If electron beam and the ion beam are "brought into contact", due to the Coulomb interaction equilibrium state in which temperatures of both beams are the same, will eventually be reached. Assuming identical cross sections in both beams, it can be proven that emittance ratio will be inversly proportional to square root of mass-ratio for those two beams. Hence, ion (heavy) beam will achieve state with considerably smaller emittance.
It is important tonote that two beams need not to be in constant contact with each other. One section of the accelerator lattice can be devoted to this cooling mechanism.