High harmonic generation in the undulators for free electron lasers

Zhukovsky, K. V.

doi:10.1016/j.optcom.2015.04.079

Cited by 40 publications

(17 citation statements)

References 26 publications

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“…They benefit from the use of special functions [38][39][40]. The mathematical instruments, used to solve DE, generally range from a variety of integral transforms [41,42] to expansion in a series of generalized orthogonal polynomials [43] with many variables and indices [44][45][46], which arise naturally in studies of physical problems, such as the radiation and dynamics of beams of charges [47][48][49][50][51][52][53][54], heat and mass transfer [55][56][57][58][59], etc. Moreover, exponential operators and matrices are currently used also for description of such nature fundamentals as neutrino and quarks in theoretical [60][61][62][63][64][65] and in experimental [66][67][68] frameworks.…”

Section: Introductionmentioning

confidence: 99%

Operational Approach and Solutions of Hyperbolic Heat Conduction Equations

Zhukovsky

2016

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Abstract:We studied physical problems related to heat transport and the corresponding differential equations, which describe a wider range of physical processes. The operational method was employed to construct particular solutions for them. Inverse differential operators and operational exponent as well as operational definitions and operational rules for generalized orthogonal polynomials were used together with integral transforms and special functions. Examples of an electric charge in a constant electric field passing under a potential barrier and of heat diffusion were compared and explored in two dimensions. Non-Fourier heat propagation models were studied and compared with each other and with Fourier heat transfer. Exact analytical solutions for the hyperbolic heat equation and for its extensions were explored. The exact analytical solution for the Guyer-Krumhansl type heat equation was derived. Using the latter, the heat surge propagation and relaxation was studied for the Guyer-Krumhansl heat transport model, for the Cattaneo and for the Fourier models. The comparison between them was drawn. Space-time propagation of a power-exponential function and of a periodic signal, obeying the Fourier law, the hyperbolic heat equation and its extended Guyer-Krumhansl form were studied by the operational technique. The role of various terms in the equations was explored and their influence on the solutions demonstrated. The accordance of the solutions with maximum principle is discussed. The application of our theoretical study for heat propagation in thin films is considered. The examples of the relaxation of the initial laser flash, the wide heat spot, and the harmonic function are considered and solved analytically.

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Section: Introductionmentioning

confidence: 99%

Operational Approach and Solutions of Hyperbolic Heat Conduction Equations

Zhukovsky

2016

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“…Высшие гармоники более чувствительны к потерям и не идеальностям пучка и ондулятора, чем основная гармоника. В квазианалитическом описании нами использовались основные зависимости поведения коэффициентов потерь, взятые из предыдущих исследований и точных расчетов с обобщенными функциями типа Эйри и Бесселя [26,27,31,42,43]. Мы предполагаем согласованный с ондулятором пучок; исследование вопросов фокусировки находится за рамками нашей модели и может быть проделано с помощью формул из [44][45][46][47][48] или соответствующих компьютерных программ.…”

Section: аналитическая модель однопроходного каскадного лсэunclassified

Генерация Мягкого Рентгеновского Излучения В Компактном Лазере На Свободных Электронах С Умножением Гармоник

Жуковский¹

2019

Журнал Технической Физики

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Single-pass free-electron lasers (FELs) with harmonic multiplication in the X-ray range are studied theoretically with the objective of producing intense radiation with the minimum possible FEL length, beam energy, and seed laser frequency. A cascade FEL with a two-frequency undulator for electron bunching at wavelengths of higher harmonics is proposed. The dynamics of radiation power in a FEL with harmonic multiplication cascades is investigated based on a well-proven phenomenological FEL model that covers all major losses for each harmonic in each FEL cascade. The effect of the beam quality on X-ray generation in a FEL is examined. It is demonstrated that electron beams with energy spread σ_ e ≤ 0.0002 are required for efficient use of harmonics in a cascade X-ray FEL. The evolution of power of harmonics in several cascade FELs at wavelengths of ~2–3 nm with multiplication of seed harmonics at a wavelength of 13.51 nm (Mo/Si reflection peak) and 11.43 nm (MoRu/Be reflection peak) is studied. It is demonstrated that the power increases to ~1 GW at a FEL length up to 40 m. In addition, the operation of multicascade FELs with a seed F _2 excimer 157-nm UV laser and harmonics of lasers with CO_2 and C_2H_2 at 30 nm with a beam of electrons with an energy of ~0.6 GeV and a current of ~1 kА is studied. The power of the modeled X-ray radiation of these FELs at λ = 2.5 and 3.3 nm increases to ~0.5 GW at ~30 m.

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“…The method of operational solution of DE demonstrated in [7][8][9][10] is applicable to a wide spectrum of physical problems, described by linear partial differential equations (PDE), such as propagation and radiation from charged particles [11][12][13][14][15][16][17][18][19], heat diffusion [20][21][22], including processes not described by Fourier law, and others [23][24][25]. In the context of the operational approach, the operational definitions for the polynomials through the operational exponent are very useful [26].The operational exponent is also applied when describing the fundamentals of structures in nature, including elementary particles and quarks [27][28][29]; such modern mathematical instruments are also used for the theoretical study of…”

Section: Introductionmentioning

confidence: 99%

“…In the case of the two-variable Hermite polynomials, the identity (18) becomes the operational definition (8) and Appèl operator for Hermite polynomials is realized by the exponential…”

Section: Introductionmentioning

confidence: 99%