Critical Length Criteria for Mirror Machines

Critical scale lengths for stability of mirror devices are determined. The analysis proceeds via a modified WKB technique which adds the effect of wave amplification due to the presence of singularities of the dielectric function. The approximate answers so determined compare favorably with the numerical solution of the appropriate equations. Results for large and small mirror ratios are presented. It is found that irrespective of the character of the wave in the infinite medium limit (e.g., drift-cone or stable negative energy wave) stabilization is effected at roughly the same magnetic scale length for all but the longest axial wavelength modes.