Beam Loading Simulation for Relativistic and Ultrarelativistic Beams in the Tracking Code RF-Track

Medical and industrial electron linacs can benefit from the X-band accelerating technology developed for the Compact Linear Collider (CLIC) at CERN. However, when high-intensity beams are injected in such high-gradient structures (>35 MV/m), the beam loading effect must be considered by design since this beam-cavity interaction can result in a considerable gradient reduction with respect to the unloaded case. Studying energy conservation, a partial differential equation (PDE) has been derived for injected beams in both the relativistic and ultrarelativistic limits. Making use of this, a specific simulation package within RF-Track has been developed, allowing realistic tracking of charged particle bunches under this effect regardless of their initial velocity. The performance of this tool has been assessed by reproducing previously obtained beam-loaded fields in CLIC main linac and CLIC Drive-Beam linac structures. In this paper, we present the analytic PDE derivation and the results of the tests.