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Manuscript Title: Numerical solution of the Fokker-Planck equation with dc electric
field. | ||

Authors: I.P. Shkarofsky, M.M. Shoucri, V. Fuchs | ||

Program title: FPLEGEND | ||

Catalogue identifier: ACJA_v1_0Distribution format: gz | ||

Journal reference: Comput. Phys. Commun. 71(1992)269 | ||

Programming language: Fortran. | ||

Computer: IBM 3092. | ||

Operating system: VMS. | ||

Keywords: Plasma physics, Kinetic model, Fokker-planck, Legendre expansion, Twodepep, Full electron-electron Collisions, Dc electric field, Non-linear conductivity. | ||

Classification: 19.8. | ||

Nature of problem:A code is presented that solves numerically the full non-relativistic Fokker-Planck equation using the IMSL package TWODEPEP, for the runaway electron distribution function in the presence of a dc electric field. Most other Fokker-Planck codes use a partially linearized form of this equation, which results in the wrong Spitzer conductivity. Here we aim to apply the full, rather than partially linearized, Fokker-Planck equation, which includes not only electron-electron collisions between the perturbed distribution and the bulk but also between the bulk and the perturbed distribution. Another new feature of this code is the calculation of the non-linear conductivity in the presence of a strong dc electric field, which in the limit of a low field reduces to the correct Spitzer conductivity. | ||

Solution method:To achieve these features, a set of partial integro-differential equations derived from a Legendre expansion of the Fokker-Planck equation is solved simultaneously for the electron distribution parts up to f3 with f0 non-Maxwellian and including the full electron-electron collision operator. The runaway distribution function and its moments yielding the non-linear conductivity, runaway rate, temperature and drift velocity are presented. Besides making amenable the treatment of the full integro-differential equation, calculations based on this expansion, being a series of one-dimensional equations, are easier to solve and require less computer time than a solution of the two- dimensional Fokker-Planck equation. This application also provides a powerful example on how to use the IMSL package TWODEPEP to solve a set of coupled non-linear differential equations. | ||

Running time:An execution on an IBM 3092 using 1000 quadratic elements and four Legendre polynomials requires a memory of 6 megabytes and an execution CPU time of about 25 minutes. |

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