Development of an analytic Beam Model with non-linear Space-Charge Forces and Envelope Stability Studies

Abstract: Space-charge—the repelling force of same-charged particles—is a major challenge in the development and application of high-current linear accelerators like spallation sources or accumulator rings. Understanding the dynamical behavior of the beam in its presence is imperative to prevent beam loss and subsequent detrimental effects. There are several established methods to examine the beam’s behavior in the presence of space-charge. On one hand, there are fast, analytic methods describing the beam as a collective, thereby describing coherent beam envelope modes. An example of such a method is the widely used, so-called envelope equation. They have been extensively employed in the frame of modeling space-charge in high-current linear and circular accelerators. On the other hand, numerical methods resolve the dynamics of single particles that comprise the beam. These methods include the incoherent dynamics of single particles, but are therefore computationally expensive. The two approaches also reveal adichotomy in particle beam modeling in which the collective beam behavior is contrasted with that of individual particles. In order to complement the established methods, an analytic model for fast parameter studies with non-linear space-charge forces was developed in Paper I. It contains the complete derivation and validation of the model and is valid for Gaussian beam profiles in 4D phase-space. It is furthermore valid for arbitrary beam angles, which allows for e.g. studies of lattice errors due to skewed quadrupoles. The analytic calculation of the space-charge kick to the beam takes the beam angle into account and introduces an additional coupling contribution to the transverse beam oscillations. Using the model developed in Paper I, Paper II examines the stability of beam envelopes in the presence of non-linear space-charge forces. In particular, different lattice errors in a circular accelerator are studied, but space-charge driven resonances are observed as well. The paper also presents a brief study of mismatched beams. In Paper III, the non-linear space-charge model is used to model a beam core in the frame of aparticle-core model. Here, single test particles are placed around the oscillating beam envelope and probe the self-field of the beam core while they co-propagate through an accelerator lattice. The study investigates particle-core and beam halo effects with mismatched beam cores.