Three dimensional simulation of high harmonic transverse optical klystron

We present the results of a three dimensional simulation code, which calculates the parameters of coherent super-radiant harmonic frequency emission by electrons which are being bunched by an external laser beam while propagating in a planar undulator. This code was written in order to simulate the TOK experiment, which is presently underway at BNL. Instead of a full numerical simulation of Maxwell's equations and the electron force equations, a semi-analytical approach is adopted. Electron trajectories are computed analytically, and the radiation fields are expanded in terms of free space eigenmodes. Phase space and energy profiles of the electron beam are incorporated by a variable space sampling according to a given distribution function, rather than via Monte Carlo simulation. Computation time of about 0.1 s/electron was achieved with the present version of the code on the IBM 3090. We present the expected radiometric parameters as a function of the electron beam parameters (emittance and energy spread), and the modulating laser beam parameters (Rayleigh length, waist position and power). Statistical averaging is carried out by weighted averaging of the initial electron moments and energy phase space distribution. This approach results in the best prediction of the expected experimental measurement of the optical parameters which can be achieved with a finite number of sampling electrons (much smaller than in the experiment), without introducing artificial noise as in the Monte Carlo approach.