Neoclassical ion transport in rotating axisymmetric plasmas

Abstract

The neoclassical theory of ion transport in rotating axisymmetric plasmas is formulated. The flow speed is allowed to be of the order of the ion thermal speed. It is shown that the ion distribution function becomes Maxwellian, with temperature uniform on a magnetic surface, and the poloidal flow decays, in a few transit or collision times, in general. A drift kinetic equation is derived which is a simple generalization of the drift kinetic equation for nonrotating plasmas. The radial gradient of the toroidal angular velocity appears as a driving term like the temperature gradient. Both gradients drive the transport of toroidal angular momentum and energy, in general; Onsager relations for the two-by-two transport matrix are derived. The off-diagonal transport coefficients are shown to be zero if the magnetic field has up–down symmetry. A simple expression for the enhancement of the ion thermal conductivity in the banana regime, caused by rotation, is derived. The neoclassical viscosity is shown not to be enhanced by rotation in the banana regime, and to be small in the collisionality parameter in the collisional regime, assuming up–down symmetry. In the collisional regime, the thermal conductivity is shown to be suppressed by the effects of rotation.

Multispecies transport theory for axisymmetric rotating plasmas

“…_ reads: leads, therefore, to the conclusion that, the Spitzer source term can be exactly transformed in an explicit contribution of the distribution function f, without need of invoking additional assumptions concerning the plasma collisionality [9]; in addition we infer that, to leading order, _ is, actually, independent of the inductive electric fici(i. f Zse{" thus formally recovering, in this respect, a formulation equivalent to that given previously by Hinton and Wong [1] and by Catto et al [2].…”

“…That a variational formulation can actually be given for the reduced kinetic equation is well known in neoclassical theory [9] and has been extended also to strong rotation theories [1,2]. Here we shall depart from the variational approaches used in …”

“…The work of Catto et al [2] extended the formulation of Hinton and Wong [1] , allowing more general expressions for the transport coefficients to be obtained and yielding, as weil, a simpler derivation for the reduced gyrokinetic equation which advances in time the one particle kinetic distribution function.…”

“…The evolution of such general equilibrium states is investigated in the framework of a transport theory, i.e., all relevant dynamical variables are required to obey a transport ordering appropriate to strongly rotating magnetoplasmas [1,2].…”

“…Until the theoretical work of ttinton and Wong [1] and Catto, Bernstein and Tessarotto [2,3], investigations of collisional transport in axisymmetric toroidal magnetoplasmas (i.e., Tokamaks), were limited to small toroidal rotationspeeds and small toroidal differential rotation (i.e., small shear in the toroidal rotation speeds)…”