Compensating tune spread induced by space charge in bunched beams

The effects of space charge play a significant role in modern-day accelerators, frequently constraining the beam parameters attainable in an accelerator or in an accelerator chain. They also can limit the luminosity of hadron colliders operating either at low energies or with sub-TeV high-brightness hadron beams. The latter is applied for strongly cooled proton and ion beams in eRHIC - the proposed future electron-ion collider at Brookhaven National Laboratory. Several schemes were proposed to compensate for space-charge effects in a coasting (e.g., continuous) hadron beam, and some have been tested. Using an appropriate transverse profile of the electron beam (or plasma column) for a coasting beam would compensate both the tune shift and the tune spread in the hadron beam. But none of these methods address the issue of compensating space-charge induced tune spread in a bunched hadron beam, i.e., the dependence of the particle's tune shift on its longitudinal position inside the bunch. In this paper we propose and evaluate a novel idea of using a copropagating electron bunch with mismatched longitudinal velocity to compensate the space-charge induced tune shift and tune spread. We present several practical examples of such a system.