Thermal barrier potential of a tandem mirror

The relation between the electrostatic potential and the low energy electron density under electron cyclotron resonance heating (ECRH) in the thermal barrier of a tandem mirror is investigated analytically and numerically. The distribution function of mirror trapped electrons at low energy is found to stretch out in the perpendicular direction to the magnetic field and to be well approximated by a bi-Maxwellian (T⊥≥T∥) rather than by a Maxwellian. Under this approximation it is found analytically that the conventionally used Boltzmann formula derived from the full Maxwellian plasma for the barrier depth is modified to another expression including the ratio between T⊥ and Te (central cell electron temperature). The bounce-averaged Fokker–Planck simulations show that T⊥/Te itself is a function of the potential depth and that the conventional formula is modified to q(φb−φe)=Te ln(αnc/nb) with α=1.5–1.8 depending on ECRH power. This expression agrees well with experimental results on GAMMA 10 [Phys. Rev. Lett. 55, 939 (1985)].