A Langevin approach to multi-scale modeling

Journal Article · 12 April 2018 · Physics of Plasmas

DOI: https://doi.org/10.1063/1.5025716 · OSTI ID:1437600

Hirvijoki, Eero  ^[1]

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1. Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)

In plasmas, distribution functions often demonstrate long anisotropic tails or otherwise significant deviations from local Maxwellians. The tails, especially if they are pulled out from the bulk, pose a serious challenge for numerical simulations as resolving both the bulk and the tail on the same mesh is often challenging. A multi-scale approach, providing evolution equations for the bulk and the tail individually, could offer a resolution in the sense that both populations could be treated on separate meshes or different reduction techniques applied to the bulk and the tail population. In this paper, we propose a multi-scale method which allows us to split a distribution function into a bulk and a tail so that both populations remain genuine, non-negative distribution functions and may carry density, momentum, and energy. The proposed method is based on the observation that the motion of an individual test particle in a plasma obeys a stochastic differential equation, also referred to as a Langevin equation. Finally, this allows us to define transition probabilities between the bulk and the tail and to provide evolution equations for both populations separately.

• Research Organization: Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
• Sponsoring Organization: USDOE; USDOE Office of Science (SC), Fusion Energy Sciences (FES) (SC-24)
• Grant/Contract Number: AC02-09CH11466; SC0016268
• OSTI ID: 1437600
• Journal Information: Physics of Plasmas, Journal Name: Physics of Plasmas Journal Issue: 4 Vol. 25; ISSN 1070-664X
• Publisher: American Institute of Physics (AIP)Copyright Statement
• Country of Publication: United States
• Language: English