Since most of the particles' motion is gyration about the magnetic field, we can integrate over the gyrophase and use the adiabatic invariance of the magnetic moment to reduce the number of velocity dimensions to one: the velocity along the magnetic field lines. The motion of the ions is driven by an equilibrium density and temperature gradient in the x direction, while the motion of the electrons is determined by quasineutrality. 19–21 We consider small electrostatic perturbations around an equilibrium with slab geometry-the equilibrium has no electric field and the magnetic field is constant and pointed in the z direction.

Since many gyro-/drift-kinetic codes use Hermite polynomials as base elements, we include an explicit calculation of their G-transform.Ī three-dimensional highly magnetized plasma is often approximated by gyrokinetic or drift-kinetic equations. We present new gyrofluid equations formed by taking moments of the G-transformed equation. This integral transform can also be used to simplify gyro-/drift-kinetic equations. This solution determines when collisions dominate and when advection (i.e., Landau damping) dominates. We exactly solve the advection-diffusion equation without the shielding term.

The commutator of this collision operator with the G-transform (the “shielding term”) is shown to be negligible. We investigate how this integral transform interacts with the Fokker-Planck collision operator. The linearized Vlasov-Poisson system can be exactly solved using the G- transform, an integral transform introduced in Morrison and Pfirsch and Morrison that removes the electric field term, leaving a simple advection equation.

Baseelements convert