Development of firehose instability of magnetosonic type in the presence of high-speed proton beams

Heading: 
1Malovichko, PP, 1Kyzyurov, YV
1Main Astronomical Observatory of the National Academy of Sciences of Ukraine, Kyiv, Ukraine
Kinemat. fiz. nebesnyh tel (Online) 2020, 36(3):21-46
https://doi.org/10.15407/kfnt2020.03.021
Start Page: Space Physics
Language: Ukrainian
Abstract: 

One of the varieties of firehose instability is considered, the cause of which is not the temperature anisotropy of plasma particles, but the dynamic pressure of the beam. It is shown that such a generation mechanism can lead to an effective increase of a low- frequency perturbations not only of the Alfven type, but also of the magnetosonic type, and also lead to an instability not only in the finite and high-pressure plasma but also in a low-pressure plasma. The characteristics of magnetosonic waves that are generated during the development of instability are investigated. The growth rate, the maximum angle of inclination of the wave vector, the propagation velocity of the perturbations, and the criterion for the development of instability are found. The influence of the beam temperature on the characteristics of the generated perturbations is studied. As an example of the development of such an instability, the process of formation of the turbulent region in front of the shock wave of the Earth, as well as before the shock wave from the supernova, is analyzed.

Keywords: firehose instability, magnetosonic waves, plasmas, solar wind, supernova remnants
References: 

1. A. F. Aleksandrov, L. S. Bogdankevich, and A. P. Rukhadze, Principles of Plasma Electrodynamics (Vysshaya Shkola, Moscow, 1978; Springer-Verlag, Berlin, 1984).
https://doi.org/10.1007/978-3-642-69247-5

2. V. B. Baranov and K. V. Krasnobaev, Hydrodynamic Theory of Cosmic Plasma (Nauka, Moscow, 1977) [in Russian].

3. A. A. Vedenov, E. P. Velikhov, and R. Z. Sagdeev. Stability of plasma, Sov. Phys. - Usp. 4, 332–369 (1961).
https://doi.org/10.1070/PU1961v004n02ABEH003341

4. A. A. Vedenov and R. Z. Sagdeev. On some properties of a plasma with an anisotropic distribution of ion velocities in a magnetic field, in Plasma Physics and the Problem of Controlled Thermonuclear Reactions (Akad. Nauk SSSR, Moscow, 1958), Vol. 3, pp. 278–284 [in Russian].

5. Yu. M. Voitenko, A. N. Krishtal’, S. V. Kuts, et al. Generation of kinetic Alfvén waves in the transition region of the solar wind, Geomagn. Aeron. 30, 901–907 (1990).

6. Yu. M. Voitenko, A. N. Krishtal’, P. P. Malovichko, et al. Generation of kinetic Alfvén waves and their role in coronal loops heating, Kinematika Fiz. Nebesnykh Tel 6 (2), 61–65 (1990).

7. Yu. M. Voitenko, A. N. Krishtal’, P. P. Malovichko, et al. Current instability and generation of kinetic Alfvén waves in the Earth’s magnetosphere, Geomagn. Aeron. 30, 402–406 (1990).

8. Yu. M. Voitenko, A. A. Likhachev, and A. K. Yukhimuk. Low-frequency hydromagnetic waves of excitation in the solar wind, Geofiz. Zh. 2 (6), 76–81 (1980).

9. N. A. Krall and A. W. Trivelpiece, Principles of Plasma Physics (McGraw-Hill, New York, 1973; Mir, Moscow, 1975).

10. P. P. Malovichko, A. N. Krishtal’, and A. K. Yukhimuk. Influence of temperature irregularities on the generation of kinetic Alfvén waves in the Earth’s magnetosphere, Kinematics Phys. Celestial Bodies 22, 41–45 (2006).

11. P. P. Malovichko and A. K. Yukhimuk. Current instability and generation of Alfvén waves in coronal loops, Kinematika Fiz. Nebesnykh Tel 8 (1), 20–23 (1992).

12. B. A. Trubnikov, Plasma Theory (Energoatomizdat, Moscow, 1996) [in Russian].

13. A. Achterberg. Mirror, firehose and cosmic-ray-driven instabilities in a high-beta plasma, Mon. Not. R. Astron. Soc. 436, 705–717 (2013).
https://doi.org/10.1093/mnras/stt1608

14. E. Amato and P. Blasi. A kinetic approach to cosmic-ray-induced streaming instability at supernova shocks, Mon. Not. R. Astron. Soc. 392, 1591–1600 (2009).
https://doi.org/10.1111/j.1365-2966.2008.14200.x

15. A. V. Artemyev, A. A. Petrukovich, R. Nakamura, et al. Statistics of intense dawn-dusk currents in the Earth’s magnetotail, J. Geophys. Res.: Space Phys. 120, 3804–3820 (2015).
https://doi.org/10.1002/2015JA021046

16. M. B. Bavassano Cattaneo, C. Basile, G. Moreno, et al. Evolution of mirror structures in the magnetosheath of Saturn from the bow shock to the magnetopause, J. Geophys. Res.: Space Phys. 103, 11961–11972 (1998).
https://doi.org/10.1029/97JA03683

17. A. R. Bell. Turbulent amplification of magnetic field and diffusive shock acceleration of cosmic rays, Mon. Not. R. Astron. Soc. 353, 550–558 (2004).
https://doi.org/10.1111/j.1365-2966.2004.08097.x

18. A. R. Bell. The interaction of cosmic rays and magnetized plasma, Mon. Not. R. Astron. Soc. 358, 181–187 (2005).
https://doi.org/10.1111/j.1365-2966.2005.08774.x

19. C. Bonifazi and G. Moreno. Reflected and diffuse ions backstreaming from the Earth’s bow shock 1. Basic properties, J. Geophys. Res.: Space Phys. 86, 4397–4404 (1981).
https://doi.org/10.1029/JA086iA06p04397

20. C. Bonifazi and G. Moreno. Reflected and diffuse ions backstreaming from the Earth’s bow shock 2. Origin, J. Geophys. Res.: Space Phys. 86, 4405–4413 (1981).
https://doi.org/10.1029/JA086iA06p04405

21. D. Burgess, E. Möbius, and M. Scholer. Ion acceleration at the Earth’s bow shock, Space Sci. Rev. 173, 5–47 (2012).
https://doi.org/10.1007/978-1-4614-6455-6_2

22. A. M. Bykov, S. M. Osipov, and D. C. Ellison. Cosmic ray current driven turbulence in shocks with efficient particle acceleration: The oblique, long-wavelength mode instability, Mon. Not. R. Astron. Soc. 410, 39–52 (2011).
https://doi.org/10.1111/j.1365-2966.2010.17421.x

23. J. B. Cao, H. S. Fu, T. L. Zhang, et al. Direct evidence of solar wind deceleration in the foreshock of the Earth, J. Geophys. Res.: Space Phys. 114, A02207 (2009).
https://doi.org/10.1029/2008JA013524

24. C. H. K. Chen, L. Matteini, A. A. Schekochihin, et al. Multi-species measurements of the firehose and mirror instability thresholds in the solar wind, Astrophys. J., Lett. 825, L26 (2016).
https://doi.org/10.3847/0004-637X/825/1/26

25. L. Chen and D. J. Wu. Kinetic Alfvén wave instability driven by electron temperature anisotropy in high-plasmas, Phys. Plasmas 17, 062107 (2010).
https://doi.org/10.1063/1.3439680

26. L. Chen, D. J. Wu, G. Q. Zhao, et al. Excitation of kinetic Alfvén waves by fast electron beams, Astrophys. J. 793, 13 (2014).
https://doi.org/10.1088/0004-637X/793/1/13

27. N. F. Cramer, The Physics of Alfvén Waves (Wiley, Berlin, 2001).
https://doi.org/10.1002/3527603123

28. S. P. Gary. Electromagnetic ion/ion instabilities and their consequences in space plasmas: A review, Space Sci. Rev. 56, 373–415 (1991).
https://doi.org/10.1007/BF00196632

29. A. Hasegawa. Drift mirror instability in the magnetosphere, Phys. Fluids 12, 2642–2650 (1969).
https://doi.org/10.1063/1.1692407

30. P. Hellinger. Comment on the linear mirror instability near the threshold, Phys. Plasmas 14, 082105 (2007).
https://doi.org/10.1063/1.2768318

31. S. P. Joy, M. G. Kivelson, R. J. Walker, et al. Mirror mode structures in the Jovian magnetosheath, J. Geophys. Res.: Space Phys. 111, A12212 (2006).
https://doi.org/10.1029/2006JA011985
https://doi.org/10.1029/2006JA011985

32. E. A. Kronberg, R. Bučík, S. Haaland, et al. On the origin of the energetic ion events measured upstream of the Earth’s bow shock by STEREO, Cluster, and Geotail, J. Geophys. Res.: Space Phys. 116, A02210 (2011).
https://doi.org/10.1029/2010JA015561

33. A. N. Kryshtal, A. D. Voitsekhovska, S. V. Gerasimenko, et al. Effect of small-scale Bernstein turbulence on low-frequency plasma waves in the preflare solar chromosphere, Kinematics Phys. Celestial Bodies 33, 149–165 (2017).
https://doi.org/10.3103/S0884591317040031

34. M. W. Kunz, A. A. Schekochihin, C. H. K. Chen, et al. Inertial-range kinetic turbulence in pressure-anisotropic astrophysical plasmas, J. Plasma Phys. 81, 325810501 (2015).
https://doi.org/10.1017/S0022377815000811

35. Y. Liu, J. D. Richardson, J. W. Belcher, et al. Plasma depletion and mirror waves ahead of interplanetary coronal mass ejections, J. Geophys. Res.: Space Phys. 111, A09108 (2006).
https://doi.org/10.1029/2006JA011890

36. P. P. Malovichko. Stability of magnetic configurations in the solar atmosphere under temperature anisotropy conditions, Kinematics Phys. Celestial Bodies 24, 236–241 (2008).
https://doi.org/10.3103/S0884591308050024

37. P. P. Malovichko. Generation of low-frequency magnetic field disturbances in coronal loops by proton and electron beams, Kinematics Phys. Celestial Bodies 26, 62–70 (2010).
https://doi.org/10.3103/S0884591310020030

38. P. P. Malovichko. Properties of dispersive Alfvén waves: 1. Kinetics (very low, intermediate, and low density plasmas), Kinematics Phys. Celestial Bodies 29, 269–284 (2013).
https://doi.org/10.3103/S0884591313060044

39. P. P. Malovichko. Properties of dispersive Alfvén waves: 2. Kinetics (finite and high density plasmas), Kinematics Phys. Celestial Bodies 30, 22–31 (2014).
https://doi.org/10.3103/S088459131401005X

40. P. P. Malovichko. Properties of dispersive Alfvén waves: 3. Hydrodynamics (very low, intermediate, and low density plasmas), Kinematics Phys. Celestial Bodies 30, 196–209 (2014).
https://doi.org/10.3103/S0884591314040035

41. P. P. Malovichko. Properties of dispersive Alfvén waves: 4. Hydrodynamics (finite and high-pressure plasmas), Kinematics Phys. Celestial Bodies 30, 223–233 (2014).
https://doi.org/10.3103/S0884591314050067

42. P. P. Malovichko. Excitation of Alfvén turbulence in the solar wind ahead of the Earth bow shock by beams of high-velocity protons, Kinematics Phys. Celestial Bodies 32, 86–99 (2016).
https://doi.org/10.3103/S0884591316020045

43. P. Malovichko, Y. Voitenko, and J. De Keyser. Compensated-current instability of kinetic Alfvén waves, Mon. Not. R. Astron. Soc. 452, 4236–4246 (2015).
https://doi.org/10.1093/mnras/stv1533

44. P. P. Malovichko, Y. M. Voitenko, and J. De Keyser. Non-resonant Alfvenic instability activated by high temperature of ion beams in compensated-current astrophysical plasmas, Astron. Astrophys. 615, A169 (2018).
https://doi.org/10.1051/0004-6361/201731710

45. L. Matteini, P. Hellinger, B. E. Goldstein, et al. Signatures of kinetic instabilities in the solar wind, J. Geophys. Res.: Space Phys. 118, 2771–2782 (2013).
https://doi.org/10.1002/jgra.50320

46. K. Meziane, M. Wilber, A. M. Hamza, et al. Evidence for a high-energy tail associated with foreshock field-aligned beams, J. Geophys. Res.: Space Phys. 112, A01101 (2007).
https://doi.org/10.1029/2006JA011751

47. E. Mobius, M. Scholer, N. Sckopke, et al. The distribution function of diffuse ions and the magnetic field power spectrum upstream of Earth’s bow shock, Geophys. Res., Lett. 14, 681–684 (1987).
https://doi.org/10.1029/GL014i007p00681

48. M. Oka, T. Terasawa, Y. Saito, and T. Mukai. Field-aligned beam observations at the quasi-perpendicular bow shock: Generation and shock angle dependence, J. Geophys. Res.: Space Phys. 110, A05101 (2005).
https://doi.org/10.1029/2004JA010688

49. E. N. Parker. Dynamical instability in an anisotropic ionized gas of low density, Phys. Rev. 109, 1874–1876 (1958). MATH
https://doi.org/10.1103/PhysRev.109.1874

50. G. Paschmann, N. Sckopke, I. Papamastorakis, et al. Characteristics of reflected and diffuse ions upstream from the Earth’s bow shock, J. Geophys. Res.: Space Phys. 86, 4355–4364 (1981).
https://doi.org/10.1029/JA086iA06p04355

51. O. A. Pokhotelov, R. Z. Sagdeev, M. A. Balikhin, et al. Nonlinear mirror waves in non-Maxwellian space plasmas, J. Geophys. Res.: Space Phys. 113, A04225 (2008).
https://doi.org/10.1029/2007JA012642

52. M. S. Rosin, A. A. Schekochihin, F. Rincon, et al. A non-linear theory of the parallel firehose and gyrothermal instabilities in a weakly collisional plasma, Mon. Not. R. Astron. Soc. 413, 7–38 (2011).
https://doi.org/10.1111/j.1365-2966.2010.17931.x

53. C. T. Russell, D. E. Huddleston, R. J. Strangeway, et al. Mirror mode structures at the Galileo–Io flyby: Observations, J. Geophys. Res.: Space Phys. 104, 17 471–17 477 (1999).
https://doi.org/10.1029/1999JA900202

54. J. Soucek, E. Lucek, and I. Dandouras. Properties of magnetosheath mirror modes observed by Cluster and their response to changes in plasma parameters, J. Geophys. Res.: Space Phys. 113, A04203 (2008).
https://doi.org/10.1029/2007JA012649

55. M. L. Stevens and J. C. Kasper. A scale free analysis of magnetic holes at 1 AU, J. Geophys. Res.: Space Phys. 112, A05109 (2007).
https://doi.org/10.1029/2006JA012116

56. R. A. Treumann, L. Brostrom, J. LaBelle, et al. The plasma wave signature of a "magnetic hole in the vicinity of the magnetopause, J. Geophys. Res.: Space Phys. 95, 19099–19114 (1990).
https://doi.org/10.1029/JA095iA11p19099

57. B. T. Tsurutani and P. Rodriguez. Upstream waves and particles: An overview of ISEE results, J. Geophys. Res.: Space Phys. 86, 4317–4324 (1981).
https://doi.org/10.1029/JA086iA06p04317

58. D. Winske and M. M. Leroy. Diffuse ions produced by electromagnetic ion beam instabilities, J. Geophys. Res.: Space Phys. 89, 2673–2688 (1984).
https://doi.org/10.1029/JA089iA05p02673

59. D. Winterhalter, M. Neugebauer, B. E. Goldstein, et al. Ulysses field and plasma observations of magnetic holes in the solar wind and their relation to mirror-mode structures, J. Geophys. Res.: Space Phys. 99, 23371–23381 (1994).
https://doi.org/10.1029/94JA01977

60. E. G. Zweibel and J. E. Everett. Environments for magnetic field amplification by cosmic rays, Astrophys. J. 709, 1412–1419 (2010).
https://doi.org/10.1088/0004-637X/709/2/1412