Kinetic description of rotating Tokamak plasmas with anisotropic temperatures in the collisionless regime

Abstract

A largely unsolved theoretical issue in controlled fusion research is the consistent kinetic treatment of slowly-time varying plasma states occurring in collisionless and magnetized axisymmetric plasmas. The phenomenology may include finite pressure anisotropies as well as strong toroidal and poloidal differential rotation, characteristic of Tokamak plasmas. Despite the fact that physical phenomena occurring in fusion plasmas depend fundamentally on the microscopic particle phase-space dynamics, their consistent kinetic treatment remains still essentially unchallenged to date. The goal of this paper is to address the problem within the framework of Vlasov-Maxwell description. The gyrokinetic treatment of charged particles dynamics is adopted for the construction of asymptotic solutions for the quasi-stationary species kinetic distribution functions. These are expressed in terms of the particle exact and adiabatic invariants. The theory relies on a perturbative approach, which permits to construct asymptotic analytical solutions of the Vlasov-Maxwell system. In this way, both diamagnetic and energy corrections are included consistently into the theory. In particular, by imposing suitable kinetic constraints, the existence of generalized bi-Maxwellian asymptotic kinetic equilibria is pointed out. The theory applies for toroidal rotation velocity of the order of the ion thermal speed. These solutions satisfy identically also the constraints imposed by the Maxwell equations, i.e., quasi-neutrality and Ampere's law. As a result, it is shown that, in the presence of nonuniform fluid and EM fields, these kinetic equilibria can sustain simultaneously toroidal differential rotation, quasi-stationary finite poloidal flows and temperature anisotropy.

Electrically charged matter in rigid rotation around magnetized black hole

“…Detailed study of this kind is outlined for the future work. Another line of future investigations concerns the interacting external and selfelectromagnetic fields, under the framework developed in papers [31,32].…”

“…Then, both the interacting external an selfelectromagnetic fields have to be considered [31][32][33]. Another scenario having almost homogeneous magnetic field can be, however, related to a black hole of stellar masŝ M being a part of a binary system with a magnetar of massM equipped with a dipole type magnetic field of strength up toB 10 12 T on its surface, the strongest magnetic field estimated to exist.…”

Collisionless kinetic regimes for quasi-stationary axisymmetric accretion disc plasmas

“…As proved in Ref. 13, if the ordering assumption X i R $ v thi is invoked (with X i denoting the ion azimuthal rotation frequency), quasi-neutrality necessarily implies that the ES potential must satisfy the ordering…”

Covariant formulation of spatially non-symmetric kinetic equilibria in magnetized astrophysical plasmas

“…This occurs in particular in the presence of temperature and pressure anisotropies, local flows, such as diamagnetic flow velocities, finite Larmor-radius (FLR), and energy-correction effects. [35][36][37][38][39][40][41][42] A qualitative feature of astrophysical magnetized plasmas is related to the occurrence of kinetic plasma regimes, which persist for long times (with respect to the observer and/or plasma characteristic times), despite the presence of macroscopic time-varying phenomena of various origin, such as flows, non-uniform gravitational/EM fields, and EM radiation, 43 possibly including that arising from singleparticle radiation-reaction processes. [4][5][6][7][8][9][10][11] It is argued that, for collisionless plasmas, these states might actually correspond-at least locally and in a suitable asymptotic senseto some kind of kinetic equilibrium, which characterizes the species KDFs.…”