Threshold of transverse mode coupling instability with arbitrary space charge

Abstract

Threshold of the transverse mode coupling instability is calculated in frameworks of the square well model at arbitrary value of space charge tune shift. A new method of calculation is developed beyond the traditional expansion technique. The square, resistive, and exponential wakes are investigated. It is shown that the instability threshold goes up without limit when the tune shift increases. A resemblance of the results to conventional case of the parabolic potential well is demonstrated and explained.