Beam dynamics and stability analysis of an intense beam in a continuously twisted quadrupole focusing channel

This paper describes the dynamics of a space-charge-dominated beam through a continuously twisted quadrupole magnet using ten independent first-order differential equations of the beam matrix elements under the assumption of linear space-charge force. Various beam optical properties of the magnet and the evolution of the emittance that results from the coupling between the two transverse planes are studied. The perturbed equations of motion around the matched beam envelopes have been derived and utilized to analyze the stability properties of the intense beam transport by calculating the eigenvalues of the transfer map over one lattice period. Detailed analysis shows the presence of instability due to parametric resonances in a twisted quadrupole channel which generally does not appear in the FODO quadrupole channel. A 2D particle-in-cell simulation code has been developed and utilized to verify the analytical results and to examine the behavior of the intense beam with Gaussian (GA) distribution in the twisted quadrupole channel.