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Manuscript Title: Beam-plasma dielectric tensor with Mathematica
Authors: A. Bret
Program title: Tensor Mathematica.nb
Catalogue identifier: ADYT_v1_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 176(2007)362
Programming language: Mathematica 4.1.
Computer: Any computer running Mathematica 4.1. Tested on DELL Dimension 5100 and IBM ThinkPad T42.
Operating system: Windows XP Pro.
RAM: 7.17 Mbytes
Keywords: Plasma physics, Dielectric tensor, Fluid equations, Instabilities.
PACS: 52.35.Qz, 52.35.Hr, 52.50.Gj, 52.57.Kk.
Classification: 19.2.

Nature of problem:
The dielectric tensor of a relativistic beam plasma system may be quite involved to calculate symbolically when considering a magnetized plasma, kinetic pressure, collisions between species, and so on. The present Mathematica Notebook performs the symbolic computation in terms of some usual dimensionless variables.

Solution method:
The linearized relativistic fluid equations are directly entered and solved by Mathematica to express the first order expression of the current. This expression is then introduced into a combination of Faraday and Ampère Maxwell's equations to give the dielectric tensor. Some additional manipulations are needed to express the result in terms of the dimensionless variables.

Restrictions:
Temperature effects are limited to small, i.e non-relativistic, temperatures. The kinetic counterpart of the present Mathematica Notebook cannot be implemented because Mathematica will usually not compute the required integrals.

Running time:
About 1 minute on a Intel Centrino 1.5 Ghz Laptop with 512 Mo of RAM.