Parallel electromagnetic field solvers using finite element methods with adaptive refinement and their application to wakefield computation of axisymmetric accelerator structure

Future Linear Colliders for High Energy Physics research will employ radio-frequency (RF) accelerating sections that typically consist of over a hundred individual cavities coupled through a beam aperture. For the Next Linear Collider (NLC) being proposed long trains of electron bunches are required to achieve the designed luminosity and energy efficiency necessary for physics studies. The goal of accelerator structure design is to maximize the energy gain of the electrons while minimizing the wakefields.; The objective of this work is to develop a finite element electromagnetic field solver with parallel implementation in order to calculate the wakefields for the accelerator structures with realistic geometry and dimensions.; The physics of the problem is governed by the Maxwell's equations and the wakefields can be computed by solving the equations in frequency domain. These equations are reduced to two-dimensional with axisymmetric geometries. To solve them numerically, the partial differential equations are discretised on unstructured mesh with a mixed finite element method involving the edge elements to avoid the spurious modes. To model the structure accurately, we use the quadratic elements together with the adaptive mesh refinement. The resulting generalized matrix eigenvalue problem is subsequently solved using the shift-inverted Lanczos algorithm.; To model the accelerators in a parallel environment, domain decomposition strategy is employed where the computational domain of the accelerator structure is partitioned according to its cavities. The global data is distributed among the nodes and the numerical operations are accomplished locally with the interprocessor communications through the message passing interface (MPI). A framework for parallel implementation of the linear solvers, which constitute the most time-consuming operation in the whole program, is used to yield high parallel efficiency.; The numerical results for the NLC and JLC detuned structures with the contributions from higher bands and wall dissipation are presented. It is the first- ever direct calculation of the wakefields for the accelerators with realistic geometry and dimension. They are obtained on Intel's Paragon XP/S 150 at ORNL and compared with the other methods and the measurements.