Abstract
Currently, the study of the scattering of ultrashort X-ray pulses (USPs) by various objects is an urgent task, in connection with the creation of powerful sources of USP generation. In this paper, the theory of the scattering of attosecond pulses by polyatomic structures is developed taking into account the magnetic component of USPs. It is shown that the scattering spectra depend not only on the structure of the target, but also on other characteristics of USPs. Results are presented of the calculation of the scattering spectra on various nanosystems, such as rings, groups of rings, carbon nanotubes (CNTs), and groups of co-directed CNTs (forest CNTs). The calculation results are presented in an analytical form, which allows a general analysis of the expressions. It was found that taking the magnetic component of the momentum into the scattering spectra into account leads to the generation of the second harmonic. In this case, the spectra have characteristic features and differ from the scattering spectra at the carrier frequency, which can complement ultra-high-resolution X-ray analysis. It is shown that the scattering spectra of some structures, for example, forest CNTs, have a strictly specified radiation direction and such material in the field of such USPs is non-reflective (completely black).
Highlights
In the last two decades, the generation of isolated attosecond pulses through the generation of high harmonics has provided a powerful tool for studying many important physical processes on the attosecond timescale [1]
The theory of the scattering of attosecond pulses by polyatomic structures is developed taking into account the magnetic component of ultrashort X-ray pulses (USPs)
It was found that taking the magnetic component of the momentum into the scattering spectra into account leads to the generation of the second harmonic
Summary
In the last two decades, the generation of isolated attosecond pulses through the generation of high harmonics has provided a powerful tool for studying many important physical processes on the attosecond timescale [1]. Large calculations can be avoided by expressing the average in Equation (3) in terms of the spatial density of atomic electrons ρ(r) Such an approach is well known: in [31], for example, it was used to calculate the spectra of USP scattering by a single atom. In the case of the coherent part of spectrum ∝ N2eN2a (for example, for sufficiently small ω0/c, one can obtain δN(p) = N2a, for Ne 1) This case corresponds to the scattering of USPs by electrons in atoms together. It can be seen from Equation (5) that in the general case it is impossible to separate the coherent and incoherent parts of the spectrum. At certain parameters of the USP, where the F(ω, n, n0) has a weak dependence on the direction of the n, the diffraction pattern is determined by the factor δN(p)
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