Threshold of transverse mode coupling instability with arbitrary space charge

The threshold of the transverse mode coupling instability is calculated in framework 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 indefinitely when the tune shift increases. A comparison with conventional case of the parabolic potential well is performed.