# Electron Beam Brightness and Undulator Radiation Brilliance for a Laser Plasma Acceleration Based Free Electron Laser

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Issues of LPA Based FEL

#### 2.1. Electron Beam Divergence Handling

#### 2.2. Energy Spread Handling

## 3. LPA Based Undulator Radiation

#### 3.1. Institute fur Optik und Quantenelektronik

#### 3.2. Max-Planck-Institut fur Quantenoptik

#### 3.3. Laboratoire d’Optique Appliquée

#### 3.4. SUPA, Department of Physics, University of Strathclyde

#### 3.5. COXINEL Experiment

#### 3.6. LUX at CFEL

## 4. Electron Beam Characteristics in the COXINEL Line

#### 4.1. Transport

#### 4.2. Baseline Reference Case

#### 4.3. Electron Beam Brightness

## 5. Undulator Radiation Characteristics

#### 5.1. Homogeneous Broadening

#### 5.2. Inhomogeneous Broadening

#### 5.3. Photon Beam Flux and Brilliance

## 6. FEL Evaluation

${a}_{1}$ = 0.45 ${a}_{6}$ = 2 ${a}_{11}$ = 0.95 ${a}_{16}$ = 1140 | ${a}_{2}$ = 0.57 ${a}_{7}$ = 0.35 ${a}_{12}$ = 3 ${a}_{17}$ = 2.2 | ${a}_{3}$ = 0.55 ${a}_{8}$ = 2.9 ${a}_{13}$ = 5.4 ${a}_{18}$ = 2.9 | ${a}_{4}$ = 1.6 ${a}_{9}$ = 2.4 ${a}_{14}$ = 0.7 ${a}_{19}$ = 3.2 | ${a}_{5}$ = 3 ${a}_{10}$ = 51 ${a}_{15}$ = 1.9 |

## 7. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**COXINEL beam line starting with the laser hutch (dark grey), gas jet (blue), a triplet of quadrupoles (grey), four dipoles (red), another set of quadrupoles (blue), undulator (purple) and a dipole dump (red).

**Figure 2.**SRW simulations of the spectral flux using the beam parameters of Table 3 for the total beam (blue) and slice beam (red). Window aperture of 1 mm x 1 mm placed at a distance 10 m from the center of the undulator. ${K}_{u}$ = 2.

**Figure 3.**Free Electron Laser (FEL) power emitted after 2 m long undulator section as the magnification ${R}_{11}$ and chicane strength ${R}_{56}$ vary.

**Table 1.**Laser and undulator characteristics used for the experiment, alongside the radiation quality produced. I the laser intensity, ${\lambda}_{L}$ the laser wavelength, E energy of the produced electron, ${\lambda}_{u}$ the undulator period, ${N}_{u}$ undulator number of periods, ${K}_{u}$ the deflection parameter, $\lambda $ the undulator radiation wavelength, $\Delta \lambda /\lambda $ the relative bandwidth, $\mathfrak{B}$ the radiation brilliance.

LPA System | Undulator | Radiation | |||||||
---|---|---|---|---|---|---|---|---|---|

Parameter | $\mathit{I}$ | ${\mathit{\lambda}}_{\mathit{L}}$ | $\mathit{E}$ | ${\mathit{\lambda}}_{\mathit{u}}$ | ${\mathit{N}}_{\mathit{u}}$ | ${\mathit{K}}_{\mathit{u}}$ | $\mathit{\lambda}$ | $\Delta \mathit{\lambda}/\mathit{\lambda}$ | $\mathfrak{B}$ |

Unit | W·cm${}^{-\mathbf{2}}$ | nm | MeV | mm | nm | % | ph/s/mm${}^{\mathbf{2}}$/mrad${}^{\mathbf{2}}$/0.1%bw | ||

[9] | 5 × 10${}^{18}$ | 740 | 65 | 20 | 50 | 0.6 | 740 | 7.4 | 6.5 × 10${}^{16}$ |

[10] | - | - | 210 | 5 | 60 | 0.55 | 18 | 30 | 1.3 × 10${}^{17}$ |

[11] | - | 800 | 120 | 18 | 30 | 1 | 230-440 | 18 | - |

[12] | 2 × 10${}^{18}$ | 800 | 105 | - | 100 | 0.38 | 160-220 | 16 | 1 × 10${}^{18}$ |

**Table 2.**COXINEL magnets relevant parameters. The three values for PMQs are for each PMQ of the triplet in the beam propagation order.

Unit | Value | ||
---|---|---|---|

Permanent magnet quadrupoles | |||

Magnetic length | mm | 40.7; 44.7; 26 | |

Minimum gradient | T/m | 98; −100; 90 | |

Maximum gradient | T/m | 181; −184; 165 | |

Bore radius | mm | 4 | |

Chicane dipoles | |||

Magnetic length | mm | 208.33 | |

Integrated field | T·mm | 130 | |

Maximum ${R}_{56}$ | mm | 32 | |

Maximum field | T | 0.53 | |

Electro magnet quadrupoles | |||

Magnetic length | mm | 213.3 | |

Maximum gradient | T/m | 20 | |

Bore radius | mm | 12 | |

Steerers | |||

Maximum integrated field | G.m | 38 | |

Undulator | |||

Period | mm | 18.16 | |

Number of periods | - | 107 | |

Minimum gap | mm | 4.5 | |

Maximum field | T | 1.2 |

**Table 3.**Baseline reference case parameters at the generation point in the gas jet and at the undulator center for ${R}_{56}$ = 0.4 mm, ${R}_{11}$ = 10 and ${R}_{126}$ = −4.4.

Parameters | Symbol | Source | Undulator | Unit | |
---|---|---|---|---|---|

Total | Slice | ||||

Energy | E | 200 | 200 | 200 | MeV |

Normalized emittance | ${\epsilon}_{N}$ | 1 | 2 | 1.13 | $\mathsf{\pi}$ mm·mrad |

Effective emittance | ${\epsilon}_{eff}$ | 2.6 | 5 | 2.8 | nm |

Divergence (rms) | ${\sigma}_{x,z}^{\prime}$ | 1 | 0.1 | 0.1 | mrad |

Beam size (rms) | ${\sigma}_{x,z}$ | 2.6 | 50 | 30 | $\mathsf{\mu}$m |

Bunch length (rms) | ${\sigma}_{l}$ | 1 | 4.3 | - | $\mathsf{\mu}$m |

Energy spread (rms) | ${\sigma}_{\gamma -slice}$ | 1 | 1 | 0.24 | % |

Total charge | Q | 34 | 34 | - | pC |

Current | ${I}_{b}$ | 4.3 | 1 | 1 | kA |

**Table 4.**FEL performance as the magnification of the beam (source to undulator center) and chicane strength are varied. ${L}_{g}$ the FEL gain length, ${L}_{sat}$ the FEL saturation length, ${P}_{sat}$ the saturation power.

Input | Beam Parameters | FEL Perfomance | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

${\mathit{R}}_{\mathbf{11}}$ | ${\mathit{R}}_{\mathbf{126}}$ | ${\mathit{R}}_{\mathbf{56}}$ | ${\mathit{\sigma}}_{\mathit{L}}$ | ${\mathit{\sigma}}_{\mathit{\gamma}}$ | ${\mathit{\sigma}}_{\mathit{x}}$ | ${\mathit{\sigma}}_{\mathit{x}}^{\prime}$ | ${\mathit{I}}_{\mathit{b}}$ | ${\mathit{L}}_{\mathit{g}}$ | ${\mathit{P}}_{\mathit{COX}}$ | ${\mathit{L}}_{\mathit{sat}}$ | ${\mathit{P}}_{\mathit{sat}}$ |

mm | $\mathsf{\mu}$m | % | $\mathsf{\mu}$m | $\mathsf{\mu}$rad | kA | m | MW | m | MW | ||

5 | −9.1 | 0.4 | 4.3 | 0.24 | 25.6 | 200 | 1 | 0.14 | 3 | 2.8 | 978 |

10 | −4.5 | 0.4 | 4.3 | 0.24 | 28.2 | 100 | 1 | 0.12 | 17 | 2.5 | 1350 |

15 | −3 | 0.4 | 4.3 | 0.24 | 39.7 | 66.7 | 1 | 0.14 | 1 | 3.1 | 1188 |

20 | −2.3 | 0.4 | 4.3 | 0.24 | 52.3 | 50 | 1 | 0.17 | 0 | 3.7 | 1011 |

30 | −1.5 | 0.4 | 4.3 | 0.24 | 78.1 | 33.3 | 1 | 0.23 | 0 | 5 | 737 |

10 | 0 | 0 | 1.6 | 1 | 26 | 100 | 2.8 | 0.17 | 0.2 | 3.5 | 1198 |

10 | −1.1 | 0.1 | 1.9 | 0.71 | 27.2 | 100 | 2.3 | 0.13 | 8 | 2.7 | 1938 |

10 | −2.3 | 0.2 | 2.5 | 0.45 | 27.9 | 100 | 1.7 | 0.11 | 70 | 2.4 | 2136 |

10 | −9.1 | 0.8 | 8.2 | 0.12 | 28.3 | 100 | 0.5 | 0.15 | 0.5 | 3 | 583 |

10 | −11.4 | 1 | 10.1 | 0.1 | 28.3 | 100 | 0.4 | 0.16 | 0.1 | 3.3 | 427 |

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**MDPI and ACS Style**

Ghaith, A.; Loulergue, A.; Oumbarek, D.; Marcouillé, O.; Valléau, M.; Labat, M.; Corde, S.; Couprie, M.-E.
Electron Beam Brightness and Undulator Radiation Brilliance for a Laser Plasma Acceleration Based Free Electron Laser. *Instruments* **2020**, *4*, 1.
https://doi.org/10.3390/instruments4010001

**AMA Style**

Ghaith A, Loulergue A, Oumbarek D, Marcouillé O, Valléau M, Labat M, Corde S, Couprie M-E.
Electron Beam Brightness and Undulator Radiation Brilliance for a Laser Plasma Acceleration Based Free Electron Laser. *Instruments*. 2020; 4(1):1.
https://doi.org/10.3390/instruments4010001

**Chicago/Turabian Style**

Ghaith, Amin, Alexandre Loulergue, Driss Oumbarek, Olivier Marcouillé, Mathieu Valléau, Marie Labat, Sebastien Corde, and Marie-Emmanuelle Couprie.
2020. "Electron Beam Brightness and Undulator Radiation Brilliance for a Laser Plasma Acceleration Based Free Electron Laser" *Instruments* 4, no. 1: 1.
https://doi.org/10.3390/instruments4010001