OBSERVATION OF SMITH-PURCELL RADIATION AT 32 GHZ FROM A MULTI-CHANNEL GRATING WITH SIDEWALLS

In a demonstration experiment at 5 GHz, we found copious emission of coherent Smith-Purcell (SP) radiation at the fundamental frequency of the evanescent surface wave, when the grating had sidewalls. Reaching higher frequencies requires a reduction in the size of the grating, which leads to a considerable reduction in power. To partially compensate this, we suggested superposing several copies of the reduced grating in parallel. A test of this concept has been performed with a seven-channel grating, at a frequency near 32 GHz. The SP radiation signals were observed directly with a fast oscilloscope. Power levels were of order 5 kW, in fair agreement with three-dimensional simulations made with the code "MAGIC". INCREASE FREQUENCY BY REDUCING THE PERIOD AND WIDTH BETWEEN SIDEWALLS A demonstration experiment in the microwave domain showed that a Smith-Purcell (SP) free electron laser (FEL), with conducting sidewalls placed at the ends of the grating's grooves, emitted intense radiation at the frequency of the surface wave on the grating [1]. In single shot operation, the ratio of emitted power to beam power exceeded 10 %. An earlier experiment, on a grating without sidewalls [2], had demonstrated emission of coherent SP radiation at the second harmonic of the surface wave. That experiment confirmed the scenario proposed in the two-dimensional (2-D) model of Andrews and Brau [3]. But the efficiency was only of order 0.1 %. In the presence of sidewalls the dispersion relation for the grating surface wave is modified [4]. In particular, the intersection of the beam line with the new dispersion relation may occur at an allowed SP frequency, which can't happen in the 2-D theory of Reference [3]. Since the beam bunching at the fundamental frequency is typically must greater than that on harmonics, the emission at the fundamental frequency is much stronger. Thus the use of sidewalls greatly increases the power. Of course, to be of practical interest, it is necessary to reach much higher frequencies, i.e., mm wavelength or less. The well-known SP relation is [5], (1/ cos )/ | n | SP L , where denotes the wavelength, L the grating period, n the order of diffraction, SP the angle with respect to the beam, and the relative velocity of the electron. In order to reach shorter wavelengths, it suffices to reduce the grating period. However, the component of the evanescent surface wave in resonance with the beam only extends to a height proportional to the wavelength. In order to reach high frequencies, the beam must closely approach the grating surface. If the grating profile is preserved (groove-depth/period and groove-width/period constant), the 2D dispersion relation of Andrews and Brau in the dimensionless variables is unchanged. The scale reduction doesn’t require a reduction in the overall size of the grating, although the task of propagating an intense and wide sheet beam at tiny distances above the grating would certainly be difficult. For the grating with sidewalls, the distance between sidewalls, w, must undergo the same reduction in scale as the period L. This rapidly leads to long thin gratings when the frequency is increased. Furthermore, our experiment requires an intense (0.5 T) longitudinal magnetic field to control the beam. At the portion of the beam nearest the grating, the image charges produce a moderately strong vertical electric field (a few kV/cm), which, combined with the magnetic field, generates a transverse E B drift. If the number of periods is too great, most of the electrons will drift into the sidewalls. If the radiated intensity is proportional to the total surface of the grating, a grating with sidewalls will suffer a power reduction proportional to the square of the scale factor. At FEL 2013 two of the authors suggested that it might be possible to superpose laterally N copies of the N-fold reduced gratings [6]. The beam used in the full-scale experiment would continue in use, except that it would be positioned to be flush with the grating top, and of 1 mm thickness. The hope was that the overall power reduction would be only 1/N, instead of 1/N. In support of this hypothesis, several simulations of multi-channel gratings were performed with the three-dimensional (3D) particlein-cell code “MAGIC” [7]. These simulations, made with 2, 4, 6, 8 and 10 channels, indicated that the radiation at the bunching frequency (N times the original bunching frequency) occurred at the same SP angle, which was approximately 140°. On the upstream wall of the simulation volume, the azimuthal distribution grew more concentrated around the vertical direction with increasing N. A simple analysis using the theory of antenna arrays was proposed to explain this tendency. It indicated that the width of the azimuthal distribution would decrease as 1/N, as would the radiated power in the principal lobe These results depend crucially on the existence of some coherence among the various channels. In the antenna theory this is assumed, but in the simulations, it is seen to be only a fair approximation. Although the simulated fields from each channel merge smoothly into the observed radiation pattern, there is no reason to expect this to occur in practice. It then becomes necessary to TUP036 Proceedings of FEL2014, Basel, Switzerland ISBN 978-3-95450-133-5 470 C op yr ig ht © 20 14 C C -B Y3. 0 an d by th e re sp ec tiv e au th or s Advanced, Alternative and Compact Concepts confirm that enough coherence takes place to produce a well-collimated radiation pattern. To test this, we carried out an experiment on a seven-channel grating with sidewalls at a frequency of approximately 32 GHz. DESCRIPTION OF THE EXPERIMENT Our previous work at frequencies of order 5 GHz used standard microwave detectors and oscilloscopes that were available. To reach higher frequency, the possibility of using a 33 GHz bandwidth oscilloscope (DSA73304) suggested dimensioning the experiment to produce radiation near 32 GHz. The dimensions of our previous and new gratings are shown in the Table. Table 1: Parameters of the Experiment Parameters Original grating 7-channel grating Peak Voltage 60-120 kV 60-120 kV Current 10-40 A 10-40 A Pulse duration FWHM 300 ns 300 ns Beam thickness 1 mm 1-2 mm Beam height 0.5 mm 0-2 mm Beam width 3.5 cm 5.2 cm Period L 2 cm 3.3 mm Groove depth H 1 cm 1.65 mm Groove width A 1 cm 1.65 mm Channel width w 4 cm 6.6 mm Number of periods 20 40 Magnetic field 1 T 0.5 T The dispersion relation (DR) for the grating is displayed in Fig. 1, along with the 2-D DR of Andrews and Brau. For beam energy of 80 keV, the operating point is at 33.2 GHz. The corresponding SP angle is 145°. 0 50