scholarly journals Gravitational Contribution to the Heat Flux in a Simple Dilute Fluid: An Approach Based on General Relativistic Kinetic Theory to First Order in the Gradients

Entropy ◽  
2017 ◽  
Vol 19 (11) ◽  
pp. 537
Author(s):  
Dominique Brun-Battistini ◽  
Alfredo Sandoval-Villalbazo ◽  
Ana Garcia-Perciante
Keyword(s):  
Heat Flux ◽  
Kinetic Theory ◽  
First Order ◽  
Relativistic Kinetic Theory ◽  
General Relativistic ◽  
Gravitational Contribution

General-relativistic kinetic theory of waves in a massive particle medium

1976 ◽  
Vol 13 (10) ◽  
pp. 2724-2735 ◽  
Author(s):  
E. Asseo ◽  
D. Gerbal ◽  
J. Heyvaerts ◽  
M. Signore
Keyword(s):  
Kinetic Theory ◽  
Massive Particle ◽  
Relativistic Kinetic Theory ◽  
General Relativistic ◽  
Particle Medium

scholarly journals Remarks on relativistic kinetic theory to first order in the gradients

2010 ◽  
Vol 165 (17-18) ◽  
pp. 1024-1028 ◽  
Author(s):  
A.L. García-Perciante ◽  
A. Sandoval-Villalbazo
Keyword(s):  
Kinetic Theory ◽  
First Order ◽  
Relativistic Kinetic Theory

Matter symmetries in general relativistic kinetic theory

1973 ◽  
Vol 14 (9) ◽  
pp. 1254-1257 ◽  
Author(s):  
R. Berezdivin ◽  
R. K. Sachs
Keyword(s):  
Kinetic Theory ◽  
Relativistic Kinetic Theory ◽  
General Relativistic

Relativistic Kinetic Theory

2017 ◽  
Author(s):  
Gregory V. Vereshchagin ◽  
Alexey G. Aksenov
Keyword(s):  
Kinetic Theory ◽  
Relativistic Kinetic Theory

Kinetic theory

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Distribution Function ◽  
Kinetic Theory ◽  
Liouville Equation ◽  
Vlasov Equation ◽  
Particle Distribution ◽  
Equations Of Motion ◽  
Poisson Brackets ◽  
Hamiltonian Form ◽  
First Order ◽  
Number Of Particles

This chapter covers the equations governing the evolution of particle distribution and relates the macroscopic thermodynamical quantities to the distribution function. The motion of N particles is governed by 6N equations of motion of first order in time, written in either Hamiltonian form or in terms of Poisson brackets. Thus, as this chapter shows, as the number of particles grows it becomes necessary to resort to a statistical description. The chapter first introduces the Liouville equation, which states the conservation of the probability density, before turning to the Boltzmann–Vlasov equation. Finally, it discusses the Jeans equations, which are the equations obtained by taking various averages over velocities.

scholarly journals Drift kinetic theory of alpha transport by tokamak perturbations

2021 ◽  
Vol 87 (2) ◽  
Author(s):  
Elizabeth A. Tolman ◽  
Peter J. Catto
Keyword(s):  
Heat Flux ◽  
Kinetic Theory ◽  
Alpha Particle ◽  
Heat Fluxes ◽  
Alpha Particles ◽  
Alpha Power ◽  
Mode Amplitude ◽  
Effective Collision Frequency ◽  
Perturbation Frequency ◽  
Particle Confinement

Upcoming tokamak experiments fuelled with deuterium and tritium are expected to have large alpha particle populations. Such experiments motivate new attention to the theory of alpha particle confinement and transport. A key topic is the interaction of alpha particles with perturbations to the tokamak fields, including those from ripple and magnetohydrodynamic modes like Alfvén eigenmodes. These perturbations can transport alphas, leading to changed localization of alpha heating, loss of alpha power and damage to device walls. Alpha interaction with these perturbations is often studied with single-particle theory. In contrast, we derive a drift kinetic theory to calculate the alpha heat flux resulting from arbitrary perturbation frequency and periodicity (provided these can be studied drift kinetically). Novel features of the theory include the retention of a large effective collision frequency resulting from the resonant alpha collisional boundary layer, correlated interactions over many poloidal transits and finite orbit effects. Heat fluxes are considered for the example cases of ripple and the toroidal Alfvén eigenmode (TAE). The ripple heat flux is small. The TAE heat flux is significant and scales with the square of the perturbation amplitude, allowing the derivation of constraints on mode amplitude for avoidance of significant alpha depletion. A simple saturation condition suggests that TAEs in one upcoming experiment will not cause significant alpha transport via the mechanisms in this theory. However, saturation above the level suggested by the simple condition, but within numerical and experimental experience, which could be accompanied by the onset of stochasticity, could cause significant transport.

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