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When modeling the propagation of charged particle beams at high currents and relativistic speeds, the space charge and beam current create significant electric and magnetic forces that tend to expand and focus the beam, respectively.

The Charged Particle Tracing interface uses an iterative procedure, in this example, to efficiently compute the strongly coupled particle trajectories and electric and magnetic fields for a beam operating at constant current. A mesh refinement study confirms that the solution agrees with the analytical expression for the shape of a relativistic beam envelope.

This model requires the Particle Tracing Module.