Edward P. Lee | Searcharxiv

arXiv2006

Efficient computation of matched solutions of the Kapchinskij-Vladimirskij envelope equations for periodic focusing lattices

A new iterative method is developed to numerically calculate the periodic, matched beam envelope solution of the coupled Kapchinskij-Vladimirskij (KV) equations describing the transverse evolution of a beam in a periodic, linear focusing lattice of arbitrary complexity. Implementation of the method is straightforward. It is highly convergent and can be applied to all usual parameterizations of the matched envelope solutions. The method is applicable to all classes of linear focusing lattices without skew couplings, and also applies to all physically achievable system parameters -- including where the matched beam envelope is strongly unstable. Example applications are presented for periodic solenoidal and quadrupole focusing lattices. Convergence properties are summarized over a wide range of system parameters.

physics.acc-ph↗

arXiv2000

MOE11 Emittance Growth from the Thermalization of Space-Charge Nonuniformities

Beams injected into a linear focusing channel typically have some degree of space-charge nonuniformity. In general, injected particle distributions with systematic charge nonuniformities are not equilibria of the focusing channel and launch a broad spectrum of collective modes. These modes can phase-mix and have nonlinear wave-wave interactions which, at high space-charge intensities, results in a relaxation to a more thermal-like distribution characterized by a uniform density profile. This thermalization can transfer self-field energy from the initial space-charge nonuniformity to the local particle temperature, thereby increasing beam phase space area (emittance growth). In this paper, we employ a simple kinetic model of a continuous focusing channel and build on previous work that applied system energy and charge conservation quantify emittance growth associated with the collective thermalization of an initial azimuthally symmetric, rms matched beam with a radial density profile that is hollowed or peaked. This emittance growth is shown to be surprisingly modest even for high beam intensities with significant radial structure in the initial density profile.

physics.acc-ph↗