Alfvén‐ion‐cyclotron instability in mirror machines

The Alfven‐ion‐cyclotron instability is studied for finite mirror‐confined plasmas with high beta without field reversal. Variation perpendicular to field lines is modeled by an effective k⊥. Variation along a representative field line is treated using the Wentzel‐Kramer‐Brillouin approximation in two ways. First, the local dispersion relation is expanded about a wavenumber and frequency corresponding to absolute instability at the machine midplane. This yields a parabolic k∥(s) and a frequency correction. Second, the local dispersion relation is evaluated exactly as a function of position, and the appropriate phase‐integral condition is used to fix the frequency. This condition is chosen using a generalized WKB formulation which is outlined. The two ways of obtaining the mode frequency agree closely. Stability boundaries are drawn in β⊥−β∥ space for two representative finite plasmas. The long thin approximation is used to model finite‐beta well deepening. For ease of computation, the bi‐Maxwellian ion ve...