Recent advances in table-top, ultrahigh intensity lasers have led to significant renewed interest in the classic problem of Thomson scattering. An important current application of these scattering processes is the generation of ultrashort-pulse-duration x rays. In this tutorial, the classical theory of nonlinear Thomson scattering of an electron in an intense laser field is presented. It is found that the orbit, and therefore its nonlinear scattering spectra, depends on the amplitude and on the phase at which the electron sees the laser electric field. Novel, simple asymptotic expansions are obtained for the spectrum of radiation that is backscattered from a laser by a counter-propagating ͑or co-propagating͒ electron. The solutions are presented in such a way that they explicitly show-at least in the single particle regime-the relative merit of using an intense laser and of an energetic electron beam in x-ray production. The close analogy with free electron laser/synchrotron source is indicated.

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The first observations and measurements are reported on suppression of the third-order intermodulation (IM3) product arising from nonlinear mixing of two drive frequencies in a klystron, by externally injecting a wave at the IM3 product frequency. Optimum amplitude and phase of the injected wave for maximum suppression are examined. Results indicate that suppression of the IM3 product by as much as 30 dB can be achieved. Experimental results compare favorably with predictions of a 1D simulation code that takes into account all kinematical and dynamical effects including charge overtaking and space charge forces.

A phase-locking model has been developed from circuit theory to qualitatively explain the various regimes observed in magnetron injection-locking experiments. The experiments utilize two continuous-wave oven magnetrons: one functions as an oscillator and the other as a driver. The model includes both magnetron-specific electronic conductance and frequency-pulling parameter. Both time and frequency domain solutions are developed from the model, allowing investigations into the growth and saturation as well as the frequency response of the output signal. This simplified model recovers qualitatively many of the phase-locking frequency characteristics observed in the experiments.