Rayleigh–Ritz based expansion method for wakefields in dielectrically lined rectangular waveguides

Highlights: • Eigenmodes of dechirpers with dielectric slabs possess analytical expressions. • The wake function in a rectangular dechirper is computed by an eigenmode expansion. • The wake function has an analytical expression. • The wake function can be effectively computed by a Python-based code. • The computation algorithm is independent of spatial discretisation. In this work, a semi-analytical method for determining wakefields in dielectrically lined rectangular waveguides is presented. This approach is based on a Rayleigh–Ritz method to analytically identify the eigenmodes of the structure, which is currently studied for the application as a so-called 'wakefield dechirper'. The electric field is subsequently determined through an eigenmode expansion, and the wakefield is calculated from the electric field. By virtue of using an analytic ansatz throughout the wakefield determination, an expression for the Green's function wakefield is found. The semi-analytical method is then benchmarked against simulations using purely numerical approaches. Compared to numerical approaches, the advantages of the presented method are the independence from any need of discretisation, the computational efficiency of the method's presented Python-based implementation and finally the opportunity to calculate a true Green's function wakefield. From this Green's function, the wake potentials of different bunch shapes can be obtained via convolution.