Study of corrections to the geometrical factor in the space charge impedance for the IPNS upgrade

Collective instabilities are an important consideration in the 2-GeV rapidly-cycling synchrotron (RCS) of the proposed 1-MW spallation neutron source upgrade due to the very high beam intensity of 1.04x1014 protons per pulse. Collective instabilities are intensity-dependent effects which arise due to the electromagnetic wake fields generated by the beam as it interacts with its surroundings. The interactions are characterized by the coupling impedance, which in the RCS is dominated by space charge effects. To minimize the space charge impedance, the vacuum chamber is constructed with a special wire rf shield. Estimating the longitudinal and transverse impedance due to space charge is critical for the beam stability analysis. The standard geometrical factors used to evaluate the space charge impedance assume a uniform, round, unbunched beam in a cylindrical, smooth beam pipe. Two corrections to the geometrical factors have been proposed to account separately for the wire rf-screening cage and the more realistic varying elliptical beam cross-section. These corrections are studied in the case of the RCS. It is found that including these details results in a correction of less than 20%