Photoelectron-counting distributions are obtained for stochastic light that is caused to scintillate by passage through a random medium. The result is applied specifically to transmission of amplitude-stabilized radiation, with and without independent additive background, and of chaotic radiation, through the turbulent atmosphere. The counting distribution is found to broaden markedly and its peak occurs at decreasing count numbers for increasing turbulence. The cases studied here are of particular interest for low-level direct optical communications and radar using single-mode lasers, multimode lasers, thermal sources, and scattering targets. The results are obtained by extending the usual formulation of photoelectron counting; a product of two random variables, the source intensity and the effect of the turbulent medium, rather than the usual single stochastic irradiance, is considered. Plots of the counting distributions for various degrees of turbulence and for several signal-to-noise ratios are presented. A possible explanation is given for the observed decrease of the log-amplitude variance to values below the saturation value in long path length and high turbulence experiments.

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Magnetostatic wiggler fields x coskz +y" sinkz, commonly used to model the undulators of free-electron lasers, violate Maxwell's equations and are "unrealizable. " Realizable wigglers that approximate the unrealizable ones near the axis have a radial variation and an axial field component, both of which affect electron motion. Exact helical equilibrium orbits are given for relativistic electrons in a combined uniform guide field and realizable wiggler, in cylindrical geometry. The parameter ka that measures the size of the helix also measures the imparted quiver motion, on which the gain of the laser depends. Hence, wigglers that impart substantial quiver motion necessarily have electrons far from the axis, for which the unrealizable wiggler model is not valid, A linearized stability analysis shows that the equilibrium helical orbits are either strongly unstable or else exhibit a secular growth, linear in time.The trajectory of an electron that starts from given position and velocity in combined guide field and wiggler is also found from the perturbation analysis, with corrections for realizability and for harmonics of practical wigglers, such as a bifilar winding. Although the helical orbits are either strongly or weakly unstable, a class of nonhelical bounded orbits is found when the secular behavior is suppressed.

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