Reliability of numerical solutions of a diffusion equation modeling rf noise-induced dilution in particle beams

摘要

The dilution process in particle beams caused by noise in the rf accelerating system has been modeled using a diffusion equation. Particle tracking can also be undertaken to determine the effects of rf noise, though it is much more computationally extensive than integrating the diffusion equation. In this paper we present the integration results using the Method of Lines (MOL) for certain important classes of noise. We will describe the numerical algorithms in detail, including those that are made to remove anomalous solutions. Reliability of the numerical results will be checked using both finite-difference and finite-element (Galerkin) methods in discretization and applying the same algorithms to the cases of linear and quadratic diffusion coefficients where exact solutions are known.