Adjoint Fokker-Planck equation and runaway electron dynamics
Abstract
The adjoint Fokker-Planck equation method is applied to study the runaway probability function and the expected slowing-down time for highly relativistic runaway electrons, including the loss of energy due to synchrotron radiation. In direct correspondence to Monte Carlo simulation methods, the runaway probability function has a smooth transition across the runaway separatrix, which can be attributed to effect of the pitch angle scattering term in the kinetic equation. However, for the same numerical accuracy, the adjoint method is more efficient than the Monte Carlo method. The expected slowing-down time gives a novel method to estimate the runaway current decay time in experiments. A new result from this work is that the decay rate of high energy electrons is very slow when E is close to the critical electric field. This effect contributes further to a hysteresis previously found in the runaway electron population.
- Authors:
-
- Princeton Univ., NJ (United States)
- Columbia Univ., New York, NY (United States)
- Publication Date:
- Research Org.:
- Columbia Univ., NY (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1468793
- Alternate Identifier(s):
- OSTI ID: 1234783
- Grant/Contract Number:
- FG02-03ER54696
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physics of Plasmas
- Additional Journal Information:
- Journal Volume: 23; Journal Issue: 1; Journal ID: ISSN 1070-664X
- Publisher:
- American Institute of Physics (AIP)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING; 70 PLASMA PHYSICS AND FUSION TECHNOLOGY
Citation Formats
Liu, Chang, Brennan, Dylan P., Bhattacharjee, Amitava, and Boozer, Allen H. Adjoint Fokker-Planck equation and runaway electron dynamics. United States: N. p., 2016.
Web. doi:10.1063/1.4938510.
Liu, Chang, Brennan, Dylan P., Bhattacharjee, Amitava, & Boozer, Allen H. Adjoint Fokker-Planck equation and runaway electron dynamics. United States. https://doi.org/10.1063/1.4938510
Liu, Chang, Brennan, Dylan P., Bhattacharjee, Amitava, and Boozer, Allen H. Wed .
"Adjoint Fokker-Planck equation and runaway electron dynamics". United States. https://doi.org/10.1063/1.4938510. https://www.osti.gov/servlets/purl/1468793.
@article{osti_1468793,
title = {Adjoint Fokker-Planck equation and runaway electron dynamics},
author = {Liu, Chang and Brennan, Dylan P. and Bhattacharjee, Amitava and Boozer, Allen H.},
abstractNote = {The adjoint Fokker-Planck equation method is applied to study the runaway probability function and the expected slowing-down time for highly relativistic runaway electrons, including the loss of energy due to synchrotron radiation. In direct correspondence to Monte Carlo simulation methods, the runaway probability function has a smooth transition across the runaway separatrix, which can be attributed to effect of the pitch angle scattering term in the kinetic equation. However, for the same numerical accuracy, the adjoint method is more efficient than the Monte Carlo method. The expected slowing-down time gives a novel method to estimate the runaway current decay time in experiments. A new result from this work is that the decay rate of high energy electrons is very slow when E is close to the critical electric field. This effect contributes further to a hysteresis previously found in the runaway electron population.},
doi = {10.1063/1.4938510},
journal = {Physics of Plasmas},
number = 1,
volume = 23,
place = {United States},
year = {Wed Jan 13 00:00:00 EST 2016},
month = {Wed Jan 13 00:00:00 EST 2016}
}
Free Publicly Available Full Text
Publisher's Version of Record
Other availability
Search WorldCat to find libraries that may hold this journal
Cited by: 4 works
Citation information provided by
Web of Science
Web of Science
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.
Works referenced in this record:
Radiation reaction induced non-monotonic features in runaway electron distributions
journal, July 2015
- Hirvijoki, E.; Pusztai, I.; Decker, J.
- Journal of Plasma Physics, Vol. 81, Issue 5
Damping of relativistic electron beams by synchrotron radiation
journal, December 2001
- Andersson, F.; Helander, P.; Eriksson, L. -G.
- Physics of Plasmas, Vol. 8, Issue 12
Synchrotron radiation from a runaway electron distribution in tokamaks
journal, September 2013
- Stahl, A.; Landreman, M.; Papp, G.
- Physics of Plasmas, Vol. 20, Issue 9
On the First Passage Time Probability Problem
journal, February 1951
- Siegert, Arnold J. F.
- Physical Review, Vol. 81, Issue 4
Current in wave-driven plasmas
journal, January 1986
- Karney, Charles F. F.; Fisch, Nathaniel J.
- Physics of Fluids, Vol. 29, Issue 1
Theory of runaway electrons in ITER: Equations, important parameters, and implications for mitigation
journal, March 2015
- Boozer, Allen H.
- Physics of Plasmas, Vol. 22, Issue 3
Effective Critical Electric Field for Runaway-Electron Generation
journal, March 2015
- Stahl, A.; Hirvijoki, E.; Decker, J.
- Physical Review Letters, Vol. 114, Issue 11
Destabilization of magnetosonic-whistler waves by a relativistic runaway beam
journal, June 2006
- Fülöp, T.; Pokol, G.; Helander, P.
- Physics of Plasmas, Vol. 13, Issue 6
Determination of the parametric region in which runaway electron energy losses are dominated by bremsstrahlung radiation in tokamaks
journal, July 2007
- Fernández-Gómez, I.; Martín-Solís, J. R.; Sánchez, R.
- Physics of Plasmas, Vol. 14, Issue 7
Growth and decay of runaway electrons above the critical electric field under quiescent conditions
journal, February 2014
- Paz-Soldan, C.; Eidietis, N. W.; Granetz, R.
- Physics of Plasmas, Vol. 21, Issue 2
Theory for avalanche of runaway electrons in tokamaks
journal, October 1997
- Rosenbluth, M. N.; Putvinski, S. V.
- Nuclear Fusion, Vol. 37, Issue 10
Experimental Observation of Increased Threshold Electric Field for Runaway Generation due to Synchrotron Radiation Losses in the FTU Tokamak
journal, October 2010
- Martín-Solís, J. R.; Sánchez, R.; Esposito, B.
- Physical Review Letters, Vol. 105, Issue 18
Relativistic limitations on runaway electrons
journal, June 1975
- Connor, J. W.; Hastie, R. J.
- Nuclear Fusion, Vol. 15, Issue 3
Theory of Two Threshold Fields for Relativistic Runaway Electrons
journal, April 2015
- Aleynikov, Pavel; Breizman, Boris N.
- Physical Review Letters, Vol. 114, Issue 15
Avalanche runaway growth rate from a momentum-space orbit analysis
journal, June 1999
- Parks, P. B.; Rosenbluth, M. N.; Putvinski, S. V.
- Physics of Plasmas, Vol. 6, Issue 6
Numerical calculation of the runaway electron distribution function and associated synchrotron emission
journal, March 2014
- Landreman, Matt; Stahl, Adam; Fülöp, Tünde
- Computer Physics Communications, Vol. 185, Issue 3
Effect of magnetic and electrostatic fluctuations on the runaway electron dynamics in tokamak plasmas
journal, October 1999
- Martín-Solís, J. R.; Sánchez, R.; Esposito, B.
- Physics of Plasmas, Vol. 6, Issue 10
On the Stochastic Theory of Neutron Transport
journal, March 1965
- Bell, George I.
- Nuclear Science and Engineering, Vol. 21, Issue 3
Electron and Ion Runaway in a Fully Ionized Gas. I
journal, July 1959
- Dreicer, H.
- Physical Review, Vol. 115, Issue 2
On the effect of synchrotron radiation and magnetic fluctuations on the avalanche runaway growth rate
journal, September 2000
- Martı́n-Solı́s, J. R.; Sánchez, R.; Esposito, B.
- Physics of Plasmas, Vol. 7, Issue 9
Momentum–space structure of relativistic runaway electrons
journal, June 1998
- Martı́n-Solı́s, J. R.; Alvarez, J. D.; Sánchez, R.
- Physics of Plasmas, Vol. 5, Issue 6
Zur Theorie des Durchgangs schneller Elektronen durch Materie
journal, January 1932
- Møller, Chr.
- Annalen der Physik, Vol. 406, Issue 5
Works referencing / citing this record:
Resolving runaway electron distributions in space, time, and energy
journal, May 2018
- Paz-Soldan, C.; Cooper, C. M.; Aleynikov, P.
- Physics of Plasmas, Vol. 25, Issue 5
A Langevin approach to multi-scale modeling
journal, April 2018
- Hirvijoki, Eero
- Physics of Plasmas, Vol. 25, Issue 4
Phase-space dynamics of runaway electrons in magnetic fields
journal, February 2017
- Guo, Zehua; McDevitt, Christopher J.; Tang, Xian-Zhu
- Plasma Physics and Controlled Fusion, Vol. 59, Issue 4
Conservative magnetic moment of runaway electrons and collisionless pitch-angle scattering
journal, August 2018
- Liu, Chang; Qin, Hong; Hirvijoki, Eero
- Nuclear Fusion, Vol. 58, Issue 10
Physics of runaway electrons in tokamaks
journal, June 2019
- Breizman, Boris N.; Aleynikov, Pavel; Hollmann, Eric M.
- Nuclear Fusion, Vol. 59, Issue 8
Evaluation of Monte Carlo tools for high-energy atmospheric physics II: relativistic runaway electron avalanches
journal, January 2018
- Sarria, David; Rutjes, Casper; Diniz, Gabriel
- Geoscientific Model Development, Vol. 11, Issue 11