Equilibria and stability of non-adiabatic Vlasov-Maxwellian plasmas

Adiabatic plasma physics, whereby particles gyrate tightly around magnetic field lines, constitutes a well studied area of plasma physics. On the other hand, plasmas in which a significant number of particles have orbits comparable to the confinement scale have many interesting properties which are not yet well understood. In particular, high energy particles appear to ignore turbulence (1), and do not behave like fluids. MHD equations cannot generally be adapted to modeling of non-adiabatic plasma; for example, the field reversed configuration is predicted in the MHD model to have a tilt mode instability which is not experimentally observed (2). We consider in this dissertation the general case of arbitrary orbit size. Specifically, the solutions which we consider are drifted Maxwellian distributions which satisfy the Vlasov equation, and we call these Vlasov-Maxwellian (or V-M) solutions. The Maxwellian form for the distribution function is chosen for its immunity to ion-ion collisional diffusion, which becomes more significant as Larmor radius is increased. We impose the condition that all Maxwellian ion species have common temperature and drift velocity so that the ion-ion collision operator collapses to zero. In section 2 we derive self-consistant equilibria for V-M plasmas. First we show that all V-M plasmas must be rigid rotors. Next we derive the V-M equilibrium equation for a single ion species. Finally we numerically evaluate several solutions in finite geometry. Solutions are found which are field reversed and have high density contrast. In section 3 an electrostatic linear stability analysis is carried out for a restricted class of V-M plasmas. The cases considered involve cylindrical geometry and are finite in the radial direction. A dispersion relation is obtained which is sufficiently simple that a complete investigation of finite orbit stability can be carried out. Both analytic and numerical stability analyses are presented.