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.
- Publication Date:
- Research Org.:
- Princeton Plasma Physics Laboratory (PPPL), Princeton, NJ (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Fusion Energy Sciences (FES)
- 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. https://doi.org/10.1063/1.5025716
Hirvijoki, Eero. Fri .
"A Langevin approach to multi-scale modeling". United States. https://doi.org/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 = {Fri Apr 13 00:00:00 EDT 2018},
month = {Fri Apr 13 00:00:00 EDT 2018}
}
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Figures / Tables:
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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Works referenced in this record:
A backward Monte-Carlo method for time-dependent runaway electron simulations
journal, September 2017
- Zhang, Guannan; del-Castillo-Negrete, Diego
- Physics of Plasmas, Vol. 24, Issue 9
Random Generation of Stochastic Area Integrals
journal, August 1994
- Gaines, J. G.; Lyons, T. J.
- SIAM Journal on Applied Mathematics, Vol. 54, Issue 4
Itô versus Stratonovich
journal, January 1981
- van Kampen, N. G.
- Journal of Statistical Physics, Vol. 24, Issue 1
A backward Monte Carlo approach to exotic option pricing
journal, April 2017
- Bormetti, G.; Callegaro, G.; Livieri, G.
- European Journal of Applied Mathematics, Vol. 29, Issue 1
Current in wave-driven plasmas
journal, January 1986
- Karney, Charles F. F.; Fisch, Nathaniel J.
- Physics of Fluids, Vol. 29, Issue 1
On the kinetic theory of rarefied gases
journal, December 1949
- Grad, Harold
- Communications on Pure and Applied Mathematics, Vol. 2, Issue 4
Higher-order time integration of Coulomb collisions in a plasma using Langevin equations
journal, June 2013
- Dimits, A. M.; Cohen, B. I.; Caflisch, R. E.
- Journal of Computational Physics, Vol. 242
Collisional delta- f scheme with evolving background for transport time scale simulations
journal, December 1999
- Brunner, S.; Valeo, E.; Krommes, J. A.
- Physics of Plasmas, Vol. 6, Issue 12
Adjoint Fokker-Planck equation and runaway electron dynamics
journal, January 2016
- Liu, Chang; Brennan, Dylan P.; Bhattacharjee, Amitava
- Physics of Plasmas, Vol. 23, Issue 1
Fokker–Planck kinetic modeling of suprathermal α -particles in a fusion plasma
journal, December 2014
- Peigney, B. E.; Larroche, O.; Tikhonchuk, V.
- Journal of Computational Physics, Vol. 278
A backward Monte Carlo approach to exotic option pricing
preprint, January 2015
- Bormetti, Giacomo; Callegaro, Giorgia; Livieri, Giulia
- arXiv
A backward Monte-Carlo method for time-dependent runaway electron simulations
text, January 2017
- Zhang, Guannan; del-Castillo-Negrete, Diego
- arXiv
Works referencing / citing this record:
Eliminating poor statistics in Monte-Carlo simulations of fast-ion losses to plasma-facing components and detectors
preprint, January 2019
- Hirvijoki, Eero
- arXiv
Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.