A program of theory and experiments on optical guiding effects in a free electron laser (FEL) will be conducted using Columbia University's existing 2 mm-wavelength Raman FEL oscillator system. In an FEL, the electron beam is the source of energy for the amplification of the radiation field. An important development has been the discovery that the electron beam, under certain conditions, can also help confine or focus the coherent radiation. This effect, known as optical guiding, has become a subject of considerable interest recently, both in the high-gain Compton and Raman regimes. Experiments for isolating guiding effects on the electron beam will be done in the regime of small-signal exponential growth and in saturation. The theory supports the experiment by developing 2D computer codes which accurately following the growth of the EM fields along the beam in an overmoded waveguide containing a filamentary beam. Theory also will explore analytically and numerically the effect of the optical guiding on the sideband instability, and experiment can study this once the optical guiding conditions are isolated. As shown in the proposal, optical guiding should occur under conditions of long wave length and low beam energy as well as at short wavelength.
