A numerical code for the calculation of relativistic electron cyclotron damping with an arbitrary distribution function at an arbitrary harmonic

摘要

The relativistic expressions for the anti-Hermitian parts of the relativistic dielectric tensor elements can be expressed as a single integral over the parallel momentum variable, allowing an arbitrary electron distribution function. A computer program has been written for the calculation of this single integral. The numerical results are tested for a relativistic Maxwellian distribution function and agree with analytical expressions for this case. The numerical code is therefore an essential element in a more general validation, evaluation and demonstration of powerful analytical results presented. The computer program is then applied to the calculation of relativistic electron cyclotron harmonic damping at any arbitrary harmonic, for any distorted electron distribution function, distorted for example by an electric field or by RF power sources, as for instance by both electron cyclotron and lower-hybrid waves, as calculated from a relativistic Fokker-Planck code. For generality, we also include the case of relativistic Landau damping, also used to check the code. Program summary: Program title: DAMPING Catalogue identifier: AEIS-v1-0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEIS-v1-0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/ licence.html No. of lines in distributed program, including test data, etc.: 84 108 No. of bytes in distributed program, including test data, etc.: 2 581 423 Distribution format: tar.gz Programming language: FORTRAN Computer: Any computer or work station Operating system: Any with a Fortran compiler RAM: 8 Mbytes, using double precision arithmetic, with 400×200 grid points, on an ALPHA server Classification: 19.8 External routines: Requires a link to the NAG libraries for the Bessel functions subroutines. Nature of problem: The computer program calculates generalized expressions for the anti-Hermitian part of the relativistic dielectric tensor in a plasma for an arbitrary distribution function, with comparison to the analytical expressions derived in [1], associated with a relativistic Maxwellian distribution, for any n-th cyclotron harmonic and for the relativistic Landau damping case when n=0. The anti-Hermitian parts of the dielectric tensor are important to know, since they determine the damping or emission of an electromagnetic wave within the plasma medium. New analytical expressions are derived for the relativistic Landau damping and for the electron cyclotron damping including the case n =1, for the case of an arbitrary distribution function. This is important since studies of the RF heating of tokamak plasmas in a fully self-consistent way involve the simultaneous description of the temporal evolution of the heated species velocity distribution function using a Fokker-Planck code, coupled to the damping of the wave on the evolving distribution function. We can evaluate numerically the degree by which a non-Maxwellian nature of the relativistic distribution function changes the Landau damping and the electron cyclotron damping, with respect to the Maxwellian case. In addition this is also important in the study of electron cyclotron emission, which can be a sensitive indicator of non-thermal electron distributions.