Resonance Driving Terms From Space Charge Potential

This note presents the calculation of the Resonance Driving Terms (RDTs) and the tune spread coming from the space charge potential of a Gaussian beam. These can be obtained by including this potential in the linear Hamiltonian of the accelerator. Through the RDTs, incoherent resonances excited by the space charge potential can be identified. The analytical method has been implemented in a self contained Python module, PySCRDT, in order to generalise the derivation and apply it to various rings and beams. The analytical approach as well as numerical examples and applications of PySCRDT are presented.