Transport equations in magnetized plasmas for non-Maxwellian distribution functions

Abstract

Non-Maxwellian distribution functions are frequently observed in space and laboratory plasmas in (quasi-) stationary states, usually resulting from long-range nonlinear wave-particle interactions [P. H. Yoon, Phys. Plasmas 19, 012304 (2012)]. Since the collisional transport described by the Boltzmann equation with the standard collisional operator implies that the plasma distribution function evolves inexorably towards a Maxwellian, the description of the transport for stationary states outside of equilibrium requires a different formulation. In this work, we approach this problem through the non-extensive statistics formalism based on the Tsallis entropy. The basic framework of the kinetic model and the required generalized form of the collision operator are selfconsistently derived. The fluid equations and the relevant transport coefficients for electrons are then found employing the method of Braginskii. As an illustrative application of the model, we employ this formalism to analyze the heat flux in solar winds. Published by AIP Publishing.

Beyond Boltzmann–Gibbs–Shannon in Physics and Elsewhere

“…Let us end this section by mentioning other selected entropic applications beyond BG in physics: long-range interacting many-body classical Hamiltonian systems (XY model [ 90 , 91 , 92 , 93 , 94 , 95 , 96 , 97 ], Heisenberg model [ 98 , 99 , 100 ], Fermi–Pasta–Ulam (FPU) model [ 101 , 102 , 103 , 104 ]) (see [ 105 , 106 ] for earlier related approaches of the original FPU model and also [ 107 ], where the existence of non-Maxwellian compact-support momenta distributions are detected for special initial conditions); quantum-entangled low-dimensional Hamiltonian systems [ 108 , 109 , 110 ]; plasma physics [ 111 , 112 , 113 , 114 , 115 ]; turbulence [ 87 , 116 ]; astrophysics, cosmology, and black holes [ 89 , 117 , 118 , 119 , 120 , 121 , 122 ]; nonlinear dynamical systems [ 123 , 124 , 125 , 126 , 127 , 128 ]; nonlinear quantum mechanics [ 129 , 130 , 131 , 132 ]; anomalous diffusion, type II superconductors, and repulsive short-range interacting systems with overdamping […”

Conclusion in the framework of nonextensive kinetics of the Jeans instability criterion for protoplanetary cloud taking into account radiation and magnetic field.

“…Определение q -гидродинамических параметров. Энтропия Тсаллиса влечёт за собой не только обобщение статистической физики и термодинамики, но и обобщение физической кинетики и гидродинамики (Oliveira, Galvao, 2018). Простейшей макроскопической величиной является q -плотность числа частиц, которая определяется соотношением…”

On the interpretation of kinetic effects from ionization in fluid models and its impact on filamentary transport

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