Higher order Fokker-Planck operators

Journal Article · Fri Nov 01 04:00:00 EST 1996 · Nuclear Science and Engineering

OSTI ID:418091

Pomraning, G C ^[1]

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1. Univ. of California, Los Angeles, CA (United States). School of Engineering and Applied Science

If the scattering interaction in linear particle transport problems is highly peaked about zero momentum transfer, a common and often useful approximation is the replacement of the integral scattering operator with the differential Fokker-Planck operator. This operator involves a first derivative in energy and second derivatives in angle. In this paper, higher order Fokker-Planck scattering operators are derived, involving higher derivatives in both energy and angle. The applicability of these higher order differential operators to representative scattering kernels is discussed. It is shown that, depending upon the details of the scattering kernel in the integral operator, higher order Fokker-Planck approximations may or may not be valid. Even the classic low-order Fokker-Planck operator fails as an approximation for certain highly peaked scattering kernels. In particular, no Fokker-Planck operator is a valid approximation for scattering involving the widely used Henyey-Greenstein scattering kernel.

• OSTI ID: 418091
• Journal Information: Nuclear Science and Engineering, Journal Name: Nuclear Science and Engineering Journal Issue: 3 Vol. 124; ISSN NSENAO; ISSN 0029-5639
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
ACCURACY
FOKKER-PLANCK EQUATION
INTEGRAL EQUATIONS
MATHEMATICAL OPERATORS
NEUTRON TRANSPORT THEORY