Generalized 3D beam dynamics model for industrial traveling wave linacs design and simulations

Beam dynamics simulations in traveling wave (TW) accelerating structures with significant beam loading is a challenging problem. Some codes are capable of calculating the TW electromagnetic fields , and some can track particles through such fields, but most cannot treat both self-consistently. A few commercial codes can model the physics correctly at the expense of many processor-hour computations to obtain converged self-consistent solutions. However, simple, accurate equations of motion for intensive beam dynamics in TW accelerating structure analysis have been previously obtained by Masunov and subsequently implemented in the Hellweg code, which was developed at the Moscow Engineering-Physics Institute. Hellweg is based on equations that allow fast simulations of beam dynamics while taking into account such effects as beam loading, space charge, and external magnetic fields . In this paper, we describe in detail some recent improvements to the Hellweg physics kernel. We have generalized the Masunov results into a 3D set of equations of motion, which include all spatial components of the radiofrequency (RF) and external magnetic fields. We have also improved the Lapostolle space charge model to the general 3D ellipsoid form for any dimensions’ ratio, consideration for the particles outside the beam core, and the fields from the neighboring bunches that can exist in the real machine. These modifications allow approaching the Hellweg accuracy to the self-consistent commercial codes while keeping the simulation time short, which is essential during the linac design and optimization stage. The implementation of these new capabilities in Hellweg is carefully benchmarked against other codes and analytical calculations. The code is freely available with an open source license.