Fluid and drift-kinetic description of a magnetized plasma with low collisionality and slow dynamics orderings. II. Ion theory

Abstract

The ion side of a closed, fluid and drift-kinetic theoretical model to describe slow and macroscopic plasma processes in a fusion-relevant, low collisionality regime is presented. It follows the ordering assumptions and the methodology adopted in the companion electron theory 1 . To reach the frequency scale where collisions begin to play a role, the drift-kinetic equation for the ion distribution function perturbation away from a Maxwellian must be accurate to the second order in the Larmor radius.The macroscopic density, flow velocity and temperature are accounted for in the Maxwellian, and are evolved by a fluid system which includes consistently the gyroviscous part of the stress tensor and second-order contributions to the collisionless perpendicular heat flux involving non-Maxwellian fluid moments. The precise compatibility among these coupled high-order fluid and drift-kinetic equations is made manifest by showing that the evolution of the non-Maxwellian part of the distribution function is such that its first three velocity moments remain equal to zero.

Coupling extended magnetohydrodynamic fluid codes with radiofrequency ray tracing codes for fusion modeling

“…The approaches developed in this work, in tandem with the theoretical foundations laid in Refs. [17][18][19]21], facilitate the development of numerical analogues for such control systems [46]. We anticipate exploring this topic in greater depth in subsequent publications; investigation of the relationship of experimentally observed Fisch and Boozer [47] and Ohkawa [48] currents to RF-induced modifications of the closures is also a topic of interest.…”

“…We will not discuss the closure calculations or their associated drift-kinetic equation here (see Refs. [18,19,35] for a rigorous treatment of these issues).…”

“…Recent theoretical work by Hegna and Callen [17] and Ramos [18,19] (hereafter, HCR) outlines a first-principles derivation of equations that can be used to simulate both TMs and the effects of externally imposed ECCD within the formalism of extended magnetohydrodynamics (extended MHD). The HCR approach, which is valid when distribution functions of the plasma species are nearly local Maxwellians, employs a multiscale ordering wherein the spatial and temporal scales of the RF fields are assumed to be much shorter than those corresponding to fluid quantities.…”

Verification of continuum drift kinetic equation solvers in NIMROD

“…While several forms for the electron and ion drift kinetic equation exist, [13][14][15] the focus here will be on the form given by Hazeltine in Ref. 8.…”

Numerical Calculation of Neoclassical Distribution Functions and Current Profiles in Low Collisionality, Axisymmetric Plasmas

“…[9,17]. It features a coupled system of ion and electron fluid and drift-kinetic (DKE) equations in general 3D real space and 2D (gyroaveraged) velocity space with Fokker-Planck-Landau linearized collision operators.…”