Collisional methods with applications to charged particle beams
In this work, we present our development of new collisional numerical methods which are the first methods that can provide an accurate microscopic description of beam dynamics with high computational efficiency. The first method is the Simò integrator which solves the N-body problem of beams by direct integration of the particles' equations of motion in the presence of external electromagnetic fields. Its development included very unique techniques to obtain accuracy while resolving all the efficiency challenges known to N-body integrators. Consequently, the Simò integrator is the first large-scale collisional numerical method in beam physics that is accurate up to machine precision with a relatively high efficiency. Then, we incorporate the Simò integrator to model collisions into our other collisional method referred to as the Particles' High-Order Adaptive Dynamics (PHAD). PHAD employs an advanced version of the fast multipole method (FMM) along with Strang splitting method, and the addition of the Simò integrator makes PHAD the first most efficient, numerically symplectic, collisional method in beam physics. For an enhanced performance, the algorithms of both the Simò integrator and PHAD were fully parallelized on a large-scale high-performance hybrid cluster. We present simulations performed by our codes of three complicated beam dynamics problems. One application is for the electron cooling of ion beams to which our simulations demonstrate and give the first insight of the microscopic description of electron cooling with accurate prediction of cooling time. The other application illustrates density modulations of electron beams due to ions from a collisional picture of the dynamics and provide conditions to obtain a strong modulation signal necessary for variants of coherent electron cooling systems. The last application considers microscopic simulations of the relaxation of certain beam perturbations which illustrates finite N effects in contrast to the kinetic limit of the collisionless methods, and the resulted relaxation times are important for applications like the beam echo.