Generalized fluid theory including non-Maxwellian kinetic effects

Abstract

The results obtained by the plasma physics community for the validation and the prediction of turbulence and transport in magnetized plasma come mainly from the use of very CPU-consuming particle-in-cell or (gyro)kinetic codes which naturally include non-Maxwellian kinetic effects. To date, fluid codes are not considered to be relevant for the description of these kinetic effects. Here, after revisiting the limitations of the current fluid theory developed in the 19th century, we generalize the fluid theory including kinetic effects such as non-Maxwellian super-thermal tails with as few fluid equations as possible. The collisionless and collisional fluid closures from the nonlinear Landau Fokker-Planck collision operator are shown for an arbitrary collisionality. Indeed, the first fluid models associated with two examples of collisionless fluid closures are obtained by assuming an analytic non-Maxwellian distribution function (e.g., the INMDF [O. Izacard, Phys. Plasmas 23, 082504 (2016) Kinetic corrections from analytic non-Maxwellian distribution functions in magnetized plasmas]). One of the main differences with the literature is our analytic representation of the distribution function in the velocity phase space with as few hidden variables as possible thanks to the use of non-orthogonal basis sets. These new non-Maxwellian fluid equations could initiate the next generation of fluid codes including kinetic effects and can be expanded to other scientific disciplines such as astrophysics, condensed matter, or hydrodynamics. As a validation test, we perform a numerical simulation based on a minimal reduced INMDF fluid model. The result of this test is the discovery of the origin of particle and heat diffusion. The diffusion is due to the competition between a growing INMDF on short time scales due to spatial gradients and the thermalization on longer time scales. The results shown here could draw the breaking of some unsolved understandings of the turbulence.

Kinetic corrections from analytic non-Maxwellian distribution functions in magnetized plasmas

“…Moreover, other details of NMDFs will be published elsewhere such as the fluid reduction (see Ref. [23]), which opens the access to the next generation of fluid codes by including non-collisional and collisional kinetic effects (see Ref. [22]), or the description of the transport.…”

“…Moreover, even if we choose to perform the qualitative fitting (without the necessity to use the experimental data) of only one published article on the electron temperature measurement discrepancy, it is at least possible (not shown here, see Ref. [23]) to fit NMDFs observed by Fokker-Planck numerical codes in presence of lower hybrid current drive or by particle in cell codes in presence of ion orbit losses. Fig.…”

Transport equations in magnetized plasmas for non-Maxwellian distribution functions

“…12,13 In order to introduce non-thermal effects in the Boltzmann-based models, alternative fluid equations approximating different long-tail distribution functions by a series of Maxwellians, with the coefficients of proportionality determined by numerically fitting the experimental data, have been lately considered, especially in numerical simulations. 2 Despite their success in recovering some quantitative experimental results, these models lack a convincing theoretical basis, in particular, regarding the adoption of the collision operator from the Boltzmann statistics, 14 which implies that the plasma has to evolve towards thermodynamic equilibrium described by a Maxwellian. Naturally, this is not consistent with stationary non-Maxwellian distribution functions since they are not stationary maxima of the Boltzmann entropy.…”

Teoria cinética não extensiva e transporte colisional em plasmas magnetizados

“…A principal diculdade teórica no estudo, ou na interpretação dos dados experimentais, do transporte em sistemas com distribuições não-maxwellianas é a falta de modelos autoconsistentes de primeiros princípios [37]. Uma forma prática de contornar essa diculdade, e que vem ganhando notoriedade ultimamente, é denir numericamente a função de distribuição coerente com os dados experimentais [38].…”

“…37) onde utilizamos a propriedade v µ ∂V µν /∂v µ = −V µν .Como termos de ordem O (U 2 ) são desprezados, apenas quando f = f 0 e η = µ o resultado será não-nulo, portanto, é direta a identicação da expressão acima com Eq. (3.30):…”