A study of high-beta ballooning modes

Abstract

Ballooning instabilities are studied in the Berkeley multiple mirror experiment. Counterstreaming theta pinch and Marshall gun source hydrogen plasmas are used to achieve a high beta ( β>25%), where β is the ratio of plasma to magnetic pressure at temperatures Te=Ti≊15 eV. Four magnetic field configurations are investigated, each at varying mirror ratios, to explore a range of drive and connection length parameters. In two of these the magnetic field is pulsed from a stable to a locally unstable configuration for initiation of ballooning activity. The other two (static) configurations are a weakly unstable local field region, and the standard linked quadrupole multiple-mirror configuration. Depending on the configuration, critical β’s are found for the onset of ballooning that vary from 5% for the most unstable configuration to greater than 25% for the standard multiple-mirror configuration. The m=1 azimuthal mode is predominant, with some admixture of m=2. The experimental results are compared with predictions from a magnetohydrodynamic theory. In the model the pressure is taken to be isotropic and constant along the axis, except in the diverging field regions at the device ends where the pressure falls to maintain beta constant, consistent with experimental observations. The theoretical results generally predict somewhat higher critical betas for the m=1 mode than those observed. Estimates of the effect of finite Larmor radii, nearby conducting walls, axially nonuniform pressure profiles and resistivity, are also given.