On the possibility of averaging the equations of an electron motion in the intense laser radiation

The problem of averaging of the relativistic motion equations of electron in the intense laser radiation, caused by the decreasing of the rate of wave phase change due to the Dopplers effect, is considered. As a result the phase can go from the fast to slow variables of the motion, so averaging over the phase becomes impossible. An analysis is presented of the conditions which are necessary for averaging of the relativistic equations of motion over the fast phase of the intense laser radiation on the base of the general principles of the averaging method. Laser radiation is considered in the paraxial approximation, where the ratio of the laser beam waist to the Rayleigh length is accepted as a small parameter. It is supposed that the laser pulse duration is of the order if the laser beam waist. In this case first-order corrections to the vectors of the laser pulse field should be taken into account. The general criterion for the possibility of the averaging of the relativistic motion equations of electron in the intense laser radiation is obtained. It is shown that an averaged description of the relativistic motion of an electron is possible in the case of a fairly moderate (relativistic) intensity and relatively wide laser beams. The known in the literature analogical criterion has been obtained earlier on the base of the numerical results.

MATHEMATICAL MODELING OF ENERGY SPECTRA FORMED AT ACCELERATING THE ELECTRONS BY RELATIVISTIC INTENSIVE GAUSSIAN AND LAGUERRE LASER PULSES

A mathematical model is constructed that describes the propagation of laser pulses in vacuum, taking into account the corrections due to their finite duration. On its basis, using Newton relativistic equations with the corresponding Lorentz force, the energy spectra of an ensemble of electrons are simulated by relativistically intense laser radiation. The characteristics of these spectra are studied for the cases of Gaussian and Laguerre optical pulses. Electronic spectra in the fixed angular ranges are localized around the relativistic maxima in the case of Gaussian pulses, but are substantially non-monoenergetic in the case of Laguerre pulses.

Generation of high-order harmonics and attosecond pulses

The interaction of atoms with intense laser radiation leads to the generation of high-order harmonics of the laser field. In the time domain, this corresponds to a train of pulses in the extreme ultraviolet range and with attosecond duration. The first section introduces the physics of high-order harmonic generation and attosecond pulses on the single atom level while the second section discusses phase matching and propagation effects. The attosecond time scale is that of the electron motion in atoms and molecules. Attosecond light pulses are used to study, for example, the dynamics of atomic or molecular photoionization. The third section will present an interferometric method developed for measuring attosecond pulses and discuss some of the applications, in particular concerning photoionization dynamics.