| Summary: | The present work explores the full role of relativistic effects in the transport of magnetically focused non-neutral cold beams. Not only relativistic effects along the transport axis are discussed, but relativistic effects associated with the transverse particle dynamics are also investigated. Transverse effects are directly connected with the amount of charge the beam transports and a proper discussion of relativistic features should include accurate analysis of all fields self-consistently created by space charge. We review and adapt the equilibrium analysis, and proceed to develop a convenient method to tackle dynamical situations. Simulations revealing how flattop initial conditions, the typical equilibrium profiles of nonrelativistic beams, evolve toward highly nonlinear states in relativistic beams are then presented and discussed.
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