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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.

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.