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Title: A Langevin approach to multi-scale modeling

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.
Authors:
ORCiD logo [1]
  1. Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
Publication Date:
Grant/Contract Number:
AC02-09CH11466; SC0016268
Type:
Accepted Manuscript
Journal Name:
Physics of Plasmas
Additional Journal Information:
Journal Volume: 25; Journal Issue: 4; Journal ID: ISSN 1070-664X
Publisher:
American Institute of Physics (AIP)
Research Org:
Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
Sponsoring Org:
USDOE Office of Science (SC), Fusion Energy Sciences (FES) (SC-24)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; plasma collisions; stochastic processes; tokamaks; plasma physics; Markov processes; multiscale methods
OSTI Identifier:
1437600
Alternate Identifier(s):
OSTI ID: 1433047

Hirvijoki, Eero. A Langevin approach to multi-scale modeling. United States: N. p., Web. doi:10.1063/1.5025716.
Hirvijoki, Eero. A Langevin approach to multi-scale modeling. United States. doi:10.1063/1.5025716.
Hirvijoki, Eero. 2018. "A Langevin approach to multi-scale modeling". United States. doi:10.1063/1.5025716.
@article{osti_1437600,
title = {A Langevin approach to multi-scale modeling},
author = {Hirvijoki, Eero},
abstractNote = {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.},
doi = {10.1063/1.5025716},
journal = {Physics of Plasmas},
number = 4,
volume = 25,
place = {United States},
year = {2018},
month = {4}
}