The equilibrium of sheared, rippled, magnetically focused beams of relativistic charged particles

The (usually neglected) effect of shear on the equilibrium of rippled, magnetically focused beams of relativistic charged particles is investigated analytically in the cold-fluid approximation. Closed expressions for the beam-related parameters and magnetic and electric fields are derived. The results obtained in this work represent the basis for the stability analysis of sheared rippled beams that is required, for example, for beam stabilization and generation of free-electron laser devices.