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Manuscript Title: Integration of Vlasov equation by quantum mechanical formalism.
Authors: V.T. Nguyen, P. Bertrand, B. Izrar, E. Fijalkow, M.R. Feix
Program title: SHRD
Catalogue identifier: ACCY_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 34(1985)295
Programming language: Fortran.
Computer: NAS 9080.
Operating system: (MVS/JES 3) NAS, CRAY OS.
RAM: 268K words
Word size: 32
Keywords: Plasma physics, Collisionless plasma, Schrodinger-poisson System, Vlasov-poisson system.
Classification: 19.3.

Nature of problem:
Collisionless plasma described by the Vlasov-Poisson system is considered starting from initial conditions electron oscillations take place, and we look for the evolution in time of the plasma density, electric potential and total energy. For near Maxwellian initial conditions Landau damping is obtained.

Solution method:
The Vlasov-Poisson system governing collisionless plasma behaviour is replaced by the Schrodinger-Poisson system of equations. To integrate this system numerically, the potential Phi(x,t) is approximated by a series of Dirac time functions. With this approximation for every time step delta T the Schrodinger equation splits into two parts, the free particle term and the acceleration which are treated separately but exactly. The first term is integrated by Fourier transformation with respect to the space variable, while the second term is integrated directly in real space. Density and potential Fourier modes are computed from the wave function using the Poisson equation.

Restrictions:
The present paper is limited to one dimensional plasma. The program is designed to study the damping of longitudinal waves. It can easily be extended to other initial value problems by changing only the initial condition (cold plasma, two stream instability, etc, can be easily treated).

Running time:
Compilation time is about 1.2 s, assembling and loading time is about 0.35 s and the execution time of the test run is about 0.7 s on the NAS 9080 computer of the CIRCE (CRNS, Orsay, France) computing centre.