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

Abstract

A closed theoretical model to describe slow, macroscopic plasma processes in a fusion-relevant collisionality regime is put forward. This formulation is a hybrid one, with fluid conservation equations for particle number, momentum and energy, and drift-kinetic closures. Intended for realistic application to the core of a high-temperature tokamak plasma, the proposed approach is unconventional in that the ion collisionality is ordered lower than in the ion banana regime of neoclassical theory.The present first part of a two-article series concerns the electron system, which is still equivalent to one based on neoclassical electron banana orderings. This system is derived such that it ensures the precise compatibility among the complementary fluid and drift-kinetic equations, and the rigorous treatment of the electric field and the Fokker-Planck-Landau collision operators. As an illustrative application, the special limit of an axisymmetric equilibrium is worked out in detail.

Numerical calculation of neoclassical distribution functions and current profiles in low collisionality, axisymmetric plasmas

“…DKES uses a variational method to calculate neoclassical quantities but uses the Lorentz collision operator, which includes only pitch angle scattering. While this is the dominant process for electron-ion collisions in low-collisionality plasmas (such as those found in the cores of reactor-grade, toroidally-confined plasmas that we would like to study), energy scattering is just as important for like-particle collisions 9 . As Belli and Candy recently showed 10 , the use of model collision operators to study the bootstrap current, even ones substantially more sophisticated than the Lorentz operator, can lead to errors of 5-10% compared to the full FokkerPlanck-Landau collision operator.…”

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

“…1 where the electron side of the system was analyzed. The present second part of the series completes the theory by developing its ion side.…”

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

“…In Section II, we present the spatially twodimensional axisymmetric equations to be solved (in CGS units), expressed in the mean flow reference frame representation as derived in Ref. [9]. We then describe in Section III the expansions and computational methods that have been used in NIES.…”

“…DKES uses a variational method to calculate neoclassical quantities but uses the Lorentz collision operator, which includes only pitch angle scattering. While this is the dominant process for electron-ion collisions in low-collisionality plasmas (such as those found in the cores of reactor-grade, toroidally-confined plasmas that we would like to study), energy scattering is just as important for like-particle collisions 9 . As Belli and Candy recently showed 10 , the use of model collision operators to study the bootstrap current, even ones substantially 2 more sophisticated than the Lorentz operator, can lead to errors of 5-10% compared to the full FokkerPlanck-Landau collision operator.…”

“…[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.…”