Spectral properties of two-harmonic undulator radiation

Dattoli, G.; Voykov, G.

doi:10.1103/physreve.48.3030

Cited by 31 publications

(15 citation statements)

References 6 publications

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“…Such a point of view has opened a new scenario offering a wealth of analytical possibilities amenable for further generalizations of practical interest in various fields involving the theory of special functions. We have indeed mentioned laser assisted processes in strong laser fields 20 , but we should also include synchrotron radiation problems regarding the emission of electron radiation in nonconventional undulator magnets [21][22][23] . Within this last framework a significant role has been played by the so called multi-index Bessel functions 24 , whose theory can be greatly simplified by the umbral formalism discussed here.…”

Section: Symbolic Derivation Of Some Addition Theoremsmentioning

confidence: 99%

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Symbolic methods for the evaluation of sum rules of Bessel functions

Babusci

Dattoli

Górska

et al. 2013

Journal of Mathematical Physics

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The use of the umbral formalism allows a significant simplification of the derivation of sum rules involving products of special functions and polynomials. We rederive in this way known sum rules and addition theorems for Bessel functions. Furthermore, we obtain a set of new closed form sum rules involving various special polynomials and Bessel functions. The examples we consider are relevant for applications ranging from plasma physics to quantum optics.

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Section: Symbolic Derivation Of Some Addition Theoremsmentioning

confidence: 99%

“…(23) In this Appendix we prove the identity (23), used in sec. III to prove the Graf's addition theorem.…”

mentioning

confidence: 99%

Symbolic methods for the evaluation of sum rules of Bessel functions

Babusci

Dattoli

Górska

et al. 2013

Journal of Mathematical Physics

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“…It has been suggested that the ideal undulator has a perfect sinusoidal magnetic field, as with the planar (Alferov et al, 1976), helical (Alferov et al, 1976;Kincaid, 1977), elliptical (Yamamoto & Kitamura, 1987), two-harmonic (Dattoli & Voykov, 1993) and figura-8 (Tanaka & Kitamura, 1995) undulators. In this case, the spectral-angular density of undulator radiation in the far-field region involves a series of Bessel functions.…”

Section: Introductionmentioning

confidence: 99%

Shift-Scale Invariance of Electromagnetic Radiation

Smolyakov¹

2012

Electromagnetic Radiation

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“…The physics contained in the superimposed two-laser scheme can be related to that of scenarios in the freeelectron-laser context [16] that employ two-frequency wigglers [17] and biharmonic undulators [18,19], that are utilized for better control of electrodynamics and emission spectrum. In the two-laser ICS case, the amplitude of the electron's oscillatory momentum is mainly supplied from longer-wavelength laser.…”

Section: Introductionmentioning

confidence: 99%

Harmonic radiation of a relativistic nonlinear inverse Compton scattering using two laser wavelengths

Sakai

Williams

Andonian

et al. 2011

Phys. Rev. ST Accel. Beams

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The use of two different wavelength lasers in the nonlinear regime of the inverse Compton scattering interaction is proposed in order to provide a new strategy for controlling scattered photon energy distributions in the x-ray to -ray spectral region. In this nonlinear interaction, the component of the relativistic electron's trajectory driven by a longer-wavelength laser with the normalized vector potential a L $ 1 is a large oscillatory figure-8; in the proposed scenario a rapid small-amplitude oscillation induced by a shorter-wavelength laser is superimposed upon this figure-8. Thus, the electron's momentum is mainly supplied from longer-wavelength laser, while the high-frequency part of the acceleration is given by shorter-wavelength laser. In this way, the harmonics radiated at high frequency from the oscillating electron can be strongly modified by the nonlinear motion initiated by the low frequency, large a L laser resulting in the generation of the harmonics with the photon energy of 4 2 @ð! L;short þ n! L;long Þ. In this paper, the electron's kinetics in the two-wavelength laser field and the concomitant emitted radiation spectrum are examined, with numerical illustrations based on a classical Lienard-Wiechert potential formalism provided.

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Spectral properties of two-harmonic undulator radiation

Cited by 31 publications

References 6 publications

Symbolic methods for the evaluation of sum rules of Bessel functions

Symbolic methods for the evaluation of sum rules of Bessel functions

Shift-Scale Invariance of Electromagnetic Radiation

Harmonic radiation of a relativistic nonlinear inverse Compton scattering using two laser wavelengths

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