| In low energy synchrotron accelerators, such as low energy boosters and medical accelerators, space charge can significantly affect the particle trajectories within the synchrotron beam, and therefore alter beam characteristics such as the tune. The attributes of beam instabilities, like the betatron resonance and the coupled resonance, which are determined by the beam tune, are therefore also modified by the space charge effect. We have developed a particle simulation model and code for tracking synchrotron beams with space charge. We have also derived an expression for the space charge tuneshift of a Gaussian beam, which is dependent upon the individual particle amplitude. Using our simulation code we have studied the integer betatron resonance. The region of instability has been found to be a function of the beam current, energy, and emittance. An equation for the region of instability has been determined. We have also studied the coupled resonance, and found an expression which defines its region of instability. |
