Macroscopic processes in a magnetized plasma, defined as those whose
characteristic length scales are always greater than the ion Larmor
gyroradius, are amenable to a fluid description of their dynamics
perpendicular to the magnetic field. However, for the low collisionality
regimes of main interest in space and magnetic fusion plasmas, the fluid
description of their parallel dynamics cannot be closed. A consistently
closed and still dimensionally reduced theory can be built based on a
hybrid fluid and kinetic formulation whereby the parallel fluid closures
are derived from solutions of drift-kinetic equations for the gyrophase averages of the distribution functions. Such a theory is presented
in this talk, emphasizing the rigorous incorporation of high-order finite Larmor radius effects and the precise consistency between the fluid and
drift-kinetic sides of the description. Attention is especially paid
to the conservation laws in the system: the fluid side accounts for exact conservation of particles, momentum and energy, while the drift-kinetic equations are manifestly shown to guarantee that the gyrophase averaged distribution functions evolve such that their, density, random parallel velocity and random kinetic energy moments remain always consistent
with the fluid conservation laws. The collisionless advection in the
drift-kinetic equations shows also the Liouville theorem conservation of phase-space volume. Two versions of the theory are explored in detail.
The first one, more apt for space applications, assumes a collisionless plasma, sonic dynamical scales, far-from-Maxwellian distribution functions and first-order accuracy in the ion Larmor radius. The second one, more
apt for application to well confined magnetic fusion experiments, assumes
a weakly collisional plasma with Fokker-Planck-Landau collision operators, subsonic dynamical scales, near-Maxwellian distribution functions and second-order accuracy in the ion Larmor radius.
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