Effects of hot electrons on the stability of a closed field line plasma

Abstract

Motivated by the electron cyclotron heating being employed on dipole experiments, the effects of a hot species on stability in closed magnetic field line geometry are investigated. The interchange stability of a plasma consisting of a fluid background with a population of kinetic hot electrons is considered. The species diamagnetic drift and magnetic drift frequencies are assumed to be of the same order, and the wave frequency is assumed to be much larger than the background drift frequencies. To illustrate the key physics issues and obtain an simpler understanding of instability mechanisms, we first examine the effects of hot electrons in cylindrical Z-pinch geometry. This linear approximation to a dipole preserves the essential feature of closed magnetic field lines. The absence of variations along the equilibrium magnetic field allows us to analytically derive an arbitrary total pressure dispersion relation, investigate a large variety of regimes, and explain the physical phenomena at work. Our analysis finds that two different types of resonant hot electron effects can modify the simple Magnetohydrodynamic (MHD) interchange stability condition. When the azimuthal magnetic field increases with radius, there is a critical pitch angle above which the magnetic drift of the hot electrons reverses. The interaction of the wave with the hot electrons with pitch angles near this critical value always results in instability. When the magnetic field decreases with radius, magnetic drift reversal is not possible and only low speed hot electrons interact with the wave. Destabilization by this weaker resonance effect can be avoided by carefully controlling the hot electron density and temperature profiles.

(cont.) Based on the insights obtained by considering a Z-pinch, we then expand our calculation to a dipole magnetic field confined plasma by retaining geometrical effects such as the poloidal variations of electric and magnetic fields. These variations cause quasi-neutrality and the radial component of Ampere's law to become a set of coupled integro-differential equations which without approximations can only be solved numerically. To obtain a semi-analytic solution we consider an interchange approximation that allows us to obtain an arbitrary beta dispersion relation that recovers the correct Z-pinch limit. In the dipole case, our analysis again shows that a weak drift resonance with slowly moving hot electrons can result in destabilization, which can be controlled by the hot electron density and temperature profiles. The specific example of a point dipole equilibrium is considered in some detail to explicitly demonstrate these results. In contrast with the Z-pinch, a strong hot electron destabilization due to magnetic drift reversal is found not to occur in a point dipole.