In circular accelerators the tune of a particle may cross a resonance line due to space charge. A self-consistent treatment requires taking into account the time-dependent space charge force in addition to the driving field errors. This is investigated by means of computer simulation for linear and non-linear resonances. The new features as compared with resonance crossing in the absence of space charge are discussed. In the case of a dipole resonance space charge is found to have a stabilizing effect, whereas it can lead to undesirable tune locking for non-linear resonances.
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Hofmann et al. (1985) studied this question.