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Advanced Quasistatic Approximation

  • ACCELERATION OF PARTICLES IN PLASMA
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Abstract

The quasistatic approximation (QSA) is an efficient method of simulating laser- and beam-driven plasma wakefield acceleration, but it becomes imprecise if some plasma particles make long longitudinal excursions in a strongly nonlinear wave, or if waves with non-zero group velocity are present in the plasma, or the plasma density gradients are sharp, or the beam shape changes rapidly. We present an extension to QSA that is free from many of its limitations and retains its main advantages of speed and reduced dimensionality. The new approach takes into account the exchange of information between adjacent plasma layers. We introduce the physical model, describe its numerical implementation, and compare the simulation results with available analytical solutions and other codes.

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REFERENCES

  1. F. Albert, M. E. Couprie, A. Debus, M. C. Downer, J. Faure, A. Flacco, L. A. Gizzi, T. Grismayer, A. Huebl, C. Joshi, M. Labat, W. P. Leemans, A. R. Maier, S. P. D. Mangles, P. Mason, et al., New J. Phys. 23, 031101 (2021). https://doi.org/10.1088/1367-2630/abcc62

  2. J.-L. Vay and R. Lehe, Rev. Accel. Sci. Technol. 9, 165 (2016). https://doi.org/10.1142/S1793626816300085

    Article  Google Scholar 

  3. K. V. Lotov, Nucl. Instrum. Methods Phys. Res., Sect. A 410, 461 (1998). https://doi.org/10.1016/S0168-9002(98)00178-8

    Article  Google Scholar 

  4. A. V. Burdakov, A. M. Kudryavtsev, P. V. Logatchov, K. V. Lotov, A. V. Petrenko, and A. N. Skrinsky, Plasma Phys. Rep. 31, 292 (2005). https://doi.org/10.1134/1.1904145

    Article  ADS  Google Scholar 

  5. C. B. Schroeder, E. Esarey, C. G. R. Geddes, C. Benedetti, and W. P. Leemans, Phys. Rev. ST Accel. Beams 13, 101301 (2010). https://doi.org/10.1103/PhysRevSTAB.13.101301

  6. K. Nakajima, A. Deng, X. Zhang, B. Shen, J. Liu, R. Li, Z. Xu, T. Ostermayr, S. Petrovics, C. Klier, K. Iqbal, H. Ruhl, and T. Tajima, Phys. Rev. ST Accel. Beams 14, 091301 (2011). https://doi.org/10.1103/PhysRevSTAB.14.091301

  7. C. B. Schroeder, E. Esarey, and W. P. Leemans, Phys. Rev. ST Accel. Beams 15, 051301 (2012). https://doi.org/10.1103/PhysRevSTAB.15.051301

  8. J.-L. Vay, Phys. Rev. Lett. 98, 130405 (2007). https://doi.org/10.1103/PhysRevLett.98.130405

  9. J.-L. Vay, C. G. R. Geddes, E. Cormier-Michel, and D. P. Grote, J. Comput. Phys. 230, 5908 (2011). https://doi.org/10.1016/j.jcp.2011.04.003

    Article  ADS  Google Scholar 

  10. P. Sprangle, E. Esarey, and A. Ting, Phys. Rev. Lett. 64, 2011 (1990). https://doi.org/10.1103/PhysRevLett.64.2011

    Article  ADS  Google Scholar 

  11. P. Mora and T. M. Antonsen, Jr., Phys. Plasmas 4, 217 (1997). https://doi.org/10.1063/1.872134

    Article  ADS  Google Scholar 

  12. N. Jain, J. Palastro, T. M. Antonsen, Jr., W. B. Mori, and W. An, Phys. Plasmas 22, 023103 (2015). https://doi.org/10.1063/1.4907159

  13. A. P. Sosedkin and K. V. Lotov, Nucl. Instrum. Methods Phys. Res., Sect. A 829, 350 (2016). https://doi.org/10.1016/j.nima.2015.12.032

    Article  Google Scholar 

  14. W. An, V. K. Decyk, W. B. Mori, and T. M. Antonsen, Jr., J. Comput. Phys. 250, 165 (2013). https://doi.org/10.1016/j.jcp.2013.05.020

    Article  ADS  MathSciNet  Google Scholar 

  15. T. Mehrling, C. Benedetti, C. B. Schroeder, and J. Osterhoff, Plasma Phys. Control. Fusion 56, 084012 (2014). https://doi.org/10.1088/0741-3335/56/8/084012

  16. A. Pukhov and J. P. Farmer, Phys. Rev. Lett. 121, 264801 (2018). https://doi.org/10.1103/PhysRevLett.121.264801

  17. W. Zhu, J. P. Palastro, and T. M. Antonsen, Phys. Plasmas 19, 033105 (2012). https://doi.org/10.1063/1.4813245

  18. C. Huang, V. K. Decyk, C. Ren, M. Zhou, W. Lu, W. B. Mori, J. H. Cooley, T. M. Antonsen, Jr., and T. Katsouleas, J. Comput. Phys. 217, 658 (2006). https://doi.org/10.1016/j.jcp.2006.01.039

    Article  ADS  Google Scholar 

  19. R. I. Spitsyn, Master thesis (Novosibirsk State University, Novosibirsk, 2016). https://star.inp.nsk.su/~dep_plasma/dip/Spitsyn_m.pdf

    Google Scholar 

  20. D. Terzani, C. Benedetti, C. B. Schroeder, and E. Esarey, Phys. Plasmas 28, 063105 (2021). https://doi.org/10.1063/5.0050580

  21. P. Sprangle, E. Esarey, J. Krall, and G. Joyce, Phys. Rev. Lett. 69, 2200 (1992). https://doi.org/10.1103/PhysRevLett.69.2200

    Article  ADS  Google Scholar 

  22. E. Esarey, P. Sprangle, J. Krall, A. Ting, and G. Joyce, Phys. Fluids B 5, 2690 (1993). https://doi.org/10.1063/1.860707

    Article  ADS  Google Scholar 

  23. K. V. Lotov, Phys. Plasmas 5, 785 (1998). https://doi.org/10.1063/1.872765

    Article  ADS  Google Scholar 

  24. R. Zgadzaj, T. Silva, V. K. Khudyakov, A. Sosedkin, J. Allen, S. Gessner, Z. Li, M. Litos, J. Vieira, K. V. Lotov, M. J. Hogan, V. Yakimenko, and M. C. Downer, Nat. Commun. 11, 4753 (2020). https://doi.org/10.1038/s41467-020-18490-w

    Article  ADS  Google Scholar 

  25. V. K. Khudiakov, K. V. Lotov, and M. C. Downer, Plasma Phys. Control. Fusion 64, 045003 (2022). https://doi.org/10.1088/1361-6587/ac4523

  26. C. Benedetti, C. B. Schroeder, C. G. R. Geddes, E. Esarey, and W. P. Leemans, Plasma Phys. Control. Fusion 60, 014002 (2018). https://doi.org/10.1088/1361-6587/aa8977

  27. W. Zhu, J. P. Palastro, and T. M. Antonsen, Phys. Plasmas 20, 073103 (2013). https://doi.org/10.1063/1.4813245

  28. K. V. Lotov, Phys. Rev. ST Accel. Beams 6, 061301 (2003). https://doi.org/10.1103/PhysRevSTAB.6.061301

  29. LCODE Framework. https://lcode.info/. Cited August 20, 2022.

  30. LCODE Manual. https://lcode.info/site-files/manual.pdf. Cited August 20, 2022.

  31. J. Crank and P. Nicolson, Math. Proc. Cambridge Philos. Soc. 43, 50 (1947). https://doi.org/10.1017/S0305004100023197

    Article  ADS  Google Scholar 

  32. D. W. Peaceman and H. H. Rachford, J. Soc. Ind. A-ppl. Math. 3, 28 (1955). https://doi.org/10.1137/0103003

    Article  Google Scholar 

  33. J. Douglas, Jr., J. Soc. Ind. Appl. Math. 3, 42 (1955). https://doi.org/10.1137/0103004

    Article  Google Scholar 

  34. E. Esarey and W. P. Leemans, Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 59, 1082 (1999). https://doi.org/10.1103/PhysRevE.59.1082

    Article  Google Scholar 

  35. R. Lehe, M. Kirchen, I. A. Andriyash, B. B. Godfrey, and J.-L. Vay, Comput. Phys. Commun. 203, 66 (2016). https://doi.org/10.1016/j.cpc.2016.02.007

    Article  ADS  MathSciNet  Google Scholar 

  36. J. Luo, M. Chen, G.-B. Zhang, T. Yuan, J.-Y. Yu, Z.‑C. Shen, L.-L. Yu, S. M. Weng, C. B. Schroeder, and E. Esarey, Phys. Plasmas 23, 103112 (2016). https://doi.org/10.1063/1.4966047

  37. F. Massimo, A. Beck, J. Derouillat, M. Grech, M. Lobet, F. Pérez, I. Zemzemi, and A. Specka, Plasma Phys. Control. Fusion 61, 124001 (2019). https://doi.org/10.1088/1361-6587/ab49cf

  38. D. Terzani and P. Londrillo, Comput. Phys. Commun. 242, 49 (2019). https://doi.org/10.1016/j.cpc.2019.04.007

    Article  ADS  MathSciNet  Google Scholar 

  39. A. Pukhov and J. Meyer-ter-Vehn, Appl. Phys. B: Lasers Opt. 74, 355 (2002). https://doi.org/10.1007/s003400200795

    Article  ADS  Google Scholar 

  40. V. Malka, Phys. Plasmas 19, 055501 (2012). https://doi.org/10.1063/1.3695389

  41. E. Esarey, C. B. Schroeder, and W. P. Leemans, Rev. Mod. Phys. 81, 1229 (2009). https://doi.org/10.1103/RevModPhys.81.1229

    Article  ADS  Google Scholar 

  42. S. Morshed, T. M. Antonsen, and J. P. Palastro, Phys. Plasmas 17, 063106 (2010). https://doi.org/10.1063/1.3432685

  43. P. V. Tuev and K. V. Lotov, in Proceedings of the 47th EPS Conference on Plasma Physics, Sitges, 2021, Paper P2.2004. http://ocs.ciemat.es/EPS2021PAP/pdf/P2.2004.pdf.

  44. Irkutsk Supercomputer Center of the Siberian Branch of the Russian Academy of Sciences. http://hpc.icc.ru. Cited August 20, 2022.

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ACKNOWLEDGMENTS

The authors are grateful to I.A. Shalimova and A.A. Gorn for helpful discussions. Simulations were performed on HPC cluster “Akademik V.M. Matrosov” [44].

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Authors and Affiliations

  1. Budker Institute of Nuclear Physics, Siberian Branch, Russian Academy of Sciences, 630090, Novosibirsk, Russia

    P. V. Tuev, R. I. Spitsyn & K. V. Lotov

  2. Novosibirsk State University, 630090, Novosibirsk, Russia

    P. V. Tuev, R. I. Spitsyn & K. V. Lotov

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  1. P. V. Tuev
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Tuev, P.V., Spitsyn, R.I. & Lotov, K.V. Advanced Quasistatic Approximation. Plasma Phys. Rep. 49, 229–238 (2023). https://doi.org/10.1134/S1063780X22601249

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