Self-consistency and coherent effects in nonlinear resonances

The influence of space charge on emittance growth is studied in simulations of a coasting beam exposed to a strong octupolar perturbation in an otherwise linear lattice, and under stationary parameters. We explore the importance of selfconsistency by comparing results with a non-self-consistent model, where the space charge electric field is kept “frozen-in” to its initial values. For Gaussian distribution functions we find that the “frozen-in” model results in a good approximation of the self-consistent model, hence coherent response is practically absent and the emittance growth is self-limiting due to space charge de-tuning. For KV or waterbag distributions, instead, strong coherent response is found, which we explain in terms of absence of Landau damping.