Deflecting forces for the case of multi mode beam-rf cavity interaction in linear accelerators

The formulae for the deflecting RF forces have been derived for the train of charged bunches, traversing a RF cavity. These forces originate from the deflection action of non symmetrical modes excited by the misaligned bunches, the infinite set of the cavity eigen modes being taken into account. Various dependencies are explored, including the effect of "mode saturation" and non linearity of RF deflecting gradient, followed by the appropriate plots.