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, $\ensuremath{\gamma}$, and the correlation time dependent average temperature anisotropy. These analytical results are verified by various computer simulations.
Highlights
Analytical approaches to the dynamics of charged particle beams that are based on the Liouville—or equivalently on the Vlasov—equation do not include effects due to the actual charge granularity
Effects of elastic Coulomb scattering like the well-known phenomenon of intrabeam scattering [11] observed for intense beams that circulate in storage rings, or the process of temperature balancing within a charged particle beam—commonly referred to as beam equipartitioning—fall into this category
We have reviewed the analytical description of emittance growth effects that are caused by the actual granularity of the charge distribution of particle beams— commonly referred to as intrabeam scattering
Summary
Analytical approaches to the dynamics of charged particle beams that are based on the Liouville—or equivalently on the Vlasov—equation do not include effects due to the actual charge granularity. In order to include these irreversible effects in our analytical description of beams, the Vlasov approach must be generalized appropriately [12,13,14,15]. This will be achieved by switching from a deterministic to a statistical treatment of beam dynamics, namely by separating the actual forces that act on the beam particles into a smooth and a fluctuating component. The reversible transient effect of “initial emittance growth”— occurring for beams with non-self-consistent phase space densities, as described by the Vlasov equation—is rendered irreversible because of the accumulated action of. We investigate the scaling of these emittance growth factors with the number of particles used in the simulation in order to distinguish computer noise related effects from those occurring within a real beam
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