Neoclassical transport of impurities in tokamak plasmas

Abstract

Tokamak plasmas are inherently comprised of multiple ion species. This is due to wall-bred impurities and, in future reactors, will result from fusion-born alpha particles. Relatively small densities nI, of highly charged non-hydrogenic impurities can strongly influence plasma transport properties whenever . The determination of the complete neoclassical Onsager matrix for a toroidally confined multispecies plasma, which provides the linear relation between the surface averaged radial fluxes and the thermodynamic forces (i.e. gradients of density and temperature, and the parallel electric field), is reviewed. A closed set of one-dimensional moment equations is presented for the time evolution of thermodynamic and magnetic field quantities which results from collisional transport of the plasma and two-dimensional motion of the magnetic flux surface geometry. The effects of neutral-beam injection on the equilibrium and transport properties of a toroidal plasma are consistently included.

Drift waves and transport

“…Most large tokamaks (IϾ1 MA) are in this low-collisionality regime. The collisional thermal flux q i ϭϪn i i neo dT i /dr (which is only one diagonal element of a large transport matrix) is given by Hinton (1982, 1986) and Hirshman and Sigmar (1981). In the small ⑀ϭr/R limit the ion thermal diffusivity from collisions is…”

“…The calculations of Hirshman and Sigmar (1981) introduce widely-used parallel viscosities that relate the parallel flows (u ʈ j ,q ʈ j ) through coefficients 1 , 2 , 3 to the surface-averaged parallel stresses from ͗B•ٌ• j ͘ and ͗B•ٌ•⍜ j ͘. In terms of the ion viscosity coefficients, the thermal diffusivity in Eq.…”

Nonlinear Drive of Tearing Mode by Microscopic Plasma Turbulence

“…The model of neoclassical viscosity is key for the study of the tearing mode. The neoclassical viscosities are given by the interpolated formula [11] as…”

Modern gyrokinetic formulation of collisional and turbulent transport in toroidally rotating plasmas

“…Later, conservation of the total energy and momentum was obtained in the gyrokinetic field theory (Sugama 2000) where all governing equations for the distribution functions and the electromagnetic fields are derived from the Lagrangian which describes the whole system consisting of particles and fields. However, Lagrangian/Hamiltonian gyrokinetic formulations basically treat collisionless systems so that Noether's theorem and conservation laws are not directly applied to collisional systems although generally, in toroidal magnetic configurations, Coulomb collisions and turbulent fluctuations cause classical (Braginskii 1965), neoclassical (Helander and Sigmar 2002;Hirshman and Sigmar 1981;Hinton and Hazeltine 1976), and turbulent transport (Horton 2012) of plasma particles, heat, and momentum as multiscale phenomena. Therefore, several theoretical studies (Brizard 2004;Madsen 2013;Sugama et al 2015;Burby et al 2015) have been done to combine the modern gyrokinetic formulations with the collision models which can keep the conservation laws and describe the collisional transport processes properly as shown later in the present paper.…”