Wake-function, impedance, and energy loss determination for two countermoving particle beams

This paper deals with the determination of wake-function, impedance and energy loss due to surrounding accelerator components two countermoving beams, i.e., beams moving in opposite directions. Differently from classical case, distance between source test charges cannot be considered constant. The defines a generalized independent particle's direction motion. From this wake-function wake-potential is derived. focuses particular on longitudinal direction. expression dissipated by transiting same vacuum chamber obtained. valid both comoving beam scenario. Subsequently, proposed model benchmarked calculating co wake-functions, corresponding impedances wake-potentials for simple geometries (a circular pipe pillbox cavity) traversed comparing results ones electromagnetic code CST Studio Suite. Finally, geometry, their rf-heating are investigated.