Spectral Form Function with Applications in Beam Physics

To describe longitudinal fine structure like microbunching within a particle beam, a classical approach is to define a bunching factor which is the Fourier transform of the particle longitudinal density distribution. Such a 1D definition of bunching factor can be generalized to a 6D spectral form function (SFF) to describe more complicated structure in phase space. The complex SFF is another complete description of beam in spectral domain and can offer complementary and valuable insight in beam dynamics study which usually invokes the real particle density distribution. The basic property and Fokker-Planck equation of the SFF is presented, along with its solution in a general coupled linear lattice. The example applications of SFF in electron storage ring physics and laser-induced microbunching are presented.