Betatron resonance instabilities in axisymmetric field-reversed systems

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Abstract
The effect of betatron resonances of the axis encircling, or ring, particles on the low frequency hydromagnetic stability of field reversed configurations is studied. It is found that modes with phase velocity parallel to the ring current are destabilized, and those with phase velocity opposite to the current are damped. For fully field reversed systems with moderate to large aspect ratio, the modes can grow on a hydromagnetic time scale. For rings with a smaller degree of field reversal, or with aspect ratio near unity, the growth rate is exponentially smaller.