Various approaches to electromagnetic field simulations for RF cavities

In the Superconducting Proton Linac (SPL) cavity, it is very important to calculate the eigenmodes precisely, because many higher order modes (HOMs) can lead to particle beam instabilities. We used and compared three different ways to calculate the eigenmodes in the SPL cavity: field simulation with hexahedron mesh in time domain, field simulation with hexahedron mesh in frequency domain and field simulation with tetrahedral mesh and higher order curvilinear elements. In this paper the principles of the three numerical methods will be introduced and compared. Finally the calculated results will be presented