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Description
It is common to assume that the velocity distributions of the species that compose a plasma are Maxwellian, which are akin to closed systems in thermodynamic equilibrium, with short range interactions. However, plasmas are by nature non-equilibrium open systems with long range interactions, and this assumption is seldom fulfilled in practice. In space plasmas velocity distributions have been systematically measured since the early days of exploration with spacecrafts, in which suprathermal tails are usually observed. This led to devise the so called $\kappa$ distributions as a fitting resource [1], whose name stems from the fact that they depend on an adjustable parameter $\kappa$, such that the Maxwellian distribution is recovered when it tends to infinity. Their theoretical basis has been later developed in the framework of non-extensive statistical physics, as proposed by Tsallis [2,3], in which a non-additive entropy is proposed, generalising the Maxwell-Gibbs entropy.
A significant wealth of results with this approach, relevant to plasma physics have been produced in recent years, some of which have been compiled by Livadiotis, with emphasis on his own work [4]. While its applications have usually been confined to space plasmas, which are extremely collisionless, it has become clear that they call for a review of fundamental concepts, such as Debye shielding [5,6], as well as the fluid models and the relevant transport coefficients, as obtained employing the Braginskii’s method [7]. The former may also be relevant to electrostatic diagnostics, such as Langmuir probes. The implications for fusion plasmas may be interesting, but they have not been explored so far. On the other hand, this approach might also provide a powerful tool for data analysis in problems where supratehrmal distributions are often observed, such as in relativistic run-away electrons [8].
The purpose of this paper is to present the state of the art on the foundations of non-Maxwellian distributions in plasma physics from the point of view of non-extensive statistical mechanics, and their possible implications in fusion research.
[1] V. M. Vasyliunas, Journal of Geofisical Research, 9, 2839 (1968).
[2] C.Tsallis, J. Statistical Physics, 52, 479 (1988).
[3] C. Tsallis, Introduction to Nonextensive Statistical Mechamics,” (Springer Verlag, New York, 2009).
[4] G. Livadiotis, “Kappa Distributions: Theory and Applications in Plasmas,” (Elsevier, Netherlands, 2017).
[5] G. Livadiotis and D.J. McComas, Journal of Plasma Physics 80, 341 (2014).
[6] L.A. Gougam and M. Tribeche, Physics of Plasmas 18, 062102 (2014).
[7] D. S. Oliveira and R.M.O. Galvao, Physics of Plasmas 25, 102308 (2018).
[8] C. Liu, D.P. Brennan, A. Bhattacharjee and A. Boozer, Physics of Plasmas, 23 010702 (2016).
| Affiliation | Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México |
|---|---|
| Country or International Organization | Mexico |
