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The effect of Landau damping is often calculated assuming a Gaussian beam distribution in all transverse degrees of freedom, which agrees reasonably well with beam measurements. However, the stability of the beam is strongly dependent on the details of the distribution. The present study focuses on the slow evolution of the transverse bunch distribution, for a bunch excited by a coherent white noise source, damped by a transverse feedback system, and with detuning dependent on the transversedoi:10.1103/physrevaccelbeams.23.034401 fatcat:dj2b3rfnhrfy5dhkw6swmaquuq