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 specially 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 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 (KDF), the bi-modal or a new interpreted non-Maxwellian (INMDF) distribution function. 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. The latter demystifies the Maxwell's demon by statistically describing non-isolated systems.The observation of non-equilibrium distribution functions is possible in a large number of areas other than laboratory plasma physics such as in astrophysics plasmas, hydrodynamic fluids and molecular dynamics, atomic physics, condensed matter, chemical reactions and in statistics (see Refs. [1][2][3][4][5]). We focus here on laboratory plasma physics with charged particles in a magnetic field relevant to tokamaks and spherical tokamaks for the purpose of energy production by fusion ener...

Generalized fluid theory including non-Maxwellian kinetic effects

“…The second reason of this failure is the misconception of the fluid reduction from the kinetic Boltzmann description, and more generally of the fluid theory: it has been difficult to expand this fluid theory here for nonequilibria based on the properties of MDFs without falling into the usual limitations, but a summarized point of view of the state-of-the-art of the fluid reduction since the 1870's clarifies our novel approach. The introduced INMDFs represent an extension of the usual fluid theory since (i) it has been shown (Izacard 2016b) The INMDF seems to prove that all accepted misunderstandings about the fluid theory mentioned previously can be bypassed.…”

“…These new parameters have been physically interpreted in Ref. (Izacard 2016b) as a displacement of a population of particles in the velocity phase space due to an external source of energy. The efficiency of the INMDF to describe a localized super-thermal tail is shown in Fig.…”

Testing nonlocal models of electron thermal conduction for magnetic and inertial confinement fusion applications

“…The plausibility of this hypothesis is supported by recent gyrokinetic simulations performed by Churchill et al 22 . Another important factor is the effect of the enhanced suprathermal population on Langmuir probe characteristics [23][24][25][26] : Ďuran et al 27 have shown that a more sophisticated interpretation of probe results can reduce but not eliminate the discrepancy. Resolution of this discrepancy is critical as excessive heat loads could erode and severely limit the lifetimes of the divertor target plates.…”

“…n c 75,(26) where n c ∈ [−154, 100] is the cell number counting from the centre of the temperature ramp. Cell size in mfp's was varied between simulations to scan a range of collisionali-…”

Effect of magnetic field on transports of charged particles in the weakly ionized plasma with power-law q-distributions in nonextensive statistics

“…The density and velocity distributions in nonequilibrium complex systems have been observed in astronomy and astrophysics, space plasmas, complex fluids, molecular dynamics, nuclear and atomic physics, condensed matter physics, chemical reaction systems, and biological systems. It has been found that the velocity distributions of the charged particles in the systems with long-range correlations are quite far from the Maxwellian distribution, with long energetic tails [1][2]. Recently, nonextensive statistics proposed by Tsallis has attracted great attention of scientific researchers, a new statistics which can study the complex systems beyond thermodynamic equilibrium [3][4].…”