An analytic treatment of multi-bunch potential well distortion for a two-be
am storage ring is presented. The longitudinal wake effects are separated i
nto: the mode loss, the synchrotron tune shift (both due to potential well
distortion) and the coherent multi-bunch coupling. Here, only the first two
effects are studied. Resulting simple analytic formulas describe the mode
loss and the synchrotron tune shift experienced by a given bunch within the
two-beam, as a function of the high order mode's parameters. One can get i
mmediately a simple quantitative answer in term of the mode loss and the sy
nchrotron tune shift experienced by each bunch form these formulas, so we c
an know how to modify the existing configuration of parasitic cavity resona
nce (via frequency tuning) so that the resulting potential well distortion
effects are minimized. When the RF cavities are symmetrically distributed a
bout the interaction points, the two beams will have same beam loading effe
cts, so we can compensate the phase shift of the two beam using the same me
thod as in one beam case.