- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Letter
  • Open Access

From filamentation to stratification: Instability dynamics in scissors-shaped relativistic beam-plasma system

X. Liu1,2, D. Wu1,2,*, and J. Zhang1,2,3,†

  • *Contact author: dwu.phys@sjtu.edu.cn
  • †Contact author: jzhang@iphy.ac.cn
PDF

Phys. Rev. Research 7, L042015 – Published 15 October, 2025

DOI: https://doi.org/10.1103/tv85-lk5j

Abstract

Counter-streaming systems are a canonical model for beam-plasma instabilities, such as the filamentation instability, which is critical in high-energy density physics. However, scenarios involving intersecting fast electron beams break the cylindrical symmetry inherent to such systems. Here, we introduce the scissors-shaped configuration, a fundamental multivelocity-component system that captures this broken symmetry. Through theoretical analysis and particle-in-cell simulations, we reveal a dramatic shift in the instability dynamics: the system undergoes a stratification mode instead of filamentation. This mode is rapidly quenched by magnetic reconnection, leading to a quasistable state with magnetic energy two orders of magnitude lower than in the counter-streaming case. This discovery establishes a principle of passive instability control via geometric configuration, offering a perspective on beam-plasma interactions in astrophysics and inertial confinement fusion. The underlying physics is verifiable in upcoming multilaser experiments.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (45)

  1. M. Tabak, J. Hammer, M. E. Glinsky, W. L. Kruer, S. C. Wilks, J. Woodworth, E. M. Campbell, and M. D. Perry, Ignition and high gain with ultrapowerful lasers, Phys. Plasmas 1, 1626 (1994).
  2. A. Caruso and V. A. Pais, The ignition of dense DT fuel by injected triggers, Nucl. Fusion 36, 745 (1996).
  3. N. G. Basov, S. Y. Gus’kov, and L. P. Feokistov, Thermonuclear gain of ICF targets with direct heating of ignitor, J. Sov. Laser Res. 13, 396 (1992).
  4. T. Yamanaka, Kongo Project Report, Institute for Laser Engineering, Osaka University (1983), p. 5.
  5. M. Tabak, D. S. Clark, S. P. Hatchett et al., Review of progress in fast ignition, Phys. Plasmas 12, 057305 (2005).
  6. H. Shiraga, H. Nagatomo, W. Theobald et al., Fast ignition integrated experiments and high-gain point design, Nucl. Fusion 54, 054005 (2014).
  7. T. Gong, H. Habara, K. Sumioka et al., Direct observation of imploded core heating via fast electrons with super-penetration scheme, Nat. Commun. 10, 5614 (2019).
  8. W. Theobald, A. A. Solodov, C. Stoeckl et al., Initial cone-in-shell fast-ignition experiments on omega, Phys. Plasmas 18, 056305 (2011).
  9. T. Taguchi, T. M. Antonsen, and K. Mima, Electron beam propagation and magnetic structure formation in a strongly magnetized, collisional plasma, High Energy Density Phys. 37, 100881 (2020).
  10. W.-M. Wang, P. Gibbon, Z.-M. Sheng et al., Magnetically assisted fast ignition, Phys. Rev. Lett. 114, 015001 (2015).
  11. T. Ma, H. Sawada, P. K. Patel et al., Hot electron temperature and coupling efficiency scaling with prepulse for cone-guided fast ignition, Phys. Rev. Lett. 108, 115004 (2012).
  12. A. P. L. Robinson, M. H. Key, and M. Tabak, Focusing of relativistic electrons in dense plasma using a resistivity-gradient-generated magnetic switchyard, Phys. Rev. Lett. 108, 125004 (2012).
  13. R. Schlickeiser, On the origin of cosmological magnetic fields by plasma instabilities, Plasma Phys. Control. Fusion 47, A205 (2005).
  14. M. Lazar, R. Schlickeiser, R. Wielebinski, and S. Poedts, Cosmological effects of Weibel-type instabilities, Astrophys. J. 693, 1133 (2009).
  15. A. Bret, Weibel, two-stream, filamentation, oblique, Bell, Buneman...Which one grows faster? Astrophys. J. 699, 990 (2009).
  16. A. Stockem, I. Lerche, and R. Schlickeiser, The relativistic filamentation instability in magnetized plasmas, Astrophys. J. 659, 419 (2007).
  17. R. Schlickeiser, S. Krakau, and M. Supsar, Plasma Effects on fast pair beams. II. Reactive versus kinetic instability of parallel electrostatic waves, Astrophys. J. 777, 49 (2013).
  18. E. S. Weibel, Spontaneously growing transverse waves in a plasma due to an anisotropic velocity distribution, Phys. Rev. Lett. 2, 83 (1959).
  19. R. Lee and M. Lampe, Electromagnetic instabilities, filamentation, and focusing of relativistic electron beams, Phys. Rev. Lett. 31, 1390 (1973).
  20. Y. Sentoku, K. Mima, P. Kaw, and K. Nishikawa, Anomalous resistivity resulting from MeV-electron transport in overdense plasma, Phys. Rev. Lett. 90, 155001 (2003).
  21. A. Bret, L. Gremillet, and M. E. Dieckmann, Multidimensional electron beam-plasma instabilities in the relativistic regime, Phys. Plasmas 17, 120501 (2010).
  22. A. P. L. Robinson, D. J. Strozzi, J. R. Davies, L. Gremillet, J. J. Honrubia, T. Johzaki, R. J. Kingham, M. Sherlock, and A. A. Solodov, Theory of fast electron transport for fast ignition, Nucl. Fusion 54, 054003 (2014).
  23. P. H. Yoon and R. C. Davidson, Exact analytical model of the classical Weibel instability in a relativistic anisotropic plasma, Phys. Rev. A 35, 2718 (1987).
  24. L. O. Silva, R. A. Fonseca, J. W. Tonge, W. B. Mori, and J. M. Dawson, On the role of the purely transverse Weibel instability in fast ignitor scenarios, Phys. Plasmas 9, 2458 (2002).
  25. A. Bret, M.-C. Firpo, and C. Deutsch, Characterization of the initial filamentation of a relativistic electron beam passing through a plasma, Phys. Rev. Lett. 94, 115002 (2005).
  26. A. Bret, M.-C. Firpo, and C. Deutsch, Collective electromagnetic modes for beam-plasma interaction in the whole k space, Phys. Rev. E 70, 046401 (2004).
  27. B. Hao, Z.-M. Sheng, and J. Zhang, Kinetic theory on the current-filamentation instability in collisional plasmas, Phys. Plasmas 15, 082112 (2008).
  28. B. Hao, Z.-M. Sheng, C. Ren, and J. Zhang, Relativistic collisional current-filamentation instability and two-stream instability in dense plasma, Phys. Rev. E 79, 046409 (2009).
  29. P. Bertrand, M. Albrecht-Marc, T. Réveillé, and A. Ghizzo, Vlasov models for laser-plasma interaction, Transp. Theory Stat. Phys. 34, 103 (2005).
  30. A. Inglebert, A. Ghizzo, T. Reveille, D. Del Sarto, P. Bertrand, and F. Califano, Multi-stream Vlasov model for the study of relativistic Weibel-type instabilities, Plasma Phys. Controlled Fusion 54, 085004 (2012).
  31. A. Inglebert, A. Ghizzo, T. Reveille, P. Bertrand, and F. Califano, Electron temperature anisotropy instabilities represented by superposition of streams, Phys. Plasmas 19, 122109 (2012).
  32. M. Honda, J. Meyer-ter Vehn, and A. Pukhov, Collective stopping and ion heating in relativistic-electron-beam transport for fast ignition, Phys. Rev. Lett. 85, 2128 (2000).
  33. Y.-J. Gu, S. Kawata, and S. V. Bulanov, Dynamic mitigation of the tearing mode instability in a collisionless current sheet, Sci. Rep. 11, 11651 (2021).
  34. A. Karmakar, N. Kumar, and A. Pukhov, Detailed particle-in-cell simulations on the transport of a relativistic electron beam in plasmas, Phys. Rev. E 80, 016401 (2009).
  35. C. Ren, M. Tzoufras, F. S. Tsung, W. B. Mori, S. Amorini, R. A. Fonseca, L. O. Silva, J. C. Adam, and A. Heron, Global simulation for laser-driven meV electrons in fast ignition, Phys. Rev. Lett. 93, 185004 (2004).
  36. R. Jung, J. Osterholz, K. Löwenbrück, S. Kiselev, G. Pretzler, A. Pukhov, O. Willi, S. Kar, and M. Borghesi, Study of electron-beam propagation through preionized dense foam plasmas, Phys. Rev. Lett. 94, 195001 (2005).
  37. M. Tatarakis, F. N. Beg, E. L. Clark, A. E. Dangor, R. D. Edwards, R. G. Evans, T. J. Goldsack, K. W. D. Ledingham, and P. A. Norreys, Propagation instabilities of high-intensity laser-produced electron beams, Phys. Rev. Lett. 90, 175001 (2003).
  38. M. S. Wei, F. N. Beg, E. L. Clark, A. E. Dangor, R. G. Evans, A. Gopal, K. W. D. Ledingham, P. McKenna, and P. A. Norreys, Observations of the filamentation of high-intensity laser-produced electron beams, Phys. Rev. E 70, 056412 (2004).
  39. J. Zhang, W. M. Wang, X. H. Yang, D. Wu, Y. Y. Ma, Z. Jiao, F. Y. Zhang, X. H. Wu, Y. T. Yuan, J. Li, and J. Q. Zhu, Double-cone ignition scheme for inertial confinement fusion, Philos. Trans. R. Soc. A 378, 1 (2020).
  40. J. Honrubia, A. Morace, and M. Murakami, On intense proton beam generation and transport in hollow cones, Matter Radiat. Extremes 2, 28 (2017).
  41. M. Roth, T. E. Cowan, M. H. Key et al., Fast ignition by intense laser-accelerated proton beams, Phys. Rev. Lett. 86, 436 (2001).
  42. See Supplemental Material at http://link.aps.org/supplemental/10.1103/tv85-lk5j for the derivations of dispersion relations of instabilities, the additional PIC simulation results, the effect of ions on linear and the bulk cavitation stage, the theoretical model and analysis of the bulk cavitation stage, the simulation results of collisional cases, and the numerical convergence analysis of large-scale PIC simulations, which includes Refs. [6, 15, 16, 17, 18, 28, 32, 33, 34, 43, 44, 45]. The material also includes one movie. Movie S1: Evolution of the magnetic field in the z−y plane (top row), fast electron beam current density (middle row), and background electron current density (bottom row). The movie compares the dynamics for the one-beam (left column), two-beam (middle column), and infinite-beam (right column) systems.
  43. X. Hu, Fundamentals of Plasma Theory (Peking University Press, Beijing, 2006).
  44. B. Hao, Z.-M. Sheng, and J. Zhang, Collisional effects on the relativistic current filamentation instability: With and without the space charge effect, Laser Part. Beams 32, 79–88 (2014).
  45. M. Fiore, M. Marti, R. A. Fonseca, and L. O. Silva, Enhancement of the filamentation instability due to collisions, Conference on Plasma Physics—34 European Physical Society (2007).

Outline

Information

Phys. Rev. Research 7, L042015– Published 15 October, 2025
  • Received 7 July 2025
  • Accepted 24 September 2025
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation