|TUP023||Modeling CSR in a Vacuum Chamber by Partial Fourier Analysis and the Discontinuous Galerkin Method||419|
Funding: Work supported by DOE contracts DE-FG-99ER41104 and DE-AC03-76SF00515.
We continue our study of CSR* from a bunch on an arbitrary curved orbit in a plane, which used a Fourier transform in s-ct. The vacuum chamber has rectangular cross section with possibly varying horizontal width. We use the slowly varying amplitude approximation, and invoke a Fourier expansion in the vertical coordinate y, which meets the boundary conditions on the top and bottom plates and makes contact with the Bessel equation of the frequency domain treatment. The fields are defined by a PDE in s and x, first order in s, which is discretized in x by finite differences (FD) or the discontinuous Galerkin method (DG). We compare results of FD and DG, and also compare to our earlier calculations in 3D (paraxial) which did not use the Fourier series in y*,**. This approach provides more transparency in the physical description, and when only a few y-modes are needed, provides a large reduction in computation time.
* See FEL13 Proceedings MOPSO06: http://accelconf.web.cern.ch/AccelConf/FEL2013/papers/mopso06.pdf
** See PRST-AB 7 054403 (2004) and Jpn. J. Appl. Phys. 51 016401 (2012).