angle piece angle to the flat surface of the angle piece.

• 

  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.