Three-dimensional theory of the Smith–Purcell free-electron laser with side walls

Abstract

We present an analytic theory for the exponential-gain (growth) regime of a Smith-Purcell free-electron laser amplifier (oscillator), which includes the effects of transverse diffraction in the optical beam. The optical mode is guided by the electron beam, having a mode width that depends upon the gain length. For the case of a wide electron beam, the dispersion relation converges with that of the 2-D theory. When the electron beam is narrow, the conventional cubic-dispersion relation is replaced by a five-halves dispersion. The dispersive properties of the grating divide device operation into four distinct regions, two amplifier and two oscillator. The number and location of physically allowed roots changes depending on operating region. Additionally, in the narrow-beam case, new challenges arise in satisfying the boundary conditions required for operation as an oscillator

Experimental demonstration of Smith–Purcell radiation enhancement by frequency multiplication in open cavity

“…After the experiment carried out at the Dartmouth University 9 where the nonlinear dependence of the submillimeter-radiation power on the electron current was detected, another mechanism of the Smith-Purcell radiation power enhancement has been intensively studied. [10][11][12][13][14][15][16][17][18] This capability is based on the excitation of a surface eigenwave of a grating for preliminary bunching of the electron beam. The arising electron bunches can produce coherent spontaneous Smith-Purcell radiation at the harmonics of the surface-wave frequency.…”

Dispersion relation for a three-dimensional lamellar grating

“…[19] AJB proposed a 3D theory for a grating with sidewalls that leads to a different dispersion relation. In particular, it does not satisfy our Eq.…”

“…They noted that with sidewalls the transverse profile of the axial component of the electric field has a cosine form, vanishing at the sidewalls, so that it couples well to a narrow beam in the middle of the grating. Andrews, Jarvis, and Brau [19] (AJB) presented a 3D dispersion relation for a lamellar grating with sidewalls, assuming cosine profiles in the grooves, as found by Li et al They examined in detail the dispersion relation for the grating used in the experiment described in Ref. [10], and showed that the predicted modes of operation for a beam of 30 keV were quite different according to whether the 2D or their new 3D theory applied.…”

“…[23], but not in Refs. [19,20]. The case of sidewalls is then obtained by constraining the transverse wave number q to take on discrete values and adding the contribution with Àq, to produce standing waves of the form cosðqxÞ, sinðqxÞ.…”

A Dual Grating Waveguide Structure for Wakefield Acceleration at THZ

“…The grating guide is used in a variety of configurations. Improved performance from the grating waveguide has been extricated with sidewalls and dual grating structure [20][21][22]. The grating based FEL (i.e., Free Electron Laser) has been devised in two beams [23] with Bragg-gratings at the end [24] and in two-stage configuration [25].…”