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Analysis of the transverse phase space diagnostic in laser wakefield accelerators using the principal planes

Zhenan Wang1, Yuhui Xia1, Qianyi Ma1, Yuekai Chen1, Letian Liu1, Zhiyan Yang1, Ziyao Tang1, Jianghao Hu1, Xueqing Yan1,2,3 et al.

Xinlu Xu1,2,*

  • 1State Key Laboratory of Nuclear Physics and Technology, and Key Laboratory of HEDP of the Ministry of Education, CAPT, School of Physics, Peking University, Beijing 100871, China
  • 2Beijing Laser Acceleration Innovation Center, Huairou, Beijing 100871, China
  • 3Institute of Guangdong Laser Plasma Technology, Baiyun, Guangzhou 510540, China

  • *Contact author: xuxinlu@pku.edu.cn
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Phys. Rev. Accel. Beams 28, 092801 – Published 24 September, 2025

DOI: https://doi.org/10.1103/rvvv-f26h

Abstract

The focus-scan scheme has been adopted to diagnose the emittance of the electron beams produced from laser wakefield accelerators. The spot size of the electron beam has an energy dependence after propagating through a beamline consisting of two or more quadrupoles, which can be used to fit the beam emittance and the Courant-Snyder (C-S) parameters. We use the concept of the principal planes to unify the analysis of the focus-scan scheme. The fitting procedures and the effects of the length variation between the source, magnets, and screen on the diagnostic are presented. Particle-in-cell simulations using plasmas with different downramp lengths are conducted to study their effects on the measurements of the emittance and C-S parameters. Our analysis provides a unified understanding of the focus-scan scheme and can be applied to beamlines consisting of more quadrupoles.

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References (43)

  1. J. Rees and L. Rivkin, Measuring emittances and sigma matrices, Stanford Linear Accelerator Center, CA, USA, Tech. Rep. No. SLAC-PUB-3305; SLAC/AP-18; ON: DE84008846, 1984.
  2. M. G. Minty and F. Zimmermann, Measurement and Control of Charged Particle Beams (Springer Nature, Berlin, 2003).
  3. S.-Y. Lee, Accelerator Physics (World Scientific, Singapore, 1999).
  4. M. Zhang, Emittance formula for slits and pepper-pot measurement, Fermi National Accelerator Laboratory, Batavia, IL, Technical Report No. FNAL-TM–1988, 1996.
  5. A. Mostacci, A. Bacci, M. Boscolo, E. Chiadroni, A. Cianchi, D. Filippetto, M. Migliorati, P. Musumeci, C. Ronsivalle, and A. R. Rossi, Analysis methodology of movable emittance-meter measurements for low energy electron beams, Rev. Sci. Instrum. 79, 013303 (2008).
  6. H. J. Qian, C. Li, Y. C. Du, L. X. Yan, J. F. Hua, W. H. Huang, and C. X. Tang, Experimental investigation of thermal emittance components of copper photocathode, Phys. Rev. ST Accel. Beams 15, 040102 (2012).
  7. E. Prat, M. Aiba, S. Bettoni, B. Beutner, S. Reiche, and T. Schietinger, Emittance measurements and minimization at the SwissFEL injector test facility, Phys. Rev. ST Accel. Beams 17, 104401 (2014).
  8. T. Tajima and J. M. Dawson, Laser electron accelerator, Phys. Rev. Lett. 43, 267 (1979).
  9. E. Esarey, C. B. Schroeder, and W. P. Leemans, Physics of laser-driven plasma-based electron accelerators, Rev. Mod. Phys. 81, 1229 (2009).
  10. M. C. Downer, R. Zgadzaj, A. Debus, U. Schramm, and M. C. Kaluza, Diagnostics for plasma-based electron accelerators, Rev. Mod. Phys. 90, 035002 (2018).
  11. A. Cianchi, M. Anania, M. Bellaveglia, M. Castellano, E. Chiadroni, M. Ferrario, G. Gatti, B. Marchetti, A. Mostacci, R. Pompili, C. Ronsivalle, A. Rossi, and L. Serafini, Challenges in plasma and laser wakefield accelerated beams diagnostic, Nucl. Instrum. Methods Phys. Res., Sect. A 720, 153 (2013), Selected Papers from the 2nd International Conference Frontiers in Diagnostic Technologies (ICFDT2).
  12. E. Brunetti, R. P. Shanks, G. G. Manahan, M. R. Islam, B. Ersfeld, M. P. Anania, S. Cipiccia, R. C. Issac, G. Raj, G. Vieux, G. H. Welsh, S. M. Wiggins, and D. A. Jaroszynski, Low emittance, high brilliance relativistic electron beams from a laser-plasma accelerator, Phys. Rev. Lett. 105, 215007 (2010).
  13. G. G. Manahan, E. Brunetti, C. Aniculaesei, M. P. Anania, S. Cipiccia, M. R. Islam, D. W. Grant, A. Subiel, R. P. Shanks, R. C. Issac, G. H. Welsh, S. M. Wiggins, and D. A. Jaroszynski, Characterization of laser-driven single and double electron bunches with a permanent magnet quadrupole triplet and pepper-pot mask, New J. Phys. 16, 103006 (2014).
  14. C. M. Sears, A. Buck, K. Schmid, J. Mikhailova, F. Krausz, and L. Veisz, Emittance and divergence of laser wakefield accelerated electrons, Phys. Rev. ST Accel. Beams 13, 092803 (2010).
  15. G. R. Plateau, C. G. R. Geddes, D. B. Thorn, M. Chen, C. Benedetti, E. Esarey, A. J. Gonsalves, N. H. Matlis, K. Nakamura, C. B. Schroeder, S. Shiraishi, T. Sokollik, J. van Tilborg, C. Toth, S. Trotsenko, T. S. Kim, M. Battaglia, T. Stöhlker, and W. P. Leemans, Low-emittance electron bunches from a laser-plasma accelerator measured using single-shot x-ray spectroscopy, Phys. Rev. Lett. 109, 064802 (2012).
  16. M. Schnell, A. Sävert, B. Landgraf, M. Reuter, M. Nicolai, O. Jäckel, C. Peth, T. Thiele, O. Jansen, A. Pukhov, O. Willi, M. C. Kaluza, and C. Spielmann, Deducing the electron-beam diameter in a laser-plasma accelerator using x-ray betatron radiation, Phys. Rev. Lett. 108, 075001 (2012).
  17. X. L. Xu, J. F. Hua, Y. P. Wu, C. J. Zhang, F. Li, Y. Wan, C.-H. Pai, W. Lu, W. An, P. Yu, M. J. Hogan, C. Joshi, and W. B. Mori, Physics of phase space matching for staging plasma and traditional accelerator components using longitudinally tailored plasma profiles, Phys. Rev. Lett. 116, 124801 (2016).
  18. Y. Zhao, W. An, X. Xu, F. Li, L. Hildebrand, M. J. Hogan, V. Yakimenko, C. Joshi, and W. B. Mori, Emittance preservation through density ramp matching sections in a plasma wakefield accelerator, Phys. Rev. Accel. Beams 23, 011302 (2020).
  19. R. Weingartner, S. Raith, A. Popp, S. Chou, J. Wenz, K. Khrennikov, M. Heigoldt, A. R. Maier, N. Kajumba, M. Fuchs, B. Zeitler, F. Krausz, S. Karsch, and F. Grüner, Ultralow emittance electron beams from a laser-wakefield accelerator, Phys. Rev. ST Accel. Beams 15, 111302 (2012).
  20. S. K. Barber, J. van Tilborg, C. B. Schroeder, R. Lehe, H.-E. Tsai, K. K. Swanson, S. Steinke, K. Nakamura, C. G. R. Geddes, C. Benedetti, E. Esarey, and W. P. Leemans, Measured emittance dependence on the injection method in laser plasma accelerators, Phys. Rev. Lett. 119, 104801 (2017).
  21. S. K. Barber, J. v. Tilborg, C. B. Schroeder, R. Lehe, H.-E. Tsai, K. K. Swanson, S. Steinke, K. Nakamura, C. G. R. Geddes, C. Benedetti, E. Esarey, and W. P. Leemans, Parametric emittance measurements of electron beams produced by a laser plasma accelerator, Plasma Phys. Controlled Fusion 60, 054015 (2018).
  22. F. Li, Z. Nie, Y. P. Wu, B. Guo, X. H. Zhang, S. Huang, J. Zhang, Z. Cheng, Y. Ma, Y. Fang, C. J. Zhang, Y. Wan, X. L. Xu, J. F. Hua, C. H. Pai, W. Lu, and W. B. Mori, Transverse phase space diagnostics for ionization injection in laser plasma acceleration using permanent magnetic quadrupoles, Plasma Phys. Controlled Fusion 60, 044007 (2018).
  23. K. Jiang, K. Feng, H. Wang, X. Yang, P. Bai, Y. Xu, Y. Leng, W. Wang, and R. Li, Measurement of electron beam transverse slice emittance using a focused beamline, High Power Laser Sci. Eng. 11, e36 (2023).
  24. J. Van Tilborg, S. Steinke, C. Geddes, N. Matlis, B. Shaw, A. Gonsalves, J. Huijts, K. Nakamura, J. Daniels, C. Schroeder et al., Active plasma lensing for relativistic laser-plasma-accelerated electron beams, Phys. Rev. Lett. 115, 184802 (2015).
  25. J. van Tilborg, S. K. Barber, C. Benedetti, C. B. Schroeder, F. Isono, H.-E. Tsai, C. G. R. Geddes, and W. P. Leemans, Comparative study of active plasma lenses in high-quality electron accelerator transport lines, Phys. Plasmas 25, 056702 (2018).
  26. S. K. Barber, J. H. Bin, A. J. Gonsalves, F. Isono, J. van Tilborg, S. Steinke, K. Nakamura, A. Zingale, N. A. Czapla, D. Schumacher, C. B. Schroeder, C. G. R. Geddes, W. P. Leemans, and E. Esarey, A compact, high resolution energy, and emittance diagnostic for electron beams using active plasma lenses, Appl. Phys. Lett. 116, 234108 (2020).
  27. F. Li, Y. P. Wu, Z. Nie, B. Guo, X. H. Zhang, S. Huang, J. Zhang, Z. Cheng, Y. Ma, Y. Fang, C. J. Zhang, Y. Wan, X. L. Xu, J. F. Hua, C. H. Pai, W. Lu, and Y. Q. Gu, On the feasibility of sub-100 nm rad emittance measurement in plasma accelerators using permanent magnetic quadrupoles, Plasma Phys. Controlled Fusion 60, 014029 (2017).
  28. J. K. Lim, P. Frigola, G. Travish, J. B. Rosenzweig, S. G. Anderson, W. J. Brown, J. S. Jacob, C. L. Robbins, and A. M. Tremaine, Adjustable, short focal length permanent-magnet quadrupole based electron beam final focus system, Phys. Rev. ST Accel. Beams 8, 072401 (2005).
  29. E. Hecht, Optics (Pearson Education India, 2012).
  30. R. Weingartner, M. Fuchs, A. Popp, S. Raith, S. Becker, S. Chou, M. Heigoldt, K. Khrennikov, J. Wenz, T. Seggebrock, B. Zeitler, Z. Major, J. Osterhoff, F. Krausz, S. Karsch, and F. Grüner, Imaging laser-wakefield-accelerated electrons using miniature magnetic quadrupole lenses, Phys. Rev. ST Accel. Beams 14, 052801 (2011).
  31. https://www.pulsar.nl/
  32. K. Floettmann, Adiabatic matching section for plasma accelerated beams, Phys. Rev. ST Accel. Beams 17, 054402 (2014).
  33. R. A. Fonseca, L. O. Silva, F. S. Tsung, V. K. Decyk, W. Lu, C. Ren, W. B. Mori, S. Deng, S. Lee, T. Katsouleas, and J. C. Adam, osiris: A three-dimensional, fully relativistic particle in cell code for modeling plasma based accelerators, Lect. Notes Comput. Sci. 2331, 342 (2002).
  34. X. Xu, F. Li, F. S. Tsung, T. N. Dalichaouch, W. An, H. Wen, V. K. Decyk, R. A. Fonseca, M. J. Hogan, and W. B. Mori, On numerical errors to the fields surrounding a relativistically moving particle in PIC codes, J. Comput. Phys. 413, 109451 (2020).
  35. B. B. Godfrey, Numerical Cherenkov instabilities in electromagnetic particle codes, J. Comput. Phys. 15, 504 (1974).
  36. X. Xu, P. Yu, S. F. Martins, F. S. Tsung, V. K. Decyk, J. Vieira, R. A. Fonseca, W. Lu, L. O. Silva, and W. B. Mori, Numerical instability due to relativistic plasma drift in EM-PIC simulations, Comput. Phys. Commun. 184, 2503 (2013).
  37. M. Chen, Z.-M. Sheng, Y.-Y. Ma, and J. Zhang, Electron injection and trapping in a laser wakefield by field ionization to high-charge states of gases, J. Appl. Phys. 99, 056109 (2006).
  38. C. McGuffey, A. G. R. Thomas, W. Schumaker, T. Matsuoka, V. Chvykov, F. J. Dollar, G. Kalintchenko, V. Yanovsky, A. Maksimchuk, K. Krushelnick, V. Y. Bychenkov, I. V. Glazyrin, and A. V. Karpeev, Ionization induced trapping in a laser wakefield accelerator, Phys. Rev. Lett. 104, 025004 (2010).
  39. X. L. Xu, J. F. Hua, F. Li, C. J. Zhang, L. X. Yan, Y. C. Du, W. H. Huang, H. B. Chen, C. X. Tang, W. Lu, P. Yu, W. An, C. Joshi, and W. B. Mori, Phase-space dynamics of ionization injection in plasma-based accelerators, Phys. Rev. Lett. 112, 035003 (2014).
  40. X. L. Xu, Y. P. Wu, C. J. Zhang, F. Li, Y. Wan, J. F. Hua, C.-H. Pai, W. Lu, P. Yu, C. Joshi et al., Low emittance electron beam generation from a laser wakefield accelerator using two laser pulses with different wavelengths, Phys. Rev. ST Accel. Beams 17, 061301 (2014).
  41. https://github.com/Wangzn1/PRAB2025_data
  42. K. Halbach, Design of permanent multipole magnets with oriented rare earth cobalt material, Nucl. Instrum. Methods 169, 1 (1980).
  43. J. Liu, H. Lu, H. Lu, H. Zhang, X. Wu, D. Wu, H. Lan, J. Zhang, J. Lv, Q. Ma, Y. Xia, Z. Wang, J. Cai, Y. Zhao, Y. Geng, X. Xu, and X. Yan, Generation of 400 pC electron bunches in laser wakefield acceleration utilizing a structured plasma density profile, Phys. Plasmas 30, 113103 (2023).

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Phys. Rev. Accel. Beams 28, 092801– Published 24 September, 2025
  • Received 19 April 2025
  • Accepted 29 August 2025
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