Kinetic corrections from analytic nonMaxwellian 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 steadystate nonMaxwellians, 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 nonMaxwellian distribution functions constructed from nonorthogonal basis sets in order to (i) use as few parameters as possible, (ii) increase the efficiency to model numerical and experimental nonMaxwellians, (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 Lab. (LLNL), Livermore, CA (United States)
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 1289360
 Report Number(s):
 LLNLJRNL686219
Journal ID: ISSN 1070664X
 Grant/Contract Number:
 AC5207NA27344
 Resource Type:
 Journal Article: Accepted Manuscript
 Journal Name:
 Physics of Plasmas
 Additional Journal Information:
 Journal Volume: 23; Journal Issue: 8; Journal ID: ISSN 1070664X
 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 nonMaxwellian distribution functions in magnetized plasmas. United States: N. p., 2016.
Web. doi:10.1063/1.4960123.
Izacard, Olivier. Kinetic corrections from analytic nonMaxwellian distribution functions in magnetized plasmas. United States. doi:10.1063/1.4960123.
Izacard, Olivier. 2016.
"Kinetic corrections from analytic nonMaxwellian distribution functions in magnetized plasmas". United States.
doi:10.1063/1.4960123. https://www.osti.gov/servlets/purl/1289360.
@article{osti_1289360,
title = {Kinetic corrections from analytic nonMaxwellian 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 steadystate nonMaxwellians, 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 nonMaxwellian distribution functions constructed from nonorthogonal basis sets in order to (i) use as few parameters as possible, (ii) increase the efficiency to model numerical and experimental nonMaxwellians, (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 nonMaxwellians. 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 bimodal or a new interpreted nonMaxwellian 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 superthermal particles, (ii) the superthermal 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 superthermal tails stays the same as the entropy of a MDF. In conclusion, the latter demystifies the Maxwell's demon by statistically describing nonisolated systems.},
doi = {10.1063/1.4960123},
journal = {Physics of Plasmas},
number = 8,
volume = 23,
place = {United States},
year = 2016,
month = 8
}

Kinetic corrections from analytic nonMaxwellian distribution functions in magnetized plasmas
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 steadystate nonMaxwellians, 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 nonMaxwellian distribution functions constructed from nonorthogonal basismore » 
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Departures of the electron energy distribution from a Maxwellian in hydrogen. I. Formulation and solution of the electron kinetic equation
We formulate and solve analytically a kinetic equation describing the balance between elastic and inelastic collisions for the free electron energy distribution function in a steadystate hydrogen plasma. The solutions obtained show that the highenergy tail of the distribution (epsilon> or approx. =9 eV) can deviate from a Maxwellian for ionization fractions n/sub e//n/sub h/9 or approx. =0.1, and that such deviations can lead to a significant changes in the collisional excitation and ionization rates of groundstate hydrogen atoms. Formulas for these rates are obtained which explicitly display their dependence on the hydrogen departure coefficients. Previous treatments of the problemmore »