# High Repetition Rate and Coherent Free-Electron Laser in the X-Rays Range Tailored for Linear Spectroscopy

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## Abstract

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## 1. Introduction

## 2. FEL Layout and Start-To-End Simulations

#### 2.1. SASE Mode

#### 2.2. Harmonic Cascade Seeded by the Harmonics of an IR Laser Generated in Gas

#### 2.3. Harmonic Cascade Seeded by an FEL Oscillator

#### 2.4. Regenerative Amplifier

## 3. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**SASE radiation at 4.16 Å. Case (a) refers to high charge multispike self amplified spontaneous emission (SASE) regime, case (b) to low charge single spike regime. (

**Left panel**): radiation growth vs. undulator coordinate; (

**Right panels**): one shot coherence degree $\mathsf{\Gamma}$ and mutual coherence degree between two uncorrelated shots ${\mathsf{\Gamma}}_{12}$ as function of the longitudinal coordinate.

**Figure 3.**$5\times 5$ cascade seeded by HHG: FEL radiation energy vs undulator position, temporal power distribution and spectrum (in the boxes) extracted at about 40 m. Seeded cascaded fresh-bunch case. First modulator (1st Mod) with 5 cm period. Second modulator (2nd Mod) with 2.8 cm period. Radiator with 1.2 cm period. The FEL simulations have been performed with GENESIS 1.3 [35].

**Figure 4.**Segmented undulator scheme for a three-stage cascade driven by an Extreme Ultraviolet-FEL Oscillator.

**Figure 5.**Intracavity energy vs number of cycles. In the boxes: radiation amplitude and spectrum at saturation.

**Figure 6.**$5\times 5$ cascade with the seed provided by a FEL oscillator: FEL energy of fundamental and harmonics generated in the various modules are presented vs the coordinate z in the undulator. Seeded cascaded fresh-bunch case. First modulator (1st Mod) with 5 cm period. Second modulator (2nd Mod) with 2.8 cm period. Radiator with 1.2 cm period. The FEL simulations have been performed with GENESIS 1.3 [35]. In the boxes, the temporal and spectral distrubution of the pulse.

**Figure 7.**Regenerative Amplifier with three diamond mirrors and one beam splitter operating at different wavelengths.

**Figure 8.**Transfer function of an optical line made by three diamond mirrors and one beam splitter vs. the photon energy.

**Figure 9.**Intracavity radiation of the regenerative amplifier at 4.16 Å. In the boxes: power at saturation and spectrum.

Electron Beam Energy | GeV | 1.6–3.8 | rms Normalized Emittance | mm mrad | 0.3–0.5 |
---|---|---|---|---|---|

Charge | pC | 8–50 | rms relative energy spread | ${10}^{-4}$ | 2–4 |

Current | kA | 1.3–1.6 | electron beam duration | fs | 2.5–16 |

**Table 2.**Undulator parameters and radiation wavelengths for the High Harmonic Generation (HHG) seeded cascade. Electron beam energy = 2.2 GeV.

${\mathit{\lambda}}_{\mathit{w}}$ | ${\mathit{a}}_{\mathit{w}}$ | Fund | 3rd Harm | 5th Harm | |
---|---|---|---|---|---|

1st Modulator | 5 cm | 3.12 | 13.6 nm | 4.53 nm | 2.72 nm |

2nd Modulator | 2.8 cm | 1.68 | 2.72 nm | 0.906 nm | 0.544 nm |

Radiator | 1.2 cm | 0.89 | 0.544 nm |

**Table 3.**Radiation characteristics of the HHG seeded cascade. $\lambda $ is the radiation wavelength, E the radiation energy, N/shot the numberof photons per shot, N/s the average number of photons, bw the relative r.m.s. bandwidth, div means divergence, length and size are the longitudinal and transverse rms pulse dimensions. The repetition rate of the source is assumed to be 100 kHz.

$\mathit{\lambda}$ | 0.544 nm | E | 10 $\mathsf{\mu}$J |
---|---|---|---|

N/shot | ${10}^{10}$ | N/s | ${10}^{15}$ |

bw | 0.07% | length | 2–3 $\mathsf{\mu}$m |

div | 35 $\mathsf{\mu}$rad | size | 75 $\mathsf{\mu}$m |

**Table 4.**Characteristics of the seed generated by the FEL oscillator at the entrance of the first modulator. Symbols are explained in Table 3.

$\mathit{\lambda}$ | 13.6 nm | E | 50 nJ |
---|---|---|---|

N/shot | $3.4\times {10}^{9}$ | N/s | $1.7\times {10}^{15}$ |

bw | 0.15% | rms length | 2 $\mathsf{\mu}$m |

div | 85 $\mathsf{\mu}$m | size | 100 $\mathsf{\mu}$m |

**Table 5.**Characteristics of the radiation of a $5\times 5$ cascade seeded by a FEL oscillator. Symbols are explained in Table 3.

$\mathit{\lambda}$ | 5.44 Å | E | 11 $\mathsf{\mu}$J |
---|---|---|---|

N/shot | $3\times {10}^{10}$ | N/s | $1.5\times {10}^{16}$ |

bw | 0.017% | rms length | 2 $\mathsf{\mu}$m |

div | 3.6 $\mathsf{\mu}$m | size | 24 $\mathsf{\mu}$m |

**Table 6.**Radiation characteristics of the regenerative amplifier. The repetition rate of the source is 1 MHz. Symbols are explained in Table 3.

$\mathit{\lambda}$ | 4.16 Å | E | 21 $\mathsf{\mu}$J |
---|---|---|---|

N/shot | $4.4\times {10}^{10}$ | N/s | $4.4\times {10}^{16}$ |

bw | 0.4% | length | 5 $\mathsf{\mu}$m |

div | 14 $\mathsf{\mu}$rad | size | 38 $\mathsf{\mu}$m |

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**MDPI and ACS Style**

Petrillo, V.; Opromolla, M.; Bacci, A.; Drebot, I.; Ghiringhelli, G.; Petralia, A.; Puppin, E.; Conti, M.R.; Rossi, A.R.; Tagliaferri, A.;
et al. High Repetition Rate and Coherent Free-Electron Laser in the X-Rays Range Tailored for Linear Spectroscopy. *Instruments* **2019**, *3*, 47.
https://doi.org/10.3390/instruments3030047

**AMA Style**

Petrillo V, Opromolla M, Bacci A, Drebot I, Ghiringhelli G, Petralia A, Puppin E, Conti MR, Rossi AR, Tagliaferri A,
et al. High Repetition Rate and Coherent Free-Electron Laser in the X-Rays Range Tailored for Linear Spectroscopy. *Instruments*. 2019; 3(3):47.
https://doi.org/10.3390/instruments3030047

**Chicago/Turabian Style**

Petrillo, Vittoria, Michele Opromolla, Alberto Bacci, Illya Drebot, Giacomo Ghiringhelli, Alberto Petralia, Ezio Puppin, Marcello Rossetti Conti, Andrea Renato Rossi, Alberto Tagliaferri,
and et al. 2019. "High Repetition Rate and Coherent Free-Electron Laser in the X-Rays Range Tailored for Linear Spectroscopy" *Instruments* 3, no. 3: 47.
https://doi.org/10.3390/instruments3030047