Dilute: A code for studying beam evolution under rf noise

Longitudinal beam dynamics under rf noise has been modeled by Dome, Krinsky, and Wang using a diffusion-in-action PDE. If the primary interest is the evolution of the beam in action, it is much simpler to integrate the model PDE than to undertake tracking simulations. Here we describe the code that we developed to solve the model PDE using the numerical Method of Lines. Features of the code include (1) computation of the distribution in action for the initial beam from a Gaussian or user-supplied distribution in longitudinal phase space, (2) computation of the diffusion coefficient for white noise or from a user-supplied spectral density for non-white noise, (3) discretization of the model PDE using finite-difference or Galerkin finite-element approximations with a uniform or non-uniform grid, and (4) integration of the system of ODEs in time by the solver RKF45 or a user-supplied ODE solver