SNS HOM damping requirements via bunch tracking

Based on Higher Order Mode (HOM) field properties, the Spallation Neutron Source (SNS) HOM damping requirements have been determined by bunch tracking simulations. Transverse instabilities are found to be absent and transverse error magnifications are found to be acceptable if the loaded cavity Q for each mode is less than 10⁸ and the expected cavity-to-cavity frequency variation due to manufacturing tolerances is present. Longitudinal instabilities are absent if the loaded cavity Q for each HOM is less than 10⁸, the loaded cavity Q for each non-pi fundamental mode has the expected value, and the expected cavity-to-cavity frequency variation is present. Each of the two cavity types has three longitudinal modes that are close enough to a bunch spacing harmonic that one of the modes may occasionally get tuned onto the resonance; the power deposited as a function of Q has been calculated for this case. Deposited power and transverse instabilities/magnifications have also been determined analytically.