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Manuscript Title: Numerical solution to Vlasov equation: the 1D code. See erratum Comp. Phys. Commun. 124(2000)359.
Authors: E. Fijalkow
Program title: vl1dper
Catalogue identifier: ADJQ_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 116(1999)329
Programming language: Fortran.
Computer: Cray C 90.
Operating system: Unix.
Keywords: Plasma physics, Collisionless plasma, Vlasov equation, Poisson equation, Eulerian, 1d plasma simulation, Distribution function, Phase space.
Classification: 19.3.

Nature of problem:
The numerical solution of the Vlasov Poisson system is commonly used to follow the evolution of plasmas. For years the most used method has been particles simulation (PIC codes). Advantages of the method are its capability to run with a small number of particles, its accurate treatment of advection and the absence of a need for velocity space meshes. The major inconvenience of that method is its inefficiency to present the behaviour of high velocity particles in near Maxwellian plasmas. These kind of plasmas are those encountered in plasma acceleration problems - as laser, plasma acceleration, fast electrons beams and so on. The advantage of the present code is its ability to treat with the same accuracy all the points of the phase-space.

Solution method:
The code is based on time splitting and the flux balance method [1]. The initial Vlasov equation is split into two equations, one for the evolution of the space variable, the second for the velocity variable. Both equations are solved iteratively by use of the Flux Balance method. The Poisson equation is solved by a method of spline interpolation [2] both to solve the potential and for, from the potential, the electric field.

Running time:
For the testrun the time is 4.98 sec. That means 0.153 mu sec/grid point/time step on a HP 9000, 180 MHz computer.

References:
[1] E. Fijalkow, A Numerical Solution to Vlasov Equation, Comp. Phys. Commun.
[2] G. Knorr, B. Joyce and A.J. Marcus, J. Comp. Phys. 38, 227-236 (1980).