# Compact LWFA-Based Extreme Ultraviolet Free Electron Laser: Design Constraints

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Main Constraints for a Compact FEL

## 3. Laser–Plasma Acceleration for EUV-FEL

## 4. Electron Beam Transport for EUV-FEL

## 5. EUV-FEL Regime

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Schematic diagram representing proposed beamline. Here, ${P}_{1}$ and ${P}_{2}$ are permanent quadrupole magnets, ${Q}_{1}$–${Q}_{8}$ are electromagnetic quadrupoles, ${C}_{1-2}$ is a pair of horizontal and vertical collimators, ${S}_{1}$–${S}_{5}$ are pairs of steering magnets (vertical and horizontal) and ${D}_{1}$–${D}_{4}$ are dipole magnets of the decompressor chicane.

**Figure 2.**Simulated electron beam horizontal and vertical envelopes (top) and beam losses (bottom) along the beamline. Arrows on the bottom plot show the position of the momentum filter collimator (${C}_{MF}$) and collimator before the undulator entrance (${C}_{U}$). Parameters: electron energy is 350 MeV, decompressor bending angle is 0.35 deg, initial bunch charge is 45 pC. The center of the single-unit undulator is located at 15 m from the source.

**Figure 3.**FWHM bunch length (orange) and slice RMS energy spread (blue) as a function of the decompressor bending angle. The solid lines represent the case for the bunch charge of 35 pC. Shaded areas represent the bunch charge variation in the range of (25–45) pC. The initial projected RMS energy spread is equal to 0.5%.

**Figure 4.**Simulated transverse and longitudinal phase space projections after each beamline section: after the source (

**a**–

**c**), after the capture block (

**d**–

**f**), after the momentum filter (

**g**–

**i**), after the decompressor (

**j**–

**l**) and in the middle of the undulator (

**m**–

**o**).

**Figure 5.**Photon pulse energy amplification for different projected energy spread in the case of the optimized decompressor angle.

**Figure 6.**Flux density in units of number of photons/pulse/mm${}^{2}$ per the energy bandwidth of 0.1% without (solid line) and with external seeding (dashed line).

Parameter | Symbol | Units | Value | |
---|---|---|---|---|

Undulator parameters | ||||

Period | ${\lambda}_{u}$ | mm | 15 | 15 |

Gap | ${g}_{u}$ | mm | 4 | 7 |

Peak magnetic field | ${B}_{0}$ | T | 1 | 0.54 |

Undulator parameter | ${K}_{0}$ | – | 1.4 | 0.75 |

LWFA-based electron beam parameters | ||||

Energy | ${W}_{k}$ | MeV | 350 | 350 |

RMS emittance (slice) | ${\epsilon}_{n}$ | $\pi $ mm mrad | <${\epsilon}_{coh,n}$ | <${\epsilon}_{coh,n}$ |

RMS beam size in undulator | <${\sigma}_{x,y}$> | $\mathsf{\mu}$m | ∼25 | ∼20 |

Energy spread (slice) | ${\sigma}_{\Delta \gamma /\gamma}$ | % | 0.25 | 0.25 |

RMS bunch length | ${\sigma}_{z}$ | $\mathsf{\mu}$m | 1 | 1 |

Total bunch charge | Q | pC | 25 | 35 |

Peak current | ${I}_{p}$ | kA | 3 | 4.2 |

LWFA-based FEL parameters | ||||

Photon radiation wavelength | ${\lambda}_{ph,1}$ | nm | 31.6 | 20.4 |

Photon radiation energy | ${E}_{ph,1}$ | eV | 39 | 60.5 |

Coherent RMS emittance | ${\epsilon}_{coh,n}$ | $\pi $ mm mrad | 1.7 | 1.2 |

1D Pierce parameter | ${\rho}_{1D}$ | – | 0.0058 | 0.0065 |

1D gain length | ${L}_{g,1D}$ | m | 0.12 | 0.1 |

1D coherence length | ${L}_{coh,1D}$ | $\mathsf{\mu}$m | 0.4 | 0.25 |

Total number of photons at saturation | ${N}_{photons}$ | – | 6.2 × 10${}^{12}$ | 3.3 × 10${}^{12}$ |

Relative FWHM frequency bandwidth | $\delta {\lambda}_{ph,1}/{\lambda}_{ph,1}$ | % | 1.2 | 1.3 |

Photon peak brilliance (0.1%BW) | ${B}_{ph}$ | ph/pulse/mm${}^{2}$/mrad${}^{2}$ | 2.6 × 10${}^{29}$ | 3.4 × 10${}^{29}$ |

1D peak power at saturation | ${P}_{ph,1D}$ | GW | 5.4 | 5.2 |

3D gain length | ${L}_{g,3D}$ | m | 0.18 | 0.18 |

3D total saturation length | ${L}_{sat,3D}$ | m | ∼3.5 | ∼3.5 |

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**MDPI and ACS Style**

Molodozhentsev, A.Y.; Kruchinin, K.O. Compact LWFA-Based Extreme Ultraviolet Free Electron Laser: Design Constraints. *Instruments* **2022**, *6*, 4.
https://doi.org/10.3390/instruments6010004

**AMA Style**

Molodozhentsev AY, Kruchinin KO. Compact LWFA-Based Extreme Ultraviolet Free Electron Laser: Design Constraints. *Instruments*. 2022; 6(1):4.
https://doi.org/10.3390/instruments6010004

**Chicago/Turabian Style**

Molodozhentsev, Alexander Yu., and Konstantin O. Kruchinin. 2022. "Compact LWFA-Based Extreme Ultraviolet Free Electron Laser: Design Constraints" *Instruments* 6, no. 1: 4.
https://doi.org/10.3390/instruments6010004