SPONTANEOUS EMISSION IN WAVE-GUIDE FREE-ELECTRON MASERS NEAR WAVE-GUIDE CUTOFF

In this work spontaneous emission is investigated in a waveguide free- electron maser, taking into account previously untreated interaction e ffects in the vicinity of the waveguide cutoff frequency. Our study is based on the exact waveguide excitation equations, formulated in the frequency domain for a single electron moving in a planar magnetostati c wiggler. An analytical solution of the amplitude of the excited wave guide mode in the frequency domain was obtained using the Green functi on technique and allows us to calculate the spectral density of the ra diated power and the time-dependent radiated field with good accuracy using a numerical inverse Fourier transform. The obtained solution sho ws that for TE-modes the spectral density of the radiated energy tends to infinity at the cutoff frequency of a lossless waveguide. The char acter of this singularity is, however, such that the total radiated en ergy is finite. The radiated electromagnetic field in the time domain has the farm of very long (of the order of tens of characteristic time s on the scale of L-w/c, where L-w is the wiggler length and c is the speed of light) pulse, lagging behind the electron, at the carrier of cutoff frequency, in addition to two finite wave packets, correspondin g to the two synchronism frequencies. The results of a numerical calcu lation of the radiated energy spectral density and of the radiated ele ctromagnetic field in the time domain are presented.