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Manuscript Title: Numerical solution to Vlasov equation: the 2D code. See erratum Comp. Phys. Commun. 124(2000)359.
Authors: E. Fijalkow
Program title: vl2dper
Catalogue identifier: ADJR_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 116(1999)336
Programming language: Fortran.
Computer: Cray C 90.
Operating system: Unix.
Keywords: Plasma physics, Collisionless plasma, Vlasov equation, Poisson equation, Eulerian, 2d plasma simulation, Distribution function, Phase space.
Classification: 19.3.

Nature of problem:
Since the seventies, two main types of code are available to simulate plasma evolution: Particles (Lagrangian) codes or Eulerian codes. The advantage of particles codes is their capacity to go to high dimensions (two or three), their inconvenience the difficulty they have to represent with a good accuracy high velocity particles, and the numerical noise of the code, due to the too low number of particles used. Hybrid methods such as the deltaF method [2] or VHS method [3] mixing particles and phase space representation have a low numerical noise. Nevertheless, as the v-space behaviour is not far from a maxwellian, a thermal noise is present. This effect is very important in acceleration processes as the contribution of a few number of fast particles present a large part of the total energy. The advantage of the actual code is very low thermal noise, and its capability to represent all phase space with the same accuracy. Actually the present code cannot be generalized to three dimensions at present because of the limited computer memory available.
The major problems where the Eulerian codes are needed are plasma acceleration problems, specially relativistic cases, solar wind studies or all problems where a low numerical noise is important.

Solution method:
The method used in the present code is time splitting to transform the Vlasov equation into a set of transport equations, and solution of the transport (in phase space) equation by a Flux Balance Method [1] (F.B.M.). The four equations we get after the splitting are solved iteratively by FBM, following a symmetrical scheme to conserve a leap frog integration in time, method. The fields are calculated once every time step.

Unusual features:
External libraries used: UNICOS Scientific Library (for FFTs), or C. Temperton's FFT991 subroutine [4].

Running time:
The actual test run takes 15810 sec for 400 time steps (neglecting the code initialization), for a grip of 64 x 128 x 127 x 127, or 0.299 mu sec per time step per grid point on a Cray C98 computer.

References:
[1] E. Fijalkow, A Numerical Solution to Vlasov Equation, Comp. Phys. Commun.
[2] T. Tajima, F.W. Perkins, Proceedings Sherwood Theory Meeting, Univ. of Maryland, (1983).
[3] D. Nunn, J. Comp. Phys. 108, 180, (1993).
[4] C. Temperton, J. Comp. Phys. 52, 198, (1983).