scholarly journals Generalized Bessel Functions and Their Use in Bremsstrahlung and Multi-Photon Processes

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 159
Author(s):  
Giuseppe Dattoli ◽  
Emanuele Di Palma ◽  
Silvia Licciardi ◽  
Elio Sabia
Keyword(s):  
Free Electron Laser ◽  
Spectral Properties ◽  
Bessel Functions ◽  
Relativistic Electrons ◽  
Bremsstrahlung Radiation ◽  
Pendulum Equation ◽  
Harmonic Content ◽  
Generalized Bessel Functions ◽  
Linearly Polarized ◽  
Electro Magnetic

The theory of Generalized Bessel Functions is reviewed and their application to various problems in the study of electro-magnetic processes is presented. We consider the cases of emission of bremsstrahlung radiation by ultra-relativistic electrons in linearly polarized undulators, including also exotic configurations, aimed at enhancing the harmonic content of the emitted radiation. The analysis is eventually extended to the generalization of the FEL pendulum equation to treat Free Electron Laser operating with multi-harmonic undulators. The paper aims at picking out those elements supporting the usefulness of the Generalized Bessel Functions in the elaboration of the theory underlying the study of the spectral properties of the bremsstrahlung radiation emitted by relativistic charges, along with the relevant flexibility in accounting for a large variety of apparently uncorrelated phenomenolgies, like multi-photon processes, including non linear Compton scattering.

scholarly journals Spontaneous and Stimulated Undulator Radiation in Symmetric and Asymmetric Multi-Periodic Magnetic Fields

Symmetry ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 135
Author(s):  
Konstantin Zhukovsky ◽  
Igor Fedorov
Keyword(s):  
Magnetic Fields ◽  
Free Electron ◽  
Free Electron Laser ◽  
Spectral Properties ◽  
Bessel Functions ◽  
High Harmonic ◽  
High Gain ◽  
Undulator Radiation ◽  
Integral Forms ◽  
High Harmonics

In this work, the radiation from electrons in multi-periodic undulator fields with symmetric and asymmetric harmonics was analyzed using generalized Bessel functions formalism. The asymmetric, symmetric, and anti-symmetric periodic magnetic fields with harmonics were studied in order to get the enhanced radiation of the high harmonics of undulator radiation (UR). The effect on the spontaneous and stimulated UR was explored. The exact integral forms for the Bessel coefficients were obtained for undulators with general symmetric and asymmetric field harmonics. Spectral properties of the radiation from several configurations of the undulator fields with harmonics were compared with each other. The resulting spontaneous UR spectrum and harmonic intensities were obtained analytically in the form of integrals and compared with the respective results that were obtained numerically with SPECTRA program. The dimensionless scaling parameter of a free electron laser (FEL)—the Pierce parameter (ρ)—was computed and compared for the different considered undulators. We studied the differences in the behavior of the high-gain single pass FEL harmonics and the spontaneous UR harmonics in the same undulators. The undulators with variable deflection parameter (k) were considered. The effect of the k parameter (deflection parameter for a common planar undulator) on the spontaneous UR and on the high-gain FEL radiation was explored. In this context, an experiment with variable strength undulators at FLASH 2 FEL was analyzed; the shorter saturated length in high harmonic self-seeding (HHSS) regime vs. self-amplified spontaneous emission (SASE) is explained.

scholarly journals On Subclasses of Uniformly Spiral-like Functions Associated with Generalized Bessel Functions

2019 ◽  
Vol 2019 ◽  
pp. 1-6 ◽  
Author(s):  
B. A. Frasin ◽  
Ibtisam Aldawish
Keyword(s):  
Integral Operator ◽  
Bessel Functions ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Generalized Bessel Functions ◽  
Necessary And Sufficient

The main object of this paper is to find necessary and sufficient conditions for generalized Bessel functions of first kind zup(z) to be in the classes SPp(α,β) and UCSP(α,β) of uniformly spiral-like functions and also give necessary and sufficient conditions for z(2-up(z)) to be in the above classes. Furthermore, we give necessary and sufficient conditions for I(κ,c)f to be in UCSPT(α,β) provided that the function f is in the class Rτ(A,B). Finally, we give conditions for the integral operator G(κ,c,z)=∫0z(2-up(t))dt to be in the class UCSPT(α,β). Several corollaries and consequences of the main results are also considered.

Analytical and numerical results onM-variable generalized Bessel functions

1992 ◽  
Vol 7 (2) ◽  
pp. 175-196 ◽  
Author(s):  
G. Dattoli ◽  
C. Mari ◽  
A. Torre ◽  
C. Chiccoli ◽  
S. Lorenzutta ◽  
...  
Keyword(s):  
Bessel Functions ◽  
Numerical Results ◽  
Generalized Bessel Functions

Generalized bessel functions and hermite polynomial

1993 ◽  
Vol 108 (2) ◽  
pp. 127-134
Author(s):  
B. Léauté ◽  
G. Marcilhacy ◽  
T. Melliti
Keyword(s):  
Hermite Polynomial ◽  
Bessel Functions ◽  
Generalized Bessel Functions

scholarly journals Unified integrals involving product of multivariable polynomials and generalized Bessel functions

2019 ◽  
Vol 38 (6) ◽  
pp. 73-83
Author(s):  
K. S. Nisar ◽  
D. L. Suthar ◽  
Sunil Dutt Purohit ◽  
Hafte Amsalu
Keyword(s):  
Bessel Function ◽  
Bessel Functions ◽  
General Character ◽  
Polynomial Functions ◽  
Finite Product ◽  
Generalized Bessel Function ◽  
Integral Formulas ◽  
Generalized Bessel Functions ◽  
Multivariable Polynomial ◽  
Integral Formulae

The aim of this paper is to evaluate two integral formulas involving a finite product of the generalized Bessel function of the first kind and multivariable polynomial functions which results are expressed in terms of the generalized Lauricella functions. The major results presented here are of general character and easily reducible to unique and well-known integral formulae.

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