Low energy RHIC operation has to be operated at an energy ranging from ? = 4.1 to ? = 10. The energy variation causes the change of revolution frequency. While the rf system for the circulating ion will operate at an exact harmonic of the revolution frequency (h=60 for 4.5 MHz rf and h=360 for 28 MHz rf.), the superconducting rf system for the cooling electron beam does not have a frequency tuning range that is wide enough to cover the required changes of revolution frequency. As a result, electron bunches will sit at different locations along the ion bunch from turn to turn, i.e. the slipping of the electron bunch with respect to the circulating ion bunch. At cooling section, ions see a coherent focusing force due to the electrons? space charge, which differs from turn to turn due to the slipping. We will try to estimate how this irregular focusing affects the transverse emittance of the ion bunch.