Unstable Ion Waves in a Bounded Ion-Beam Plasma System

Abstract

A dispersion relation is derived for an ion-beam plasma system in a conducting cylinder. The dispersion relation obtained is examined numerically in order to clarify the boundary effect on the propagation of the longitudinal waves. Many eigen modes are found. These modes are found to be unstable even if they are expected to be stable in an infinite system. This instability is caused by an interaction of the ion beam with the wave which is influenced to propagate obliquely by a finite radius of the cylinder. The unstable frequency range shifts from higher to lower mode with increasing a length of the cylinder. The growth rate of the unstable waves is large for large value of b m , n / a , where a and b m , n are the radius of the cylinder and the n th zero of the m th order Bessel function of the first kind respectively.