On the theory of some Čerenkovian effects

First measurements of the longitudinal bunch profile of a 28.5 GeV beam using coherent Smith-Purcell radiation

“…The various theoretical approaches to the solution of this problem that have been suggested over the years can be divided into two broad categories: (a) the emission process is described in terms of waves reflected by the grating surface from the evanescent waves that accompany the electron beam [7,[21][22][23] or (b) the emission is due to the acceleration of surface charges induced on the grating surface by the electrons in the bunch [3,10,[24][25][26]. A detailed description of the various theories is beyond the scope of this paper, but in all cases there is an exponential dependence of the yield on the bunch-grating spacing; this exponential factor also involves a parameter that describes the coupling efficiency between beam and grating.…”

Coherent Smith–Purcell radiation: Theories and simulations

“…Although the physical picture they proposed is basically correct, considerable effort has been devoted since then to calculating the angular distribution of SP radiation. Toraldo di Francia [8] presented an alternative model in which the evanescent electromagnetic wave accompanying the electron is diffracted by the grating into both propagating modes and evanescent grating modes. The work of van den Berg [9] provided a detailed description of the phenomenon, and established an integral equation for the electromagnetic field produced by an electron moving above an infinitely long grating.…”

Fiber optic probe of free electron evanescent fields in the optical frequency range

“…2-4 Indeed, general interest in the physics of optical evanescent fields has grown substantially in recent years, most notably in the context of "perfect/super-lenses," 5,6 optical forces, [7][8][9][10][11] and the entire field of plasmonics and photonic metamaterials. [12][13][14][15] Moving free electrons also carry exponentially decaying "evanescent" fields [16][17][18] that may interact with nanostructures in the same manner as optical evanescent fields. The limited awareness of these electron fields is mainly derived from the fact that they decay on the sub-optical-wavelength scale (except in the case of highly relativistic electrons 19,20 ), making experimental studies based on the visible/near-infrared frequency components of such fields extremely challenging.…”

“…[16][17][18] In cylindrical coordinates, the transverse and longitudinal components of this field are proportional to K 1 (xx/vc) and c À1 K 0 (xx/vc) where K 0 and K 1 are the modified Bessel functions of the second kind, x is the frequency of the electromagnetic field, x is the distance from the electron, and c is the Lorentz factor. 18 The dispersion of the field is given by x ¼ vq where q is the wave vector component in the propagation direction.…”