scholarly journals Calculation of anisotropic transport coefficients for an ultrarelativistic Boltzmann gas in a magnetic field within a kinetic approach

2020 ◽  
Vol 101 (5) ◽  
Author(s):  
Zhengyu Chen ◽  
Carsten Greiner ◽  
Anping Huang ◽  
Zhe Xu
Keyword(s):  
Magnetic Field ◽  
Transport Coefficients ◽  
Kinetic Approach ◽  
Boltzmann Gas ◽  
Anisotropic Transport

scholarly journals Relativistic non-resistive viscous magnetohydrodynamics from the kinetic theory: a relaxation time approach

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Ankit Kumar Panda ◽  
Ashutosh Dash ◽  
Rajesh Biswas ◽  
Victor Roy
Keyword(s):  
Magnetic Field ◽  
Relaxation Time ◽  
Transport Coefficients ◽  
Second Order ◽  
Navier Stokes ◽  
Relaxation Time Approximation ◽  
Moment Approximation ◽  
System Of Particles ◽  
Anisotropic Transport ◽  
The Magnetic Field

Abstract We derive the relativistic non-resistive, viscous second-order magnetohydrodynamic equations for the dissipative quantities using the relaxation time approximation. The Boltzmann equation is solved for a system of particles and antiparticles using Chapman-Enskog like gradient expansion of the single-particle distribution function truncated at second order. In the first order, the transport coefficients are independent of the magnetic field. In the second-order, new transport coefficients that couple magnetic field and the dissipative quantities appear which are different from those obtained in the 14-moment approximation [1] in the presence of a magnetic field. However, in the limit of the weak magnetic field, the form of these equations are identical to the 14-moment approximation albeit with different values of these coefficients. We also derive the anisotropic transport coefficients in the Navier-Stokes limit.

A GENERALIZED VARIATIONAL PRINCIPLE FOR TRANSPORT PHENOMENA

1958 ◽  
Vol 36 (10) ◽  
pp. 1308-1318 ◽  
Author(s):  
G. E. Tauber
Keyword(s):  
Magnetic Field ◽  
Variational Principle ◽  
Ritz Method ◽  
Transport Coefficients ◽  
Distribution Functions ◽  
Generalized Variational Principle ◽  
Lattice Vibrations ◽  
Arbitrary Direction ◽  
Energy Surfaces ◽  
Thermomagnetic Phenomena

A generalized variational principle has been formulated which takes the phonon distribution functions and the external magnetic field into account, is valid for an arbitrary direction of the electric field and polarization of the lattice vibrations, and does not depend on any special form of the energy surfaces. The various transport coefficients, for both thermoelectric and thermomagnetic phenomena, are obtained by the Ritz method in terms of infinite determinants without requiring an explicit solution of the transport equations.

Kinetic Approach to the Helium Transport in Divertor Plasma Along Magnetic Field

1990 ◽  
Vol 30 (1) ◽  
pp. 133-138
Author(s):  
S. I. Krasheninnikov ◽  
T. K. Soboleva ◽  
K. Gaz
Keyword(s):  
Magnetic Field ◽  
Kinetic Approach

scholarly journals Proton temperature-anisotropy-driven instabilities in weakly collisional plasmas: Hybrid simulations

2014 ◽  
Vol 81 (1) ◽  
Author(s):  
Petr Hellinger ◽  
Pavel M. Trávníček
Keyword(s):  
Magnetic Field ◽  
Langevin Equation ◽  
Transport Coefficients ◽  
Two Dimensional ◽  
Temperature Anisotropy ◽  
Coulomb Collisions ◽  
Proton Temperature ◽  
Collisionless Plasmas ◽  
High Beta ◽  
Kinetic Instabilities

Kinetic instabilities in weakly collisional, high beta plasmas are investigated using two-dimensional hybrid expanding box simulations with Coulomb collisions modeled through the Langevin equation (corresponding to the Fokker-Planck one). The expansion drives a parallel or perpendicular temperature anisotropy (depending on the orientation of the ambient magnetic field). For the chosen parameters the Coulomb collisions are important with respect to the driver but are not strong enough to keep the system stable with respect to instabilities driven by the proton temperature anisotropy. In the case of the parallel temperature anisotropy the dominant oblique fire hose instability efficiently reduces the anisotropy in a quasilinear manner. In the case of the perpendicular temperature anisotropy the dominant mirror instability generates coherent compressive structures which scatter protons and reduce the temperature anisotropy. For both the cases the instabilities generate temporarily enough wave energy so that the corresponding (anomalous) transport coefficients dominate over the collisional ones and their properties are similar to those in collisionless plasmas.

scholarly journals MHD Seismology of the Solar Corona with SOHO and TRACE

2001 ◽  
Vol 203 ◽  
pp. 353-355 ◽  
Author(s):  
V. M. Nakariakov
Keyword(s):  
Magnetic Field ◽  
Solar Corona ◽  
Decay Time ◽  
Transport Coefficients ◽  
Mhd Waves ◽  
The Mean ◽  
Temporal And Spatial ◽  
Wave Phenomena ◽  
The Magnetic Field ◽  
Imaging Telescopes

Recent discoveries of MHD wave motions in the solar corona done with EUV imaging telescopes onboard SOHO and TRACE provide an observational basis for the MHD seismology of the corona. Measuring the properties of MHD waves and oscillations (periods, wavelengths, amplitudes, temporal and spatial signatures), combined with theoretical modeling of the wave phenomena, allow us to determine values of the mean parameters of the corona (the magnetic field strength, transport coefficients, etc.). As an example, we consider post-flare decaying oscillations of loops, observed with TRACE (14th July 1998 at 12:55 UT). An analysis of the oscillations shows that they are quasi-harmonic, with a period of about 265 s, and quickly decaying with the decay time of about 14.5 min. The period of oscillations allows us to determine the Alfvén speed in the oscillating loop about 770 km/s. This value can be used for deduction of the value of the magnetic field in the loop (giving 10-30 G). The decay time, in the assumption that the decay is caused by viscous (or resistive) dissipation, gives us the Reynolds number of 105.3-6.1 (or the Lundquist number of 105.0-5.8).

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