Multispecies transport theory for axisymmetric rotating plasmas

Abstract

A reduced gyrokinetic equation is derived for a multispecies toroidal axisymmetric plasma with arbitrary toroidal differential rotation speeds and in the presence of a finite induced electric field. The kinetic equation obtained, extending previous results obtained by Hinton and Wong [Phys. Fluids 28, 3082 (1985)] and by Catto et al. [Phys. Fluids 30, 2784 (1987)], has a form suited for transport applications, via variational techniques; in particular it exhibits the feature that all source terms, including the Spitzer source term, carrying the contribution due to the inductive electric field, appear to be acted upon by the collision operator. Moreover, the equation displays a new contribution due to ‘‘explicit’’ velocity perturbations, here proven to be consistent with transport ordering, whose evaluation appears relevant for transport calculations. In addition, general expressions are obtained for the neoclassical fluxes in terms of a variational principle, as well as for the classical ones, retaining, in both cases, the contributions due to Spitzer’s inductive terms.

Kinetic axisymmetric gravitational equilibria in collisionless accretion disk plasmas

“…( 31) determines only Φ ∼ and not the total ES potential. Note that this solution for the electrostatic potential Φ ∼ can be shown to be consistent with earlier treatments appropriate for Tokamak plasma equilibria [24,36]. This can be exactly recovered thanks to the arbitrariness in defining the pseudo-densities and by taking the limit of isotropic temperatures and zero gravitational potential, as in the case of laboratory plasmas.…”

“…Gyrokinetic theory allows one to derive the adiabatic invariants of the system [28,29]; by construction, these are quantities conserved only in an asymptotic sense, i.e., only to a prescribed order of accuracy. As is well known, gyrokinetic theory is a basic prerequisite for the investigation both of kinetic instabilities (see for example [32][33][34]) and of equilibrium flows occurring in magnetized plasmas [24,[35][36][37][38]. For astrophysical plasmas close to compact objects, this generally involves the treatment of strong gravitational fields which needs to be based on a covariant formulation (see [39][40][41][42]).…”

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

“…which applies in the subset of thermal particles. Notice that the assumption on ε s is consistent with the requirement of finite inverse aspect-ratio (see below), while, as recalled above, the ordering on σ s is required for the treatment of Tokamak equilibria in the presence of strong toroidal differential rotation [10][11][12][13]. The same orderings are of course invoked also for the validity of the GK theory (see Ref.…”

“…In Refs. [10][11][12] these were prescribed imposing the kinetic constraint Λ * s = Λ * s (ψ * s ). By performing a perturbative expansion in the canonical momentum (see also the related discussion in Section 6), it was shown that f * s recovers the Chapman-Enskog form, with the leading-order Maxwellian KDF carrying isotropic temperature T s (ψ), species-independent toroidal angular rotation velocity Ω 0 (ψ) (see definition given by Eq.…”

Axi-symmetric Gravitational MHD Equilibria in the Presence of Plasma Rotation

“…For this purpose, we first notice that it must be necessarily a function only of the independent first integrals of motion and/or of the relevant independent adiabatic invariants (at least for the leading orders in ε). In axisymmetry these are well known [7,8] in particular the canonical momentum p ϕs and the total particle energy, E s = Msv 2 2 + Zse ε Φ + 1 ε U grav . In the following we assume that the plasma is strongly magnetized in the sense that for all species s = e, i r Ls L ∼ ε,…”