Uniform bunch formation by RF voltage modulation with a band-limited white signal

Uniform bunch formation by RF voltage modulation with a band-limited white signal is proposed to relax the space-charge effects in proton synchrotrons. A unique feature of this method is to increase the bunching factor without the longitudinal emittance blow-up, in principle. The beam dynamics is discussed based on the diffusion equation and computer simulations. The temporal evolution, time constant and equilibrium distribution are derived.