Transverse collective instability excited by a non-uniform nu -shift in intense beams

A model which describes the effect of a non-uniform space charge nu - shift on the resistive wall instability associated with transverse collective oscillations of a beam of particles is proposed. It successfully predicts the overall characteristics of the instability as observed at the CERN ISR: (1) the observation of a current limitation in spite of the proportionate increase in nu -spread as charge is stacked; and (2) the fact that at the onset of instability, beam losses occur at a particular edge of the beam. The model consists simply of the original model of the resistive wall instability, augmented with the effect on the zero-order betatron tune of the equilibrium space-charge forces. It is shown that, under certain circumstances, the space charge distortion of the equilibrium betatron tune distribution function can permit the instability. An important result is that the stable region in W-space (W is a complex quantity depending on the beam characteristics and its environment) is not diminished by the distortion, but rather shifted. A consequence of this result is that an optimization of design should allow stability, even as the beam intensifies and distortion increases. (7 refs).