Transverse mode coupling instability of a bunch with space charge and wake field is considered in frameworks of the boxcar model. Eigenfunctions of the bunch without wake are used as the basis for solution of the equations with the wake field included. Dispersion equation for the bunch eigentunes is presented in the form of an infinite continued fraction and also as the recursive relation with arbitrary number of the basis functions. It is shown that the influence of space charge on the instability essentially
depends on the wake sign. In particular, threshold of the negative wake increases in absolute value until the space charge tune shift is rather small, and goes down at higher space charge. The explanation is developed by analysis of the bunch spectrum.
Full text: arXiv 1603.03744