Simulation of Coherent Smith-Purcell Radiation

Summary form only given. Incoherent Smith-Purcell (SP) radiation was discovered in the 50´s. It arises when an electron beam passes above a conducting grating of period L. For a given beam velocity (v=betac), this emission occurs at all angles with a wavelength given by the following diffraction formula lambda=L/n(1/beta-cos thetas). Today, there is a revival of interest in studying table-top SP sources, particularly in the THz domain where medical applications are emerging. Such a source should have a reasonable level of power which requires a coherent process of SP emission. We have studied numerically a SP configuration by using the particle-in-cell code MAGIC in a 2D-cartesian geometry. Our simulations, which are performed in the GHz regime, show strong electron beam bunching associated with highly directional coherent SP emission. This is due to the excitation of an electromagnetic wave in the grating region which is evanescent in the direction perpendicular to the beam and which propagates forward but has negative group velocity. The frequency of this wave cannot match any wavelength given by the above relation; its role is to strongly bunch the beam. The resulting modulated current contains many harmonics of this evanescent mode of the grating and these can satisfy the SP relationship for particular angles. Furthermore, we observe that the SP gain is proportional to the cube root of the beam current, in agreement with previous theoretical studies by Brau and co-workers