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Manuscript Title: Beam-plasma dielectric tensor with Mathematica | ||

Authors: A. Bret | ||

Program title: Tensor Mathematica.nb | ||

Catalogue identifier: ADYT_v1_0Distribution 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. |

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