Abstract
In this paper, a simplified theoretical model that allows prediction of the final stationary state attained by an initially mismatched beam is presented. The proposed stationary state has a core-halo distribution. Based on the incompressibility of the Vlasov phase-space dynamics, the core behaves as a completely degenerate Fermi gas, where the particles occupy the lowest possible energy states accessible to them. On the other hand, the halo is given by a tenuous uniform distribution that extends up to a maximum energy determined by the core-particle resonance. This leads to a self-consistent model in which the beam density and self-fields can be determined analytically. The theory allows one to estimate the emittance growth and the fraction of particles that evaporate to the halo in the relaxation process. Self-consistent $N$-particle simulation results are also presented and are used to verify the theory.
Highlights
In experiments that require the transport of intense beams, space-charge forces make it virtually impossible to launch a beam with a distribution that corresponds to an exact equilibrium state
A quantification of the amount of emittance growth and halo formation that can be expected becomes an important issue in the design of such systems
In order to estimate these, a good knowledge of the mechanisms that lead to beam relaxation and, especially, of the final stationary state reached by the beam is necessary
Summary
In experiments that require the transport of intense beams, space-charge forces make it virtually impossible to launch a beam with a distribution that corresponds to an exact equilibrium state. We are dealing with purely classical particles, the conservation of volume in the phase space imposed by the Vlasov equation leads to a Pauli-like exclusion principle for the beam particles Taking this into account, in this paper we propose that the stationary state for the core corresponds to a completely degenerate Fermi gas, where the particles occupy the lowest possible energy. This leads to a self-contained model where the beam density and self-fields can be determined analytically as a function of two parameters—the core size and the halo density These parameters are, in turn, readily obtained by numerically solving two algebraic equations that correspond to the conservation of the total number of particles and the energy of the system.
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