Potential for luminosity improvement for low-energy RHIC operation with long bunches

Electron cooling was proposed to increase luminosity of the RHIC collider for heavy ion beams at low energies. Luminosity decreases as the square of bunch intensity due to the beam loss from the RF bucket as a result of the longitudinal intra beam scattering (IBS), as well as due to the transverse emittance growth because of the transverse IBS. Both transverse and longitudinal IBS can be counteracted with electron cooling. This would allow one to keep the initial peak luminosity close to constant throughout the store essentially without the beam loss. In addition, the phase-space density of the hadron beams can be further increased by providing stronger electron cooling. Unfortunately, the defining limitation for low energies in RHIC is expected to be the space charge. Here we explore an idea of additional improvement in luminosity, on top of the one coming from just IBS compensation and longer stores, which may be expected if one can operate with longer bunches at the space-charge limit in a collider. This approach together with electron cooling may result in about 10-fold improvement in total luminosity for low-energy RHIC program