Stochastic effects in real and simulated charged particle beams

Abstract

The Vlasov equation embodies the smooth field approximation of the self-consistent equation of motion for charged particle beams. This framework is fundamentally altered if we include the fluctuating forces that originate from the actual charge granularity. We thereby perform the transition from a reversible description to a statistical mechanics description covering also the irreversible aspects of beam dynamics. Taking into account contributions from fluctuating forces is mandatory if we want to describe effects such as intrabeam scattering or temperature balancing within beams. Furthermore, the appearance of "discreteness errors" in computer simulations of beams can be modeled as "exact" beam dynamics that are being modified by fluctuating "error forces." It will be shown that the related emittance increase depends on two distinct quantities: the magnitude of the fluctuating forces embodied in a friction coefficient, g, and the correlation time dependent average temperature anisotropy. These analytical results are verified by various computer simulations.

Parametic Study of the current limit within a single driver-scaletransport beam line of an induction Linac for Heavy Ion Fusion

“…one obtains two coupled linearized differential equations which exhibit two independent solutions that lead to two fundamental oscillation modes [66]:…”

Coulomb scattering within a spherical beam bunch in a high current linear accelerator

“…For non-neutral plasmas or charged-particle beams, Jansen indicates that it is more realistic to use the mean interparticle distance [16]. In the accelerator community a similar argument is often followed (see, for example, Le Duff [9] and Struckmeier [21]). We note that Jansen's arguments are valid mainly for low density beams, used in electron and ion beam lithography instruments.…”

Characteristics of the fourth order resonance in high intensity linear accelerators

“…Studies have been done in the early days related with the envelope equation [6], the particle-core model [7][8][9][10] and the envelope instability [11,12]. In order to avoid the envelope instability, linac designers have applied the design rule to keep  o < 90 [1][2][3] in designing high-intensity linear accelerators, where  o is the zero-current phase advance per cell.…”