Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia named after Patrice Lumumba (RUDN University)2686610.22363/2658-4670-2021-29-2-105-113ArticlesСтатьиResearch ArticleOn the possibility of averaging the equations of an electron motion in the intense laser radiationО возможности усреднения релятивистских уравнений движения электрона в поле мощного лазерного излученияhttps://orcid.org/0000-0003-4686-4229Milant’evVladimir P.МилантьевВ. П.

Doctor of Physical and Mathe- matical Sciences, Professor of Institute of Physical Research and Technology

milantiev-vp@rudn.ruPeoples’ Friendship University of Russia (RUDN University)Российский университет дружбы народов28062021292VOL 29, NO2 (2021)ТОМ 29, №2 (2021)10511328062021Copyright ©; 2021, Milant’ev V.P.Copyright ©; 2021, Милантьев В.П.2021Milant’ev V.P.Милантьев В.П.http://creativecommons.org/licenses/by/4.0https://journals.rudn.ru/miph/article/view/26866

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 Doppler’s 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.

Рассмотрена проблема усреднения релятивистских уравнений движения электрона в поле мощного лазерного излучения, вызванная уменьшением скорости изменения фазы волны из-за эффекта Доплера. Вследствие этого фаза может перейти из числа «быстрых» в число «медленных» переменных движения, так что усреднение по фазе становится невозможным. На основе общих принципов метода усреднения проведён анализ условий, при которых допустимо усреднение уравнений движения по «быстрой» фазе излучения. Лазерное излучение рассматривается в параксиальном приближении, в котором малым параметром является отношение сужения лазерного пучка к рэлеевской длине. Предполагается, что протяжённость импульса сопоставима с порядком сужения лазерного пучка. В этом случае необходимо учитывать поправки первого порядка к векторам поля лазерного импульса. Получен общий критерий, определяющий возможность усреднения релятивистских уравнений движения частицы в поле мощного лазерного излучения. Показано, что усреднённое описание релятивистского движения электрона возможно в случае достаточно умеренной (релятивистской) интенсивности и относительно широких лазерных пучков. Известный в литературе аналогичный критерий был получен ранее на основе численных расчётов.

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