  A method is presented that enables to compute the parameters of matched beams
with space charge in cyclotrons with emphasis on the effect of the
transverse-longitudinal coupling. Equations describing the
transverse-longitudinal coupling and corresponding tune-shifts in first order
are derived for the model of an azimuthally symmetric cyclotron. The
eigenellipsoid of the beam is calculated and the transfer matrix is transformed
into block-diagonal form. The influence of the slope of the phase curve on the
transverse-longitudinal coupling is accounted for. The results are generalized
and numerical procedures for the case of an AVF cyclotron are presented. The
algorithm is applied to the PSI Injector II and Ring cyclotron and the results
are compared to TRANSPORT.
