Beam-plasma dielectric tensor with Mathematica

We present a Mathematica notebook allowing for the symbolic calculation of the 3×3 dielectric tensor of a electron-beam plasma system in the fluid approximation. Calculation is detailed for a cold relativistic electron beam entering a cold magnetized plasma, and for arbitrarily oriented wave vectors. We show how one can elaborate on this example to account for temperatures, arbitrarily oriented magnetic field or a different kind of plasma. Ireland Computer for which the program is designed and others on which it has been tested: Computers: Any computer running Mathematica 4.1. Tested on DELL Dimension 5100 and IBM ThinkPad T42. Operating systems under which the program has been tested: Windows XP Pro Programming language used: Mathematica 4.1 Memory required to execute with typical data: 7.17 Mbytes No. of lines in distributed program, including test data, etc.: 19 No. of bytes in distributed program, including test data, etc.: 4 172 Distribution format: .nb Nature of physical 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. Method of solution: 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 on the complexity of the problem: 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. Unusual features of the program: none.