CALCULATION OF THE ANGULAR SPECTRUM OF THE COHERENT HARMONICS RADIATED IN THE FREE ELECTRON LASER

WE PROPOSE TO INVESTIGATE THE MEANS FOR REDUCING THE HARMONIC POWER RADIATED BY THE FEL. THIS REQUIRES FIRST AN ANALYTIC FORMULATION OF THE ANGULAR AND SPECTRAL DEPENDENCE OF THE INTENSITY FOR THE CONSTANT PERIOD AND TAPERED UNDULATORS, BOTH IN THE LINEAR POLARIZED AND THE CIRCULAR POLARIZED CONFIGURATIONS. WE PROPOSE TO PERFORM THIS CALCULATION IN THE PHASE I EFFORT AND TO GENERATE EXPRESSIONS WHICH RELATE THE EMITTED INTENSITIES TO THE LASER INTENSITY AT THE FUNDAMENTAL. THE ANALYTIC WORK PROVIDES THE FOUNDATION FOR THE CONSTRUCTION OF A NUMERICAL CODE IN THE PHASE II EFFORT WHICH WOULD ALLOW US TO CALCULATE THE HARMONIC POWER PRODUCED IN THE FEL SYSTEMS NOW UNDER CONSTRUCTION AT BOEING AND LIVERMORE, AND TO ASSESS THE PERFORMANCE OF THE PROPOSED TECHNIQUES FOR REDUCING THE HARMONIC POWER.