Stabilization of propagating light ion beam by its rotating motion

The stability of propagating proton beam with rotation around the propagation axis is examined here numerically. If the electron number density of the background gas in the reactor is chosen to be so small that the electron mean free path is longer than the mean electron Larmor radius but the number density is high enough to satisfy that the plasma frequency of the background gas is larger than 10¹⁰ rad/s, then the charge of the ion beam is neutralized within 1 ns but the current of the ion beam is not neutralized. Thus the Lorentz force by the self-induced magnetic field in the azimuthal direction confines the propagating ion beam in a small radius. The macro-instability can be suppressed by the action of the self-induced magnetic field in the propagation direction. The propagating ion beam with rather high rotating velocity is obtained first in the steady-state in equilibrium. Then the dispersion relation is derived through the linearized system of equations for perturbed quantities. The velocity ratio of the mean rotating velocity to the propagating one in order to stabilize the macro-instability can be described for the given steady-state solution of the propagating ion beam.