A comparison of Vlasov with drift kinetic and gyrokinetic theories

A kinetic consideration of an axisymmetric equilibrium with vanishing electric field near the magnetic axis shows that del f should not vanish on axis within the framework of Vlasov theory while it can either vanish or not in the framework of both a drift kinetic and a gyrokinetic theories (f is either the pertinent particle or the guiding center distribution function). This different behavior, relating to the reduction of phase space which leads to the loss of a Vlasov constant of motion, may result in the construction of different currents in the reduced phase space than the Vlasov ones. This conclusion is indicative of some limitation on the implications of reduced kinetic theories in particular as concerns the physics of energetic particles in the central region of magnetically confined plasmas.Comment: 9 page

Lyapunov stability of flowing MHD plasmas surrounded by resistive walls

A general stability condition for plasma-vacuum systems with resistive walls is derived by using the Frieman Rotenberg lagrangian stability formulation [Rev. Mod. Phys. 32, 898 (1960)]. It is shown that the Lyapunov stability limit for external modes does not depend upon the gyroscopic term but upon the sign of the perturbed potential energy only. In the absence of dissipation in the plasma such as viscosity, it is expected that the flow cannot stabilize the system.Comment: 9 page

Tokamak-like Vlasov equilibria

Vlasov equilibria of axisymmetric plasmas with vacuum toroidal magnetic field can be reduced, up to a selection of ions and electrons distributions functions, to a Grad-Shafranov-like equation. Quasineutrality narrow the choice of the distributions functions. In contrast to two-dimensional translationally symmetric equilibria whose electron distribution function consists of a displaced Maxwellian, the toroidal equilibria need deformed Maxwellians. In order to be able to carry through the calculations, this deformation is produced by means of either a Heaviside step function or an exponential function. The resulting Grad-Shafranov-like equations are established explicitly.Comment: 11 page