Transfer matrix of a Glaser magnet to study the dynamics of non-axisymmetric beam

A Glaser magnet, having bell-shaped distribution of axial field, is often used to focus charged particle beams in the low energy section of accelerators and in many other devices. The transfer matrix of a Glaser magnet available in the literature is only for a rotationally axisymmetric beam. The objective of this paper is to obtain the 4D transfer matrix of a Glaser magnet for a non-axisymmetric beam having different emittances in the two transverse planes. Starting from the Hamiltonian of a single particle motion we have obtained the 4×4 linear transfer matrix of the Glaser magnet in symplectic form. The matrix so derived has been used to estimate the beam envelope through a Glaser magnet using the well known sigma matrix method. We have also studied the emittance growth that results from the coupling between the two transverse planes as the beam passes through the Glaser magnet.