A theoretical analysis of Smith-Purcell radiation at very high energies is presented. The energy per unit frequency and solid angle is expressed in closed form as a function of the grating geometry, beam energy, and viewing angles. A certain choice of grating geometry is shown to optimize the output energy for a particular order of radiation. Scaling laws are derived for the energy emitted into all orders of radiation in the relativistic limit. It is shown that the total energy emitted into each order scales as the three-halves power of the beam voltage.

We report on experimental and theoretical investigations of a 17 GHz RF photocathode electron gun. This is the first photocathode electron gun to operate at a frequency above 2.856 GHz. The 1.5 cell, π−mode, copper cavity was tested with 50 ns pulses from a 17.150 GHz klystron amplifier built by Haimson Research Corp. A Bragg filter was used at the RF gun to reduce the reflection of parasitic modes back into the klystron. Coupling hole theory in conjunction with cold test measurements was used to determine the field profile in the RF gun. The particle in cell code MAGIC as well as coupled envelope equations were used to simulate the beam dynamics in the RF gun. With power levels of 4 MW, the on axis electric field at the cathode exceeds 300 MV/m, corresponding to an average accelerating gradient of 200 MV/m over the first half cell of the gun. Breakdown was observed at power levels above 5 MW. Electron bunches were produced by 20 µJ, 1 ps UV laser pulses impinging on the RF gun copper photocathode and were measured with a Faraday cup to have up to 0.1 nC of charge. This corresponds to a peak current of about 100 A, and a density at the cathode of 8.8 kA/cm 2 . Multiple output electron bunches were obtained for multiple laser pulses incident on the cathode. Phase scans of laser induced electron emission reveal an overall phase stability of better than ±20°, corresponding to ±3 ps synchronization of the laser pulses to the phase of the microwave field. A Browne-Buechner magnetic spectrometer indicated that the RF gun generated 1MeV electrons with a single shot rms energy spread of less than 2.5%, in good agreement with theoretical predictions.3