# Compression of Ultra-High Brightness Beams for a Compact X-ray Free-Electron Laser

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## Abstract

**:**

## 1. Introduction

## 2. A Design for a Compact X-ray Free-Electron Laser

#### 2.1. Electron Source

#### 2.2. XFEL Parameters and Performance

#### 2.3. Summary of Beamline Layout

## 3. First Compression Stage

#### 3.1. Design and Longitudinal Dynamics

#### 3.2. Emittance Growth in Single Chicane Design

#### 3.3. Partial Cancellation of Emittance Growth with Double Chicane

## 4. Second Compression Stage

#### 4.1. Review and Modification of the ESASE Technique

#### 4.2. Application of the LABC Method to the Compact XFEL

#### 4.3. CSR Effects in the Second Bunch Compressor

## 5. Discussion

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Emma, P.; Akre, R.; Arthur, J.; Bionta, R.; Bostedt, C.; Bozek, J.; Brachmann, A.; Bucksbaum, P.; Coffee, R.; Decker, F.-J.; et al. First lasing and operation of an angstrom-wavelength free-electron laser. Nat. Photonics
**2010**, 4, 641–647. [Google Scholar] [CrossRef] - Rosenzweig, J.B. The Birth of the 5th Generation Light Source. In Proceedings of the CERN Seminar, Geneva, Switzerland, 25 January 2013. [Google Scholar]
- Linac Coherent Light Source (LCLS) Conceptual Design Report; SLAC-R-593; Inspire: Capalaba, Australia, 2002.
- Graves, W.S.; Chen, J.P.J.; Fromme, P.; Holl, M.R.; Kirian, R.; Malin, L.E.; Schmidt, K.E.; Spence, J.C.H.; Underhill, M.; Weierstall, U.; et al. ASU Compact XFEL. In Proceedings of the 38th Free Electron Laser Conference, Santa Fe, NM, USA, 25 August 2017.
- Van Tilborg, J.; Barber, S.K.; Isono, F.; Schroeder, C.B.; Esarey, E.; Leemans, W.P. Free-electron lasers driven by laser plasma accelerators. Aip Conf. Proc.
**2017**, 1812, 020002. [Google Scholar] - Huang, Z.; Baxevanis, P.; Benedetti, C.; Ding, Y.; Ruth, R.; Schroeder, C.; Wang, D.; Zhang, T. Compact laser-plasma-accelerator-driven free-electron laser using a transverse gradient undulator. Phys. Rev. Lett.
**2012**, 109, 204801. [Google Scholar] [CrossRef] [PubMed] - Rosenzweig, J.B.; Candler, R.; Carlsten, B.; Castorina, G.; Croia, M.; Fukasawa, A.; Karkare, S.; Hasings, J.; Ma, Y.; Majernik, N.; et al. Towards an Ultra-Compact X-Ray Free Electron Laser. New J. Phys.
**2019**, submitted. [Google Scholar] - Cahill, A.D.; Rosenzweig, J.B.; Dolgashev, V.A.; Tantawi, S.G.; Weathersby, S. High gradient experiments with X-band cryogenic copper accelerating cavities. Phys. Rev. Spec. Top. Accel. Beams
**2018**, 10, 21. [Google Scholar] [CrossRef] - Dolgashev, V.A.; Lewandowski, J.R.; Martin, D.W.; Tantawi, S.G.; Weathersby, S.P.; Yeremian, A.D. Study of RF Breakdown in Normal Conducting Cryogenic Structure. In Proceedings of the 3rd International Particle Accelerator Conference, New Orleans, LA, USA, 20–25 May 2012. [Google Scholar]
- Rosenzweig, J.B.; Cahill, A.; Dolgashev, V.; Emma, C.; Fukasawa, A.; Li, R.; Limborg, C.; Maxson, J.; Musumeci, P.; Nause, A.; et al. Next generation high brightness beams from ultrahigh field cryogenic rf photoinjectors. Phys. Rev. Spec. Top. Accel. Beams
**2019**, 2, 22. [Google Scholar] - Rosenzweig, J.B.; Cahill, A.; Carlsten, B.; Castorina, G.; Croia, M.; Emma, C.; Fukasawa, A.; Spataro, B.; Alesini, D.; Dolgashev, V.; et al. Ultra-high brightness electron beams from very-high field cryogenic radiofrequency photocathode sources. Nucl. Instrum. Methods Sect. A
**2018**, 224, 99. [Google Scholar] [CrossRef] - O’Shea, F.H.; Marcus, G.; Rosenzweig, J.B.; Scheer, M.; Bahrdt, J.; Weingartner, R.; Gaupp, A.; Grüner, F. Short period, high field cryogenic undulator for extreme performance X-ray free electron lasers. Phys. Rev. Spec. Top. Accel. Beams
**2010**, 7, 13. [Google Scholar] [CrossRef] - Harrison, J.; Hwang, Y.; Paydar, O.; Wu, J.; Threlkeld, E.; Rosenzweig, J.; Musumeci, P.; Candler, R. High-gradient microelectromechanical system quadrupole magnets for particle beam focusing and steering. Phys. Rev. Spec. Top. Accel. Beams
**2015**, 2, 18. [Google Scholar] - Saldin, E.L.; Schneidmiller, E.A.; Yurkov, M.V. On the coherent radiation of an electron bunch moving in an arc of a circle. Nucl. Instrum. Methods Phys. Res. Sect. A
**1997**, 398, 2–3. [Google Scholar] [CrossRef] - Carlsten, B.E.; Raubenheimer, T.O. Emittance growth of bunched beams in bends. Phys. Rev. E
**1995**, 51, 2. [Google Scholar] [CrossRef] [PubMed] - Huang, Z.; Borland, M.; Emma, P.; Wu, J.; Limborg, C.; Stupakov, G.; Welch, J. Suppression of microbunching instability in the linac coherent light source. Phys. Rev. Spec. Top. Accel. Beams
**2004**, 7, 7. [Google Scholar] [CrossRef] - Xie, M. Design optimization for an X-ray free-electron laser driven by SLAC linac. In Proceedings of the 1995 Particle Accelerator Conference, Piscataway, NJ, USA, 1–5 May 1995; p. 183. [Google Scholar]
- Marcus, G.; Hemsing, E.; Rosenzweig, J. Gain length fitting formula for free-electron lasers with strong space-charge effects. Phys. Rev. Spec. Top. Accel. Beams
**2011**, 8, 14. [Google Scholar] [CrossRef] - Stupakov, G.; Bane, K.L.F.; Emma, P.; Podobedov, B. Resistive wall wakefields of short bunches at cryogenic temperatures. Phys. Rev. Spec. Top. Accel. Beams
**2015**, 3, 18. [Google Scholar] [CrossRef] - Harrison, J.; Joshi, A.; Lake, J.; Candler, R.; Musumeci, P. Surface-micromachined magnetic undulator with period length between 10 μm and 1 mm for advanced light sources. Phys. Rev. Spec. Top. Accel. Beams
**2012**, 7, 15. [Google Scholar] - Borland, M. Elegant: A Flexible SDDS-Compliant Code for Accelerator Simulation; Advanced Photon Source LS-287; Argonne National Laboratory: Lemont, IL, USA, 2000. [Google Scholar]
- Zholents, A. Method of an enhanced self-amplified spontaneous emission for hard X-ray free electron lasers. Phys. Rev. Spec. Top. Accel. Beams
**2005**, 4, 8. [Google Scholar] - Emma, P. X-Band RF Harmonic Compensation for Linear Bunch Compression in the LCLS; SLAC-TN-05-004; Stanford Linear Accelerator Center (SLAC): Menlo Park, CA, USA, 2001. [Google Scholar]
- Behtouei, M.; Faillace, L.; Ferrario, M.; Spataro, B.; Variola, A. Initial Electromagnetic and Beam Dynamics Design of a Klystron Amplifier for Ka-Band Accelerating Structures. INFN-19-12/LNF. 2019. Available online: http://www.lnf.infn.it/sis/preprint/detail-new.php?id=5440 (accessed on 1 October 2019).
- Jing, Y.; Hao, Y.; Litvinenko, V.N. Compensating effect of the coherent synchrotron radiation in bunch compressors. Phys. Rev. Spec. Top. Accel. Beams
**2013**, 7, 16. [Google Scholar] [CrossRef] - Marinelli, A.; MacArthur, J.; Emma, P.; Guetg, M.; Field, C.; Kharakh, D.; Lutman, A.A.; Ding, Y.; Huang, Z. Experimental demonstration of a single-spike hard-X-ray free-electron laser starting from noise. Appl. Phys. Lett.
**2017**, 15, 111. [Google Scholar] [CrossRef] - Marksteiner, Q.R.; Anisimov, P.M.; Lewellen, J.W.; Yampolsky, N.A.; Carlsten, B. Using Laser Compression to Enhance Hard X-ray FEL Performance; LA-UR-13-23470; Los Alamos National Laboratory: Los Alamos, NM, USA, 2013. [Google Scholar]
- Marksteiner, Q.R.; Yampolsky, N.; Lewellen, J.; Anisimov, P.; Carlsten, B. Low Current ESASE for Mitigation of CSR, Microbunching, and Resistive Wakes in a Sub-Angstrom XFEL. In Proceedings of the The High-Energy X-Ray FEL Workshop, Santa Fe, NM, USA, 27–28 June 2019. [Google Scholar]
- Anisimov, P.M. Laser-Assisted Bunch Compression for High Energy X-ray Free Electron Lasers. In Proceedings of the 39th International Free-Electron Laser Conference, Hamburg, Germany, 26–30 August 2019. [Google Scholar]
- Hemsing, E.; Stupakov, G.; Xiang, D.; Zholents, A. Beam by design: Laser manipulation of electrons in modern accelerators. Rev. Mod. Phys.
**2016**, 3, 86. [Google Scholar] [CrossRef]

**Figure 1.**Input beam phase space from the TOPGUN design. On the left, the current profile is plotted in blue along with, in red, the slice normalized emittance. On the right, the longitudinal phase space is shown. In both plots, the beam head is to the right.

**Figure 2.**Using the Ming Xie fitting equations modified to include space-charge effects, the 3D gain length as a function of the spot size in the undulator is plotted.

**Figure 3.**The schematic shows, in a simplified manner, the various elements present in the beamline as well as their approximate sizes. Altogether, the system should remain extremely compact at a total length of less than 30 m.

**Figure 4.**On the left, the current profile after the first compressor is shown. On the right, the longitudinal phase space is plotted. In both plots the beam head is to the right.

**Figure 5.**Dependence of the transverse angle on the longitudinal coordinate are shown, on the left without coherent synchrotron radiatio (CSR) effects and with CSR effects on the right. In both plots, the beam head is to the right.

**Figure 6.**The variation of transverse angle with longitudinal bunch coordinate are shown for the S-shaped chicane design for the first compressor, on the left without CSR effects and with CSR effects on the right. In both plots, the beam head is to the right.

**Figure 7.**The longitudinal phase space after the first bunch compressor is shown after the remaining energy chirp was removed using a passive dechirper cavity. The beam head is to the right.

**Figure 8.**Peak current of the microbunches as a function of normalized modulation amplitude and chicane compression. The white contour line denotes 4 kA current.

**Figure 9.**Optimal modulation amplitude and compression from the peak current contour with $A=19.13$ and $B=0.0635$. On the left, the longitudinal phase space of one microbunch shown is at 1.2 GeV, nominally at the entrance of the undulator. On the right, the associated current profile is plotted with the blue vertical lines indicating where the current falls to half of its peak value. In both plots, the beam head is to the right.

**Table 1.**The nominal design parameters for a soft X-ray free-electron laser (XFEL) are given. Beam parameters are based on a cryogenic-rf photoinjector, and undulator parameters are based on cryogenic, small-gap undulator work performed at the University of California, Los Angeles (UCLA) [12].

Beam Parameter | Value | Undulator Parameter | Value |
---|---|---|---|

Energy U (GeV) | 1.2 | Resonant Wavelength ${\lambda}_{r}$ (nm) | 1.2 |

Peak Current ${I}_{pk}$ (A) | 4000 | Undulator Period ${\lambda}_{u}$ (mm) | 9 |

Avg. Current ${I}_{avg}$ (A) | 400 | Undulator Strength K | 0.97 |

Bunch Charge Q (pC) | 100 | Pierce Parameter $\rho $ | $4.85\times {10}^{-3}$ |

Norm. Emittance ${\u03f5}_{n}$ ($\mathsf{\mu}$m) | 0.055 | 1D Gain Length ${L}_{1d}$ (cm) | 8.5 |

Energy Spread ${\sigma}_{\delta}$ | <10${}^{-3}$ | Ming Xie 3D Gain Length ${L}_{3d}$ (cm) | 11.5 |

Spot Size ${\sigma}_{r}$ ($\mathsf{\mu}$m) | 4 | Ming Xie Sat. Length ${L}_{sat}$ (m) | 2.3 |

**Table 2.**The optimal S-chicane parameters for emittance growth cancellation are reported, resulting in the compression by a factor of 20 needed in the first stage. ${\beta}_{x}$ and ${\alpha}_{x}$ refer to the beam Twiss parameters, and the drift length refers to the drifts between the outer bend magnet pairs.

First Chicane | Value | Second Chicane | Value |
---|---|---|---|

Bend Angle ${\theta}_{1}$ (deg) | 8.3 | Bend Angle ${\theta}_{2}$ (deg) | 4.2 |

Magnet Length ${L}_{b1}$ (m) | 0.2 | Magnet Length ${L}_{b2}$ (m) | 0.2 |

Drift Length ${L}_{d1}$ (m) | 1.24 | Drift Length ${L}_{d2}$ (m) | 0.26 |

${R}_{56}$ (mm) | 57.7 | ${R}_{56}$ (mm) | 4.3 |

Entrance ${\beta}_{x}$ (m) | 11.5 | Entrance ${\beta}_{x}$ (m) | 5.0 |

Entrance ${\alpha}_{x}$ | 3.7 | Entrance ${\alpha}_{x}$ | 2.5 |

**Table 3.**The parameters for the laser modulator and final chicane are given for the optimal dimensionless modulation amplitude and compressor strength discussed in the text.

Laser Modulator | Value | Chicane | Value |
---|---|---|---|

Beam Energy U (MeV) | 400 | Beam Energy U (GeV) | 1.2 |

Undulator Period ${\lambda}_{u}$ (cm) | 15 | Bend Angle $\theta $ (deg) | 2.76 |

Peak Undulator Field ${B}_{u}$ (T) | 0.87 | Magnet Length ${L}_{b}$ (m) | 0.2 |

Number of Periods ${N}_{u}$ | 5 | Drift Length ${L}_{d}$ (m) | 1 |

Laser Wavelength ${\lambda}_{l}$ ($\mathsf{\mu}$m) | 10 | ${R}_{56}$ (mm) | 5.27 |

Laser Waist ${w}_{l}$ (mm) | 0.6 | ||

Laser Peak Power ${P}_{L}$ (MW) | 60 |

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**MDPI and ACS Style**

Robles, R.; Rosenzweig, J.
Compression of Ultra-High Brightness Beams for a Compact X-ray Free-Electron Laser. *Instruments* **2019**, *3*, 53.
https://doi.org/10.3390/instruments3040053

**AMA Style**

Robles R, Rosenzweig J.
Compression of Ultra-High Brightness Beams for a Compact X-ray Free-Electron Laser. *Instruments*. 2019; 3(4):53.
https://doi.org/10.3390/instruments3040053

**Chicago/Turabian Style**

Robles, River, and James Rosenzweig.
2019. "Compression of Ultra-High Brightness Beams for a Compact X-ray Free-Electron Laser" *Instruments* 3, no. 4: 53.
https://doi.org/10.3390/instruments3040053