Experimental and Theoretical Studies of Instabilities in a High‐Energy Neutral Injection Mirror Machine

Recent observations with the Phoenix high‐energy neutral injection experiment are described. At densities where the electron plasma frequency is greater than the ion cyclotron frequency, strong emission at the ion cyclotron frequency and ½ the ion cyclotron frequency is observed. This is interpreted on the basis of the theory of electrostatic instability developed by Harris and others. Experimentally, the instability results in strong scattering of ions out of the transverse direction but so far as can be observed, there is no actual loss of plasma. Above a density of 5 × 108 particles/cm3, accumulation of particles is limited by the development of strong low‐frequency (∼100 kc/sec) oscillations which appear to be an m = 1 displacement of ions and electrons rotating at half the ion precession frequency. This mode is approximately independent of density. During periods of strong emission at the ion cyclotron frequency, however, another mode is observed, the frequency of which is approximately proportional to density. These observations suggest an m = 1 precessional drift instability. The existing theories concerning this low‐frequency instability are fully discussed. We present a new calculation in which the cylindrical plasma shape and the associated boundary conditions are taken into account. Its predictions are in reasonable agreement with the experiment. The electric field inside the plasma is found to be nonuniform even for the m = 1 mode, so that finite Larmor radius effects are to be expected for this mode, contrary to common belief. The full equation for the electric potential valid for all densities and including the first order finite Larmor radius effect is presented. However, the finite Larmor radius effect is found to be small at densities around 108 particles/cm3, and at magnetic fields above 10 kG.