Higher order mode analysis of the SNS superconducting linac

Higher order modes (HOM's) of monopoles, dipoles, quadrupoles and sextupoles in β=0.61 and β=0.81 6-cell superconduting (SC) cavities for the Spallation Neutron Source (SNS) project, have been found up to about 3 GHz and their properties such as R/Q, trapping possibility, etc have been figured out in concerning with the manufacturing imperfection. Main issues of HOM's are beam instabilities (published separately) and HOM induced power especially from TM monopoles. The time structure of SNS beam has three different time scales of pulses, which are micro-pulse, midi-pulse and macro-pulse. Each time structure will generate resonances. When a mode is near these resonance frequencies, the induced voltage could be large and accordingly the resulting HOM power, too. In order to understand the effects from such a complex beam time structure on the mode excitation and resulting HOM power, analytic expressions are developed. With these analytic expressions, the induced HOM voltage and HOM power were calculated by assuming external Q for each HOM.