  Transverse mode coupling instability of a bunch with space charge and wake
field is considered within the frameworks of the boxcar model. Eigenfunctions
of the bunch without wake are used as a basis for the solution of the equations
with the wake field included. A dispersion equation for constant wake is
presented in the form of an infinite continued fraction and also as the
recursive relation with an arbitrary number of the basis functions. Realistic
wake fields are considered as well including resistive wall, square, and
oscillating wakes. It is shown that the TMCI threshold of the negative wake
grows up in absolute value when the SC tune shift increases. Threshold of
positive wake goes down at the increasing SC tune shift. The explanation is
developed by an analysis of the bunch spectrum.
