UNM, Albuquerque, New Mexico, USA
BNL, Upton, Long Island, New York, USA
In our self-consistent algorithm for calculating 2D CSR effects we reduce the field calculation to a 2D integral over the 2D charge and current densities of the bunch and their time history. Our code VM3@A (Vlasov-Maxwell Monte-carlo Method @ Albuquerque) implements this in a time stepping algorithm as discussed in PRST-AB 12, 080704 (2009). A major expense is the integration over history at each time step. By going to Fourier space the 2D integral is reduced to a 1D convolution over history. This may on its own have a computational advantage, however, using the kernel compression technique of Alpert, Greengard and Hagstrom [1, 2], we approximate the convolution kernel by a sum of exponentials. This allows a time step to be taken using information only from the previous time step, thus eliminating the integral over history. Of course 2D Fourier transforms must be calculated at each step, these can be done with an FFT (or NFFT). We discuss the flop count for the two approaches. In addition we implement this as an option in VM3@A and compare efficiencies of our new and old approaches in the context of a bunch compressor system for the LCLS.
[1] SIAM J. Numer. Anal. 37(2000) 1138. See also PhD thesis at http://web.njit.edu/~jiang/pub.html
[2] S. R. Lau, J. Math. Phys. 46, 102503, (2005). Supported by DE-FG02-99ER41104
