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Three-dimensional theory of the Smith–Purcell free-electron laser with side walls
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Image of FIG. 1.
FIG. 1.

Geometry of the grating and electron beam viewed from in front of the beam. The electron beam width is and it extends to infinity in . The side wall spacing, or grating width, is and the walls are high compared to the fundamental wavelength.

Image of FIG. 2.
FIG. 2.

Geometry of grating structure viewed from the side. The grating period is , slot depth is , and slot width is . The electrons travel in the direction.

Image of FIG. 3.
FIG. 3.

Grating dispersion curves for values of and beam line for the parameters in Table I. The dispersion curve predicted by the 2D theory is also plotted. The lowest transverse mode is well separated from the higher order modes. The group velocity of the lowest mode is negative, compared to the positive group velocity predicted by the 2D theory.

Image of FIG. 4.
FIG. 4.

Gain coefficient as a function of the beam voltage for only the lowest order transverse mode and for the exact equation. The gain is dominated by the lowest order mode.

Image of FIG. 5.
FIG. 5.

Experimental spectrum of radiation from a grating with parameters close to those in Table I. The evanescent wave is clearly observed near the predicted wavelength of .

Image of FIG. 6.
FIG. 6.

Growth rate compared with simulations by Li et al. (Ref. 17).


Generic image for table
Table I.

Grating and beam parameters used in the calculations.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Three-dimensional theory of the Smith–Purcell free-electron laser with side walls