COMPLETE SPHERICAL HARMONICS SOLUTION OF THE BOLTZMANN EQUATION FOR NEUTRON TRANSPORT IN HOMOGENEOUS MEDIA WITH CYLINDRICAL GEOMETRY

Journal Article · Tue Dec 01 04:00:00 EST 1959 · Nuclear Sci. and Eng.

OSTI ID:4204465

Kofink, W

It is shown that the treatment of the transport equation in cylindrical geometry does not involve essentially more tedious calculations than the treatment in plane geometry. A complete solution is given for homogeneous media including the complementary solutions. Every partial solution contains in its expansion of spherical harmonics some functions of a parameter with appropriate coefficients. It will be shown that these functions are Legendre polynomials and Legendre functions of the second kind as in the case of plane geometry for the "main" solution, and derivatives of these functions for the "complementary" solutions. They are solutions of the recursion relations for the expansion and yield a further recursion relation for the coefficients. Tables of these coefficients are given up to the eleventh spherical harmonic approximation and a general formula is derived for them. Two examples are worked out, a first based upon the supposition of a linearly anisotropic scattering law, and a second in which two higher terms of anistropy are added to this law. (auth)

• Research Organization: Princeton Univ., N.J.
• NSA Number: NSA-14-004643
• OSTI ID: 4204465
• Journal Information: Nuclear Sci. and Eng., Journal Name: Nuclear Sci. and Eng. Vol. Vol: 6
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

ANISOTROPY
BOLTZMANN EQUATION
CONFIGURATION
CYLINDERS
DIFFERENTIAL EQUATIONS
HOMOGENEOUS REACTORS
LEGENDRE FUNCTIONS
LEGENDRE POLYNOMIALS
MATHEMATICS
NEUTRONS
PHYSICS
SCATTERING
TRANSPORT THEORY