Spikes and Solitary Waves in the Free-Electron Laser at Columbia University.

Experimental and numerical studies of spiking have been carried out with the Columbia FEL operated at a frequency of 24GHz. We present real time measurement of the FEL radiation power with high resolution taken by a transient digitizer. The data shows high power spikes occurring randomly or in a sequence, its period or spacing not related to the radiation round trip time in the laser resonator. The spike width is also measured indirectly with an auto-correlation technique using a Young's double -slit apparatus. The average spike width is found to be 450 +/- 100 psec. A simulation code has been used to design our microwave FEL. The slippage of the FEL is varied by changing the diameter of the drift tube (waveguide); the slippage is zero when the electron axial speed equals the wave group velocity. Two drift tubes (DT) of different sizes have been used in the experiment: for a 24mm diameter DT, the slippage is about 300psec; for a 17mm DT, the slippage is zero (at 23GHz) to about 60psec across the frequency bands of emitted radiation. Measurements of the FEL spectrum are reported, and at zero slippage, there are no sidebands. Spiking was observed with or without slippage. A Ginzburg-Landau equation (GLE) solitary wave theory is extended to include the space-charge effect and the 2D cylindrical waveguide for our microwave Raman FEL. Numerical simulations have been carried out to study the evolution of the radiation field from different initial conditions. For certain initial conditions, solitary wave solutions are found and their features are compared with the experimentally observed spikes. The GLE also acts like a bandwidth filter, in that initial noise input can evolve into spike pulses that resemble the experimental observations. A simple model is set up to study the effect of the electron beam current fluctuations. Small signal pulses can be generated by the current irregularities, and some of these pulses resemble the analytic solutions of the GLE and proceed to become solitary waves. Thus it is possible for the current fluctuation to initiate solitary spiking pulses.