Theory of longitudinal beam halo in RF linacs. I. Core/test-particle formulation

For intense beams, the analysis of tenuous halo components of the particle distribution that surround the main core of the beam can be challenging. So-called core/test-particle models in which a test-particle is evolved in the applied and space-charge forces of the beam core have been instrumental in understanding the structure and extent of transverse beam halo produced by resonant particle interactions with the oscillating space-charge forces of a mismatched beam core. Here we present a core/test-particle model developed for the analysis of longitudinal beam halo in intense, ion-beam rf linacs. Equations of motion are derived for a test-particle moving interior to, and exterior to, a uniform density ellipsoidal beam bunch. Coupled transverse-longitudinal mismatch modes of the ellipsoidal beam envelope are analyzed. Typical parameters suggest the possibility of a low-order resonant interaction between longitudinal particle oscillations and a low-frequency envelope mode. Properties of this resonance are analyzed in an accompanying paper by the authors in these proceedings