Classification of Space-Charge Resonances and Instabilities in High-intensity Linear Accelerators

As the beam intensity increases in modern high-power accelerators, self-field effects of the beam become significant and it is the utmost goal to minimize the beam loss of halo particles by avoiding or minimizing contributions of various halo mechanisms. There are two distinct families of space-charge halo mechanisms in high-intensity linear accelerators, and yet they need to be differentiated: resonances (single particle resonances or incoherent resonances) and instabilities (parametric resonances or coherent resonances). What we call resonances are resonances of the beam particle excited through the space-charge nonlinear multipoles. What we call instabilities (or envelope instabilities) are instabilities of the beam envelope. Instabilities are also called parametric resonances because they are parametric resonances of the envelope equation. They would better be called envelope parametric resonances to distinguish them from particle parametric resonances. Resonances and instabilities may look alike in the phase space, and yet they have distinct differences. Instabilities (or envelope parametric resonances) do not have the resonant frequency component. Various orders of resonances and instabilities are presented along with the beam distributions with which the particular mechanism is observed.