Kinetic corrections from analytic non-Maxwellian distribution functions in magnetized plasmas
Abstract
In magnetized plasma physics, almost all developed analytic theories assume a Maxwellian distribution function (MDF) and in some cases small deviations are described using the perturbation theory. The deviations with respect to the Maxwellian equilibrium, called kinetic effects, are required to be taken into account especially for fusion reactor plasmas. Generally, because the perturbation theory is not consistent with observed steady-state non-Maxwellians, these kinetic effects are numerically evaluated by very central processing unit (CPU)-expensive codes, avoiding the analytic complexity of velocity phase space integrals. We develop here a new method based on analytic non-Maxwellian distribution functions constructed from non-orthogonal basis sets in order to (i) use as few parameters as possible, (ii) increase the efficiency to model numerical and experimental non-Maxwellians, (iii) help to understand unsolved problems such as diagnostics discrepancies from the physical interpretation of the parameters, and (iv) obtain analytic corrections due to kinetic effects given by a small number of terms and removing the numerical error of the evaluation of velocity phase space integrals. This work does not attempt to derive new physical effects even if it could be possible to discover one from the better understandings of some unsolved problems, but here we focus on themore »
- Authors:
-
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
- Publication Date:
- Research Org.:
- Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1289360
- Alternate Identifier(s):
- OSTI ID: 1280200
- Report Number(s):
- LLNL-JRNL-686219
Journal ID: ISSN 1070-664X
- Grant/Contract Number:
- AC52-07NA27344
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physics of Plasmas
- Additional Journal Information:
- Journal Volume: 23; Journal Issue: 8; Journal ID: ISSN 1070-664X
- Publisher:
- American Institute of Physics (AIP)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 70 PLASMA PHYSICS AND FUSION; entropy; particle distribution functions; Maxwell equations; probe plasma diagnostics; cumulative distribution functions
Citation Formats
Izacard, Olivier. Kinetic corrections from analytic non-Maxwellian distribution functions in magnetized plasmas. United States: N. p., 2016.
Web. doi:10.1063/1.4960123.
Izacard, Olivier. Kinetic corrections from analytic non-Maxwellian distribution functions in magnetized plasmas. United States. https://doi.org/10.1063/1.4960123
Izacard, Olivier. Tue .
"Kinetic corrections from analytic non-Maxwellian distribution functions in magnetized plasmas". United States. https://doi.org/10.1063/1.4960123. https://www.osti.gov/servlets/purl/1289360.
@article{osti_1289360,
title = {Kinetic corrections from analytic non-Maxwellian distribution functions in magnetized plasmas},
author = {Izacard, Olivier},
abstractNote = {In magnetized plasma physics, almost all developed analytic theories assume a Maxwellian distribution function (MDF) and in some cases small deviations are described using the perturbation theory. The deviations with respect to the Maxwellian equilibrium, called kinetic effects, are required to be taken into account especially for fusion reactor plasmas. Generally, because the perturbation theory is not consistent with observed steady-state non-Maxwellians, these kinetic effects are numerically evaluated by very central processing unit (CPU)-expensive codes, avoiding the analytic complexity of velocity phase space integrals. We develop here a new method based on analytic non-Maxwellian distribution functions constructed from non-orthogonal basis sets in order to (i) use as few parameters as possible, (ii) increase the efficiency to model numerical and experimental non-Maxwellians, (iii) help to understand unsolved problems such as diagnostics discrepancies from the physical interpretation of the parameters, and (iv) obtain analytic corrections due to kinetic effects given by a small number of terms and removing the numerical error of the evaluation of velocity phase space integrals. This work does not attempt to derive new physical effects even if it could be possible to discover one from the better understandings of some unsolved problems, but here we focus on the analytic prediction of kinetic corrections from analytic non-Maxwellians. As applications, examples of analytic kinetic corrections are shown for the secondary electron emission, the Langmuir probe characteristic curve, and the entropy. This is done by using three analytic representations of the distribution function: the Kappa distribution function, the bi-modal or a new interpreted non-Maxwellian distribution function (INMDF). The existence of INMDFs is proved by new understandings of the experimental discrepancy of the measured electron temperature between two diagnostics in JET. As main results, it is shown that (i) the empirical formula for the secondary electron emission is not consistent with a MDF due to the presence of super-thermal particles, (ii) the super-thermal particles can replace a diffusion parameter in the Langmuir probe current formula, and (iii) the entropy can explicitly decrease in presence of sources only for the introduced INMDF without violating the second law of thermodynamics. Moreover, the first order entropy of an infinite number of super-thermal tails stays the same as the entropy of a MDF. In conclusion, the latter demystifies the Maxwell's demon by statistically describing non-isolated systems.},
doi = {10.1063/1.4960123},
journal = {Physics of Plasmas},
number = 8,
volume = 23,
place = {United States},
year = {Tue Aug 02 00:00:00 EDT 2016},
month = {Tue Aug 02 00:00:00 EDT 2016}
}
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Works referenced in this record:
Numerical studies of current generation by radio-frequency traveling waves
journal, January 1979
- Karney, Charles F. F.; Fisch, Nathaniel J.
- Physics of Fluids, Vol. 22, Issue 9
Effect of Secondary Electron Emission on Electron Cross-Field Current in $E \times B$ Discharges
journal, April 2011
- Raitses, Y.; Kaganovich, I. D.; Khrabrov, A.
- IEEE Transactions on Plasma Science, Vol. 39, Issue 4
Boltzmann’s theorem for systems with frictional dissipation
journal, March 2011
- Bizarro, João P. S.
- Physical Review E, Vol. 83, Issue 3
A problem in the interpretation of tokamak Langmuir probes when a fast electron component is present
journal, September 1995
- Stangeby, P. C.
- Plasma Physics and Controlled Fusion, Vol. 37, Issue 9
Inclusion of ion orbit loss and intrinsic rotation in plasma fluid rotation theory
journal, January 2016
- Stacey, W. M.; Wilks, T. M.
- Physics of Plasmas, Vol. 23, Issue 1
Modification of the electron energy distribution function during lithium experiments on the National Spherical Torus Experiment
journal, October 2012
- Jaworski, M. A.; Bell, M. G.; Gray, T. K.
- Fusion Engineering and Design, Vol. 87, Issue 10
Electron acceleration in three-dimensional magnetic reconnection with a guide field
journal, October 2015
- Dahlin, J. T.; Drake, J. F.; Swisdak, M.
- Physics of Plasmas, Vol. 22, Issue 10
Global-wave solutions with self-consistent velocity distributions in ion cyclotron heated plasmas
journal, June 2006
- Jaeger, E. F.; Harvey, R. W.; Berry, L. A.
- Nuclear Fusion, Vol. 46, Issue 7
Entropy balance in a multi-component system of gases derived by Grad's method
journal, January 1970
- Kranyš, Miroslav
- Archive for Rational Mechanics and Analysis, Vol. 39, Issue 4
Dark matter direct detection with non-Maxwellian velocity structure
journal, February 2010
- Kuhlen, Michael; Weiner, Neal; Diemand, Jürg
- Journal of Cosmology and Astroparticle Physics, Vol. 2010, Issue 02
Investigation of the Thomson scattering-ECE discrepancy in ICRF heated plasmas at Alcator C-Mod
journal, May 2012
- White, A. E.; Hubbard, A. E.; Hughes, J. W.
- Nuclear Fusion, Vol. 52, Issue 6
A fast non-Fourier method for Landau-fluid operators
journal, May 2014
- Dimits, A. M.; Joseph, I.; Umansky, M. V.
- Physics of Plasmas, Vol. 21, Issue 5
Detecting non-Maxwellian electron velocity distributions at JET by high resolution Thomson scattering
journal, March 2011
- Beausang, K. V.; Prunty, S. L.; Scannell, R.
- Review of Scientific Instruments, Vol. 82, Issue 3
Impact of carbon and tungsten as divertor materials on the scrape-off layer conditions in JET
journal, August 2013
- Groth, M.; Brezinsek, S.; Belo, P.
- Nuclear Fusion, Vol. 53, Issue 9
Modification of alpha-particle emission spectrum in beam-injected deuterium-tritium plasmas
journal, April 2009
- Matsuura, H.; Nakao, Y.
- Physics of Plasmas, Vol. 16, Issue 4
Probe measurements of electron energy distribution function at intermediate and high pressures and in a magnetic field
journal, November 1994
- Arslanbekov, R. R.; Khromov, N. A.; Kudryavtsev, A. A.
- Plasma Sources Science and Technology, Vol. 3, Issue 4
Kinetic effects in tokamak scrape-off layer plasmas
journal, May 1997
- Batishchev, O. V.; Krasheninnikov, S. I.; Catto, Peter J.
- Physics of Plasmas, Vol. 4, Issue 5
Production of Thermonuclear Power by Non-Maxwellian Ions in a Closed Magnetic Field Configuration
journal, May 1971
- Dawson, J. M.; Furth, H. P.; Tenney, F. H.
- Physical Review Letters, Vol. 26, Issue 19
Fast electron bremsstrahlung in axisymmetric magnetic configuration
journal, September 2008
- Peysson, Y.; Decker, J.
- Physics of Plasmas, Vol. 15, Issue 9
Bistable intrinsic charge fluctuations of a dust grain subject to secondary electron emission in a plasma
journal, October 2015
- Shotorban, B.
- Physical Review E, Vol. 92, Issue 4
Computational challenges in magnetic-confinement fusion physics
journal, May 2016
- Fasoli, A.; Brunner, S.; Cooper, W. A.
- Nature Physics, Vol. 12, Issue 5
Consequences of entropy bifurcation in non-Maxwellian astrophysical environments
journal, January 2008
- Leubner, M. P.
- Nonlinear Processes in Geophysics, Vol. 15, Issue 4
A study of the accuracy of various Langmuir probe theories
journal, October 1994
- Sudit, Isaac D.; Woods, R. Claude
- Journal of Applied Physics, Vol. 76, Issue 8
Dynamics of ion temperature gradient turbulence and transport with a static magnetic island
journal, February 2016
- Izacard, Olivier; Holland, Christopher; James, Spencer D.
- Physics of Plasmas, Vol. 23, Issue 2
A thermodynamical analysis of rf current drive with fast electrons
journal, August 2015
- Bizarro, João P. S.
- Physics of Plasmas, Vol. 22, Issue 8
Generalized fluid theory including non-Maxwellian kinetic effects
journal, March 2017
- Izacard, Olivier
- Journal of Plasma Physics, Vol. 83, Issue 2
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
Plasma diagnostics in the Tokamak Fusion Test Reactor using emission of electron cyclotron radiation at arbitrary frequencies
journal, June 1996
- Fidone, I.; Giruzzi, G.; Taylor, G.
- Physics of Plasmas, Vol. 3, Issue 6
Effect of ion orbit loss on the structure in the H-mode tokamak edge pedestal profiles of rotation velocity, radial electric field, density, and temperature
journal, September 2013
- Stacey, Weston M.
- Physics of Plasmas, Vol. 20, Issue 9
An estimate of the ion orbit loss rate in tokamaks
journal, October 1992
- Shaing, K. C.
- Physics of Fluids B: Plasma Physics, Vol. 4, Issue 10
Non-local approach to kinetic effects on parallel transport in fluid models of the scrape-off layer
journal, April 2013
- Omotani, J. T.; Dudson, B. D.
- Plasma Physics and Controlled Fusion, Vol. 55, Issue 5
Kinetic neoclassical transport in the H-mode pedestal
journal, July 2014
- Battaglia, D. J.; Burrell, K. H.; Chang, C. S.
- Physics of Plasmas, Vol. 21, Issue 7
Kinetic theory of desorption: Energy and angular distributions
journal, March 1983
- Leuth�usser, U.
- Zeitschrift f�r Physik B Condensed Matter, Vol. 50, Issue 1
Observation of non-Maxwellian electron distributions in the NSTX divertor
journal, July 2013
- Jaworski, M. A.; Bell, M. G.; Gray, T. K.
- Journal of Nuclear Materials, Vol. 438
“Lagrangian Temperature”: Derivation and Physical Meaning for Systems Described by Kappa Distributions
journal, July 2014
- Livadiotis, George
- Entropy, Vol. 16, Issue 8
Comparative study of secondary-electron emission from positron and electron bombardment of Ni, Si, and MgO
journal, December 1988
- Mayer, Rulon; Weiss, Alex
- Physical Review B, Vol. 38, Issue 16
Comparative analyses of plasma probe diagnostics techniques
journal, December 2015
- Godyak, V. A.; Alexandrovich, B. M.
- Journal of Applied Physics, Vol. 118, Issue 23
Neoclassical transport of impurities in tokamak plasmas
journal, September 1981
- Hirshman, S. P.; Sigmar, D. J.
- Nuclear Fusion, Vol. 21, Issue 9
Impact of bulk non-Maxwellian electrons on electron temperature measurements (invited)
journal, March 2003
- de la Luna, E.; Krivenski, V.; Giruzzi, G.
- Review of Scientific Instruments, Vol. 74, Issue 3
Non-diffusive transport of suprathermal ions by intermittent turbulent structures
journal, November 2015
- Furno, I.; Bovet, A.; Fasoli, A.
- Plasma Physics and Controlled Fusion, Vol. 58, Issue 1
Probe measurements of electron-energy distributions in plasmas: what can we measure and how can we achieve reliable results?
journal, May 2011
- Godyak, V. A.; Demidov, V. I.
- Journal of Physics D: Applied Physics, Vol. 44, Issue 23
On the kinetic theory of rarefied gases
journal, December 1949
- Grad, Harold
- Communications on Pure and Applied Mathematics, Vol. 2, Issue 4
Theory of Secondary Electron Emission by High-Speed Ions
journal, October 1957
- Sternglass, E. J.
- Physical Review, Vol. 108, Issue 1
Langmuir Probe Evaluation of the Plasma Potential in Tokamak Edge Plasma for Non-Maxwellian EEDF: Langmuir Probe Evaluation of the Plasma Potential in Tokamak Edge Plasma for Non-Maxwellian EEDF
journal, April 2014
- Popov, Tsv. K.; Dimitrova, M.; Ivanova, P.
- Contributions to Plasma Physics, Vol. 54, Issue 3
Discrepancy between modelled and measured radial electric fields in the scrape-off layer of divertor tokamaks: a challenge for 2D fluid codes?
journal, May 2007
- Chankin, A. V.; Coster, D. P.; Asakura, N.
- Nuclear Fusion, Vol. 47, Issue 5
Electric probes for plasmas: The link between theory and instrument
journal, October 2002
- Demidov, V. I.; Ratynskaia, S. V.; Rypdal, K.
- Review of Scientific Instruments, Vol. 73, Issue 10
Non‐Maxwellian H and F velocity distributions in an H 2 –F 2 reaction
journal, December 1975
- Riley, Merle E.; Matzen, M. Keith
- The Journal of Chemical Physics, Vol. 63, Issue 11
Asymptotic Theory of the Boltzmann Equation
journal, January 1963
- Grad, Harold
- Physics of Fluids, Vol. 6, Issue 2
Electron energy distribution function, plasma potential and electron density measured by Langmuir probe in tokamak edge plasma
journal, April 2009
- Popov, Tsv K.; Ivanova, P.; Stöckel, J.
- Plasma Physics and Controlled Fusion, Vol. 51, Issue 6
Ignition threshold for non-Maxwellian plasmas
journal, November 2015
- Hay, Michael J.; Fisch, Nathaniel J.
- Physics of Plasmas, Vol. 22, Issue 11
Dust in tokamaks: An overview of the physical model of the dust in tokamaks code
journal, April 2010
- Bacharis, Minas; Coppins, Michael; Allen, John E.
- Physics of Plasmas, Vol. 17, Issue 4
ICRF heating of TFTR plasmas fuelled by deuterium - tritium neutral beam injection
journal, May 1996
- Taylor, G.; LeBlanc, B.; Murakami, M.
- Plasma Physics and Controlled Fusion, Vol. 38, Issue 5
Nonlocal closures for plasma fluid simulations
journal, May 2004
- Held, E. D.; Callen, J. D.; Hegna, C. C.
- Physics of Plasmas, Vol. 11, Issue 5
Langmuir probe measurements of the electron energy distribution function in magnetized gas discharge plasmas
journal, March 2012
- Popov, Tsv K.; Ivanova, P.; Dimitrova, M.
- Plasma Sources Science and Technology, Vol. 21, Issue 2
On the causes of temperature change in inhomogeneous low-density astrophysical plasmas
journal, October 1992
- Scudder, Jack D.
- The Astrophysical Journal, Vol. 398
Interpretation of divertor Langmuir probe measurements during the ELMs at JET
journal, August 2011
- Tskhakaya, D.; Jachmich, S.; Eich, T.
- Journal of Nuclear Materials, Vol. 415, Issue 1
A possible role of radial electric field in driving parallel ion flow in scrape-off layer of divertor tokamaks
journal, July 2007
- Chankin, A. V.; Coster, D. P.; Asakura, N.
- Nuclear Fusion, Vol. 47, Issue 8
The Gaussian radial basis function method for plasma kinetic theory
journal, October 2015
- Hirvijoki, E.; Candy, J.; Belli, E.
- Physics Letters A, Vol. 379, Issue 42
Origin of secondary‐electron‐emission yield‐curve parameters
journal, August 1975
- Dionne, Gerald F.
- Journal of Applied Physics, Vol. 46, Issue 8
Neutral-beam-driven tokamak fusion reactors
journal, April 1977
- Jassby, D. L.
- Nuclear Fusion, Vol. 17, Issue 2
A comparison of emissive probe techniques for electric potential measurements in a complex plasma
journal, July 2011
- Sheehan, J. P.; Raitses, Y.; Hershkowitz, N.
- Physics of Plasmas, Vol. 18, Issue 7
Works referencing / citing this record:
Testing nonlocal models of electron thermal conduction for magnetic and inertial confinement fusion applications
journal, September 2017
- Brodrick, J. P.; Kingham, R. J.; Marinak, M. M.
- Physics of Plasmas, Vol. 24, Issue 9
Transport equations in magnetized plasmas for non-Maxwellian distribution functions
journal, October 2018
- Oliveira, D. S.; Galvão, R. M. O.
- Physics of Plasmas, Vol. 25, Issue 10
Incorporating kinetic effects on Nernst advection in inertial fusion simulations
journal, June 2018
- Brodrick, J. P.; Sherlock, M.; Farmer, W. A.
- Plasma Physics and Controlled Fusion, Vol. 60, Issue 8
Theory and simulations of spherical and cylindrical Langmuir probes in non-Maxwellian plasmas
journal, June 2019
- Darian, D.; Marholm, S.; Mortensen, M.
- Plasma Physics and Controlled Fusion, Vol. 61, Issue 8