Particle and energy exchange between untrapped and electrostatically confined populations in magnetic mirrors

Abstract

The effect of passing particles on the confinement of particles trapped in a magnetic mirror with confining electrostatic potential is examined. Exact relations between the particle and energy fluxes and the distribution functions for two auxiliary boundary value problems are derived. Approximate analytic expressions for these fluxes, asymptotically valid for large ratio of confining potential energy to trapped-particle temperature and either large or small mirror ratio, are obtained. The results are applied to the determination of the ambipolar potential and the temperature difference between trapped and untrapped electrons in a stream-stabilized conventional mirror machine such as 2XIIB and in the plug cells of a tandemmirror machine. An important result is that, under a wide range of conditions, the potential difference Φ between the plug and the barrier of a thermal-barrier tandem-mirror machine is given by eΦ = Tep ln [(np/nb) (Tec/Tep)1/2], a modification of the Maxwell-Boltzmann result.