Stability properties of an intense relativistic non-neutral electron ring in a modified betatron accelerator

Abstract

Equilibrium and stability properties of an intense electron ring located at the midplane of an externally applied mirror field are investigated within the framework of the linearized Vlasov–Maxwell equations, including the important influence of equilibrium self-fields and an applied field Bext0θ in the toroidal direction. It is assumed that the ring is thin and that ν/γb≪1, where ν is Budker’s parameter and γbmc2 is the characteristic electron energy. Equilibrium and stability properties are calculated for the choice of equilibrium distribution function in which all electrons have the same value of energy in a frame of reference rotating with angular velocity ωb in the minor cross section of the ring, and a Lorentzian distribution in canonical angular momentum Pθ. Negative-mass and resistive-wall stability properties are calculated, and a closed dispersion relation is obtained for the case where the ring is located inside a toroidal conductor with finite resistivity and minor radius ac much less than the major radius R0. One of the most important features of the stability analysis is that the negative-mass instability in a high-current ring can be stabilized by equilibrium self-field effects in circumstances where the self-fields are sufficiently intense. Moreover, a modest spread Δ in canonical angular momentum can stabilize the resistive-wall instability.ufoff