  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 obtained
in the form of an infinite continued fraction. It is shown that 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 to zero at higher space
charge. The explanation of this behavior is developed by analysis of the bunch
spectrum. A comparison of the results with published articles is represented.
