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Title: A Langevin approach to multi-scale modeling

Abstract

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:
Research Org.:
Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Fusion Energy Sciences (FES) (SC-24)
OSTI Identifier:
1437600
Alternate Identifier(s):
OSTI ID: 1433047
Grant/Contract Number:  
AC02-09CH11466; SC0016268
Resource 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)
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

Citation Formats

Hirvijoki, Eero. A Langevin approach to multi-scale modeling. United States: N. p., 2018. Web. doi:10.1063/1.5025716.
Hirvijoki, Eero. A Langevin approach to multi-scale modeling. United States. doi:10.1063/1.5025716.
Hirvijoki, Eero. Fri . "A Langevin approach to multi-scale modeling". United States. doi:10.1063/1.5025716. https://www.osti.gov/servlets/purl/1437600.
@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}
}

Journal Article:
Free Publicly Available Full Text
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Figures / Tables:

FIG. 1 FIG. 1: The transition probability and its complement as a function of energy normalized to the temperature for M = 10 and different N. Notice the steepening of Φ with increasing N which reflects that the particles become less collisional at higher energies.

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    Figures / Tables found in this record:

      Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.