Space-charge effects in twisted quadrupoles

This paper presents analytical and numerical solutions of space-charge effects in the beam in the twisted quadrupole. It considers the effects of space-charge forces on an elliptical beam with a uniform particle distribution. Effects of the space charge on the transfer matrix of the twisted quadrupole are examined and the transfer matrix is explicitly derived. The numerical solution of the beam line segment consisting of two drift lengths separated by a twisted quadrupole (electrostatic) in the case of 10 eV and 25 keV proton beam is performed, taking into account the effects of the fringe fields.