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

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## Abstract

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## 1. Introduction

## 2. Bremsstrahlung Radiation in Linearly Polarized Undulators and Emergence of GBF

## 3. Radiation Emission in Non Standard Undulator Structures and GBF

- ${\omega}_{u}$ along the x direction
- $3\phantom{\rule{0.166667em}{0ex}}{\omega}_{u}$ along y
- $2\phantom{\rule{0.166667em}{0ex}}{\omega}_{u},\phantom{\rule{0.166667em}{0ex}}6\phantom{\rule{0.166667em}{0ex}}{\omega}_{u}$ along z

## 4. GBF and Electromagnetic Processes: Concluding Remarks

## 5. Final Comments

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Permanent magnet block arrangement in undulators (the arrow denotes the direction of the magnetization vector), on axis field distribution and electron beam trajectory (see, e.g., reference [20] for further comments on the undulator field distribution).

**Figure 3.**3-D plots of ${}^{\left(3\right)}{J}_{n}(x,y)$ (

**a**) $n=0$; (

**b**) $n=1$; with the respective contour plots (

**c**) $n=0$; (

**d**) $n=1$.

**Figure 4.**(

**a**) ${J}_{n}(x,y)$ vs. y for different values of x ($n=0$), (

**b**) ${J}_{n}(x,y)$ vs. x for different values of x ($n=1$).

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**MDPI and ACS Style**

Dattoli, G.; Di Palma, E.; Licciardi, S.; Sabia, E.
Generalized Bessel Functions and Their Use in Bremsstrahlung and Multi-Photon Processes. *Symmetry* **2021**, *13*, 159.
https://doi.org/10.3390/sym13020159

**AMA Style**

Dattoli G, Di Palma E, Licciardi S, Sabia E.
Generalized Bessel Functions and Their Use in Bremsstrahlung and Multi-Photon Processes. *Symmetry*. 2021; 13(2):159.
https://doi.org/10.3390/sym13020159

**Chicago/Turabian Style**

Dattoli, Giuseppe, Emanuele Di Palma, Silvia Licciardi, and Elio Sabia.
2021. "Generalized Bessel Functions and Their Use in Bremsstrahlung and Multi-Photon Processes" *Symmetry* 13, no. 2: 159.
https://doi.org/10.3390/sym13020159