Space charge effect of the high intensity proton beam during the resonance extraction for the Mu2e experiment at Fermilab

The proposed Mu2e experiment to search for direct μ → e conversion at Fermilab plans slow, resonant extraction of a beam with 3 x 1012 protons from the Debuncher ring. Space charge of this high intensity beam is a critical factor, since it induces significant betatron tune spread and consequently affects resonance extraction processes, such as spill uniformity and beam losses. This study shows the multi-particle simulation results in the early stages of resonance extraction and spill uniformity in the presence of 2D and 3D space charge effects. We have presented the results of the third-integer resonance extraction in early stage for the Mu2e experiment in the presence of space charge effects. In order to track particles and to calculate self-consistent space charge effects, Synergia2 was used, which is capable of parallel computing. The space charge tune shift was computed and was reasonable value compared with the analytical calculation. Locations of the septum and Lambertson were chosen so that particles are kicked and extracted efficiently. The spill rates for with and without space charge effects were uniform, but should be improved for the early stage after the sextupole field ramping.