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Manuscript Title: FPPAC88: a two-dimensional multispecies nonlinear Fokker-Planck package.
Authors: A.A. Mirin, M.G. McCoy, G.P. Tomaschke, J. Killeen
Program title: FPPAC88
Catalogue identifier: AAQU_v3_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 51(1988)373
Programming language: Fortran.
Computer: CRAY-1.
Operating system: CTSS.
RAM: 250K words
Word size: 64
Keywords: Plasma physics, Kinetic model, Two-dimensional, Multispecies, Implicit, Nonlinear, Fokker-Planck.
Classification: 19.8.

Nature of problem:
The complete nonlinear multispecies Fokker-Planck collision operator for a plasma in two-dimensional velocity space is solved. The operator is expressed in terms of spherical coordinates (v=speed, theta=angle between velocity and magnetic field directions, phi=azimuthal angle) under the assumption of azimuthal symmetry. Provision is made for additional physics contributions.

Solution method:
The Fokker-Planck equation is solved using finite differences. Spatial derivatives are approximated by central differences, with the exception of the advective terms which are approximated by combined central/upwind formulae designed to accommodate situations in which advection dominates diffusion. Time-advancement is accomplished through either implicit operator splitting, an alternating direction implicit (ADI) algorithm, or fully implicit differencing. (In the latter case the user must supply his own nine-banded linear systems solver.) The Fokker-Planck coefficients and their derivatives are computed by expanding the distribution functions and the Rosenbluth potentials in Legendre series, and equating the respective series coefficients.

Reasons for new version:
The most important new feature is the modification of the spatial differencing to accommodate situations in which advection dominates diffusion (e.g. the slowing down of 14 MeV fusion protons in a deuteron background). Another important change is the discontinuance of the CDC- 7600 version of FPPAC; thus the NEW VERSION, FPPAC88, is applicable to machines with a single fast memory, in particular the Cray-1 with the CFT compiler.

Restrictions:
The user must specify the number of meshpoints in the two coordinate directions as well as the number of Legendre polynomials used to calculate the Fokker-Planck coefficients. Sufficient accuracy for most problems is attainable on the Cray-1. However, double precision should be used on a 32-bit-word machine.

Unusual features:
None

Running time:
9.6 ms/meshpoint/species on the Cray-1 are required to compute the Fokker-Planck coefficients. 1.9 ms/meshpoint are required to time- advance the distribution function for one species using implicit operator splitting. These times vary to some extent with the mesh configuration due to variations in vectorization efficiency.