The inverse Smith-Purcell effect is a candidate for laser-driven hnacs utilizing the interaction between laser light and an electron beam traveling just in front of a metallic grating. We have performed experiments to study electron energy spread as a function of electron beam position above the grating. A submillimeter wave laser (CH,F, 496 pm) is used as a driving source. It is found that the energy spread characteristics show exponential decay of the interaction strength (field intensity) in the direction perpendicular to the grating surface, as a classical theory on the effect predicts.
We show that near a simple focus-focus value in a Liouville integrable Hamiltonian system with two degrees of freedom lines of locally constant rotation number in the image of the energy-momentum map are spirals determined by the eigenvalue of the equilibrium. From this representation of the rotation number we derive that the twist condition for the isoenergetic KAM condition vanishes on a curve in the image of the energy-momentum map that is transversal to the line of constant energy. In contrast to this, we also show that the frequency map is non-degenerate for every point in a neighbourhood of a simple focus-focus point.
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