M=1Cyclotron-Mode Klystron Instability

Abstract

The transverse beam breakup instability, for a uniform axial focusing magnetic field, has been investigated utilizing the approach of the well-known klystron instability. An expression for the gain is obtained. It is proportional to the beam current and the cavity equivalent shunt resistivity at the radius of the beam surface and inversely proportional to the cyclotron frequency and the cavity frequency, resulting in instability at high beam current, in contrast to the standard klystron instability which occurs at low currents and is self-stabilized at high beam currents.