Beta enhancement by relativistic electron rings in bumpy tori

Abstract

The maximum achievable beta (ratio of plasma pressure to magnetic pressure) value in a bumpy torus such as Elmo (EBT) is determined primarily by the stability of the system to the interchange modes. These modes have as their source of free energy the drifts of the hot electron component that arise from the curvature and gradients of the confining magnetic field. At low (compared to the ion gyro) frequencies the only modes that exist are the core plasma and hot electron interchange, but at frequencies near the ion cyclotron frequency, instabilities arising from coupling of the interchange and compressional Alfven wave also appear. In most, if not all previous treatments of these instabilities, the hot electrons were treated as non-relativistic. In this paper we re-examine these modes using a relativistic formulation for the hot electrons which we also treat as highly anisotropic by neglecting their parallel momenta relative to the perpendicular momenta and their rest mass energy. We find a significant enhancement in the ion beta value as a result of treating the ring electrons relativistically. For typical present day EBT parameters we find that the value of the ion beta increases by about 50% as a result of increasing the hot electron mean energy from about several keV to few MeV. At such an energy the microwave power for heating these electrons is also optimum since the drag on the background plasma also reaches its minimum value.