A new approach to the evaluation and solution of the relativistic kinetic dispersion relation and verification with continuum kinetic simulation

Arrighi, W. J.; Banks, J. W.; Berger, R. L.; Chapman, T.; Odu, A. Gianesini; Gorman, J.

doi:10.1016/j.jcp.2024.113001

Title: A new approach to the evaluation and solution of the relativistic kinetic dispersion relation and verification with continuum kinetic simulation

Journal Article · 11 April 2024 · Journal of Computational Physics

DOI: https://doi.org/10.1016/j.jcp.2024.113001 · OSTI ID:2472506

Arrighi, W. J. ^[1];

^[2]; Berger, R. L. ^[1]; Chapman, T. ^[1]; Odu, A. Gianesini ^[2]; Gorman, J. ^[2]

Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
Rensselaer Polytechnic Inst., Troy, NY (United States)

Here, the present work describes a new approach to evaluation and root finding for the kinetic dispersion relation of Langmuir waves, which is central to the analytical understanding of collisionless damping in plasmas. The plasma dispersion function is solved to machine precision using direct integration in the complex plane in combination with an analytic evaluation of the residue to account for the deformation along the Landau contour. To efficiently attain machine precision, the contour is displaced in the complex plane prior to integration, and numerical subtleties related to the placement of the contour are discussed. The approach is generic in that it applies to arbitrary distribution functions, with the present manuscript focused on relativistic cases. Detailed verification of results via direct kinetic simulation in a variety of configuration space dimensions is also presented. Finally, the technique is applied to the challenging case of highly relativistic (i.e. extremely hot) plasmas. Here we show both qualitative agreement with prior work, as well as the disappearance of the Landau root which would have significant implication for real-life observation or experiment.

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Research Organization:: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

Sponsoring Organization:: USDOE; USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC52-07NA27344

OSTI ID:: 2472506

Report Number(s):: LLNL--JRNL-859459; 1085481

Journal Information:: Journal of Computational Physics, Journal Name: Journal of Computational Physics Vol. 508; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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Title: A new approach to the evaluation and solution of the relativistic kinetic dispersion relation and verification with continuum kinetic simulation

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