Four-way rf beam separator

A method for separating a continuous beam of relativistic particles into four pulsed beams is investigated theoretically. The separation is periodic with period 2..pi../..omega.. so that each of the four beams consists of current pulses of duration ..pi../..omega... The separation is accomplished by a series of rf cavities in the beam line. The cavities operate in the TM/sub 110/ and have frequencies, ..omega.., 3..omega.., 5..omega.., 7..omega.., etc. The transverse momentum imparted to the beam particles results in a time-dependent displacement of the beam centroid at a position downstream of the cavity array. The mathematical limitations imposed by truncating a Fourier series are discussed, and an expression derived for the necessary phase and amplitude of each cavity. The rf induced by the beam in the cavities is treated in detail, and does not appear to be a serious problem.