Christopher K. Allen (LANL)
Perturbation analysis, along with a weighted polynomial expansion of the self-fields, is used to construct approximate halo particle trajectories. The analysis is based on the particle-core model of halo formation. Here, the self-fields of the core are expanded in a polynomial where the coefficients are chosen to minimize the least-square error from the true fields. The error is weighted against the core distribution so that the expanded fields are an laveragedn representation of the fields felt by halo test particles. Keeping the nonlinear terms in this expansion retains the stability of the halo particles in the model, which is not possible with Hillms equation used previously in particle-core studies. From this model, we employ perturbation analysis to construct approximate solutions for the halo particle trajectories. These solutions can provide quantitative information on the halo formation, such as amplitude and time constants, accurate when the relative beam mismatch is small.
*Work supported by US Department of Energy
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