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Alfvén wave collisions, the fundamental building block of plasma turbulence. I. Asymptotic solution
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1.
1. H. Alfvén, “Existence of electromagnetic-hydrodynamic waves,” Nature 150, 405406 (1942).
http://dx.doi.org/10.1038/150405d0
2.
2. P. S. Iroshinikov, “The turbulence of a conducting fluid in a strong magnetic field,” Astron. Zh. 40, 742 (1963)
2. R. S. Iroshnikov, [Sov. Astron. 7, 566 (1964)].
3.
3. R. H. Kraichnan, “Inertial range spectrum of hydromagnetic turbulence,” Phys. Fluids 8, 13851387 (1965).
http://dx.doi.org/10.1063/1.1761412
4.
4. G. G. Howes, S. C. Cowley, W. Dorland, G. W. Hammett, E. Quataert, and A. A. Schekochihin, “Astrophysical gyrokinetics: Basic equations and linear theory,” Astrophys. J. 651, 590614 (2006).
http://dx.doi.org/10.1086/506172
5.
5. A. A. Schekochihin, S. C. Cowley, W. Dorland, G. W. Hammett, G. G. Howes, E. Quataert, and T. Tatsuno, “Astrophysical gyrokinetics: Kinetic and fluid turbulent cascades in magnetized weakly collisional plasmas,” Astrophys. J. Supp. 182, 310377 (2009).
http://dx.doi.org/10.1088/0067-0049/182/1/310
6.
6. A. A. Galeev and V. N. Oraevskii, “The stability of Alfvén waves,” Sov. Phys. Dokl. 7, 988 (1963).
7.
7. R. Z. Sagdeev and A. A. Galeev, Nonlinear Plasma Theory (New York, Benjamin, 1969).
8.
8. A. Hasegawa, “Kinetic theory of MHD instabilities in a nonuniform plasma,” Sol. Phys. 47, 325330 (1976).
http://dx.doi.org/10.1007/BF00152271
9.
9. N. F. Derby, Jr., “Modulational instability of finite-amplitude, circularly polarized Alfven waves,” Astrophys. J. 224, 10131016 (1978).
http://dx.doi.org/10.1086/156451
10.
10. M. L. Goldstein, “An instability of finite amplitude circularly polarized Alfven waves,” Astrophys. J. 219, 700704 (1978).
http://dx.doi.org/10.1086/155829
11.
11. S. R. Spangler and J. P. Sheerin, “Properties of Alfven solitons in a finite-beta plasma,” J. Plasma Phys. 27, 193198 (1982).
http://dx.doi.org/10.1017/S0022377800026519
12.
12. J.-I. Sakai and U. O. Sonnerup, “Modulational instability of finite amplitude dispersive Alfven waves,” J. Geophys. Res. 88, 90699079, doi:10.1029/JA088iA11p09069 (1983).
http://dx.doi.org/10.1029/JA088iA11p09069
13.
13. S. R. Spangler, “The evolution of nonlinear Alfven waves subject to growth and damping,” Phys. Fluids 29, 25352547 (1986).
http://dx.doi.org/10.1063/1.865545
14.
14. T. Terasawa, M. Hoshino, J.-I. Sakai, and T. Hada, “Decay instability of finite–amplitude circularly polarized Alfven waves—A numerical simulation of stimulated Brillouin scattering,” J. Geophys. Res. 91, 41714187, doi:10.1029/JA091iA04p04171 (1986).
http://dx.doi.org/10.1029/JA091iA04p04171
15.
15. V. Jayanti and J. V. Hollweg, “On the dispersion relations for parametric instabilities of parallel-propagating Alfvén waves,” J. Geophys. Res. 98, 1324713252, doi:10.1029/93JA00920 (1993).
http://dx.doi.org/10.1029/93JA00920
16.
16. J. V. Hollweg, “Beat, modulational, and decay instabilities of a circularly polarized Alfven wave,” J. Geophys. Res. 99, 23431, doi:10.1029/94JA02185 (1994).
http://dx.doi.org/10.1029/94JA02185
17.
17. V. I. Shevchenko, R. Z. Sagdeev, V. L. Galinsky, and M. V. Medvedev, “The DNLS equation and parametric decay instability,” Plasma Phys. Rep. 29, 545549 (2003).
http://dx.doi.org/10.1134/1.1592552
18.
18. Y. M. Voitenko and M. Goossens, “Nonlinear coupling of Alfvén waves with widely different cross-field wavelengths in space plasmas,” J. Geophys. Res. 110, A10S01, doi:10.1029/2004JA010874 (2005).
http://dx.doi.org/10.1029/2004JA010874
19.
19. C. N. Lashmore-Davies, “Modulational instability of a finite amplitude Alfven wave,” Phys. Fluids 19, 587589 (1976).
http://dx.doi.org/10.1063/1.861493
20.
20. E. Mjolhus, “On the modulational instability of hydromagnetic waves parallel to the magnetic field,” J. Plasma Phys. 16, 321334 (1976).
http://dx.doi.org/10.1017/S0022377800020249
21.
21. K. Mio, T. Ogino, S. Takeda, and K. Minami, “Modulational instability and envelope-solitons for nonlinear Alfven waves propagating along the magnetic field in plasmas,” J. Phys. Soc. Jpn. 41, 667673 (1976).
http://dx.doi.org/10.1143/JPSJ.41.667
22.
22. H. K. Wong and M. L. Goldstein, “Parametric instabilities of the circularly polarized Alfven waves including dispersion,” J. Geophys. Res. 91, 56175628, doi:10.1029/JA091iA05p05617 (1986).
http://dx.doi.org/10.1029/JA091iA05p05617
23.
23. P. K. Shukla, N. Shukla, and L. Stenflo, “Kinetic modulational instability of broadband dispersive Alfvén waves in plasmas,” J. Plasma Phys. 73, 153157 (2007).
http://dx.doi.org/10.1017/S0022377806006271
24.
24. C. Lacombe and A. Mangeney, “Non-linear interaction of Alfven waves with compressive fast magnetosonic waves,” Astron. Astrophys. 88, 277 (1980).
25.
25. G. Brodin and L. Stenflo, “Three-wave coupling coefficients for MHD plasmas,” J. Plasma Phys. 39, 277284 (1988).
http://dx.doi.org/10.1017/S0022377800013027
26.
26. V. P. Kucherenko and A. K. Yukhimuk, “Nonlinear interaction of kinetic Alfven waves,” Kinematics and Physics of Celestial Bodies 9, 3338 (1993).
27.
27. A. K. Yukhimuk, V. M. Fedun, E. K. Sirenko, Y. M. Voitenko, and A. D. Voytsekhovskaya, “Nonlinear interaction of MHD waves and solar corona heating,” Kinematika Fiz. Nebesnykh Tel Suppl. 3, 477480 (2000).
28.
28. B. D. G. Chandran, “Weak compressible magnetohydrodynamic turbulence in the solar corona,” Phys. Rev. Lett. 95, 2650041 (2005).
http://dx.doi.org/10.1103/PhysRevLett.95.265004
29.
29. P. K. Shukla, G. Brodin, and L. Stenflo, “Nonlinear interaction between three kinetic Alfvén waves,” Phys. Lett. A 353, 7375 (2006).
http://dx.doi.org/10.1016/j.physleta.2005.11.079
30.
30. G. Brodin, L. Stenflo, and P. K. Shukla, “Nonlinear interactions between three inertial Alfvén waves,” J. Plasma Phys. 73, 913 (2007).
http://dx.doi.org/10.1017/S0022377806004788
31.
31. F. Mottez, “Non-propagating electric and density structures formed through non-linear interaction of Alfvén waves,” Ann. Geophys. 30, 8195 (2012).
http://dx.doi.org/10.5194/angeo-30-81-2012
32.
32. P. Goldreich and S. Sridhar, “Toward a theory of interstellar turbulence II. Strong Alfvénic turbulence,” Astrophys. J. 438, 763775 (1995).
http://dx.doi.org/10.1086/175121
33.
33. G. G. Howes, S. C. Cowley, W. Dorland, G. W. Hammett, E. Quataert, and A. A. Schekochihin, “A model of turbulence in magnetized plasmas: Implications for the dissipation range in the solar wind,” J. Geophys. Res. 113, A05103, doi:10.1029/2007JA012665 (2008); e-print arXiv:0707.3147.
http://dx.doi.org/10.1029/2007JA012665
34.
34. G. G. Howes, J. M. Tenbarge, and W. Dorland, “A weakened cascade model for turbulence in astrophysical plasmas,” Phys. Plasmas 18, 102305 (2011); e-print arXiv:1109.4158 [astro-ph.SR].
http://dx.doi.org/10.1063/1.3646400
35.
35. S. Sridhar and P. Goldreich, “Toward a theory of interstellar turbulence. 1: Weak Alfvenic turbulence,” Astrophys. J. 432, 612621 (1994).
http://dx.doi.org/10.1086/174600
36.
36. S. Boldyrev, “Spectrum of magnetohydrodynamic turbulence,” Phys. Rev. Lett. 96, 115002 (2006); e-print arXiv:astro-ph/0511290.
http://dx.doi.org/10.1103/PhysRevLett.96.115002
37.
37. J. V. Shebalin, W. H. Matthaeus, and D. Montgomery, “Anisotropy in MHD turbulence due to a mean magnetic field,” J. Plasma Phys. 29, 525547 (1983).
http://dx.doi.org/10.1017/S0022377800000933
38.
38. J. Cho and E. T. Vishniac, “The anisotropy of magnetohydrodynamic Alfvénic turbulence,” Astrophys. J. 539, 273282 (2000).
http://dx.doi.org/10.1086/309213
39.
39. J. Maron and P. Goldreich, “Simulations of incompressible magnetohydrodynamic turbulence,” Astrophys. J. 554, 11751196 (2001).
http://dx.doi.org/10.1086/321413
40.
40. J. Cho and A. Lazarian, “The anisotropy of electron magnetohydrodynamic turbulence,” Astrophys. J. Lett. 615, L41L44 (2004).
http://dx.doi.org/10.1086/425215
41.
41. J. Cho and A. Lazarian, “Simulations of electron magnetohydrodynamic turbulence,” Astrophys. J. 701, 236252 (2009); e-print arXiv:0904.0661 [astro-ph.EP].
http://dx.doi.org/10.1088/0004-637X/701/1/236
42.
42. J. M. TenBarge and G. G. Howes, “Evidence of critical balance in kinetic Alfvén wave turbulence simulations,” Phys. Plasmas 19, 055901 (2012).
http://dx.doi.org/10.1063/1.3693974
43.
43. D. C. Robinson and M. G. Rusbridge, “Structure of turbulence in the zeta plasma,” Phys. Fluids 14, 24992511 (1971).
http://dx.doi.org/10.1063/1.1693359
44.
44. S. J. Zweben, C. R. Menyuk, and R. J. Taylor, “Small-scale magnetic fluctuations inside the macrotor tokamak,” Phys. Rev. Lett. 42, 12701274 (1979).
http://dx.doi.org/10.1103/PhysRevLett.42.1270
45.
45. D. Montgomery and L. Turner, “Anisotropic magnetohydrodynamic turbulence in a strong external magnetic field,” Phys. Fluids 24, 825831 (1981).
http://dx.doi.org/10.1063/1.863455
46.
46. J. W. Belcher and L. Davis, “Large-amplitude Alfvén waves in the interplanetary medium, 2,” J. Geophys. Res. 76, 35343563, doi:10.1029/JA076i016p03534 (1971).
http://dx.doi.org/10.1029/JA076i016p03534
47.
47. F. Sahraoui, M. L. Goldstein, G. Belmont, P. Canu, and L. Rezeau, “Three dimensional anisotropic k spectra of turbulence at subproton scales in the solar wind,” Phys. Rev. Lett. 105, 131101 (2010).
http://dx.doi.org/10.1103/PhysRevLett.105.131101
48.
48. Y. Narita, S. P. Gary, S. Saito, K.-H. Glassmeier, and U. Motschmann, “Dispersion relation analysis of solar wind turbulence,” Geophys. Res. Lett. 38, L05101, doi:10.1029/2010GL046588 (2011).
http://dx.doi.org/10.1029/2010GL046588
49.
49. D. Montgomery, “Major disruptions, inverse cascades, and the Strauss equations,” Phys. Scr. T2A, 83 (1982).
http://dx.doi.org/10.1088/0031-8949/1982/T2A/009
50.
50. J. C. Higdon, “Density fluctuations in the interstellar medium: Evidence for anisotropic magnetogasdynamic turbulence i. model and astrophysical sites,” Astrophys. J. 285, 109123 (1984).
http://dx.doi.org/10.1086/162481
51.
51. D. Montgomery and W. H. Matthaeus, “Anisotropic modal energy transfer in interstellar turbulence,” Astrophys. J. 447, 706 (1995).
http://dx.doi.org/10.1086/175910
52.
52. C. S. Ng and A. Bhattacharjee, “Interaction of shear-Alfven wave packets: Implication for weak magnetohydrodynamic turbulence in astrophysical plasmas,” Astrophys. J. 465, 845 (1996).
http://dx.doi.org/10.1086/177468
53.
53. P. Goldreich and S. Sridhar, “Magnetohydrodynamic turbulence revisited,” Astrophys. J. 485, 680688 (1997).
http://dx.doi.org/10.1086/304442
54.
54. S. Galtier, S. V. Nazarenko, A. C. Newell, and A. Pouquet, “A weak turbulence theory for incompressible magnetohydrodynamics,” J. Plasma Phys. 63, 447488 (2000).
http://dx.doi.org/10.1017/S0022377899008284
55.
55. Y. Lithwick and P. Goldreich, “Compressible magnetohydrodynamic turbulence in interstellar plasmas,” Astrophys. J. 562, 279296 (2001).
http://dx.doi.org/10.1086/323470
56.
56. Y. Lithwick and P. Goldreich, “Imbalanced weak magnetohydrodynamic turbulence,” Astrophys. J. 582, 12201240 (2003).
http://dx.doi.org/10.1086/344676
57.
57. H. R. Strauss, “Nonlinear, three-dimensional magnetohydrodynamics of noncircular tokamaks,” Phys. Fluids 19, 134140 (1976).
http://dx.doi.org/10.1063/1.861310
58.
58. J. E. Borovsky, “The velocity and magnetic field fluctuations of the solar wind at 1 AU: Statistical analysis of Fourier spectra and correlations with plasma properties,” J. Geophys. Res. (Space Physics) 117, A05104 (2012).
http://dx.doi.org/10.1029/2011JA017499
59.
59. S. Boldyrev, J. C. Perez, J. E. Borovsky, and J. J. Podesta, “Spectral scaling laws in magnetohydrodynamic turbulence simulations and in the solar wind,” Astrophys. J. Lett. 741, L19 (2011); e-print arXiv:1106.0700 [astro-ph.GA].
http://dx.doi.org/10.1088/2041-8205/741/1/L19
60.
60. K. D. Nielson, G. G. Howes, and W. Dorland, “Alfvén wave collisions, the fundamental building block of plasma turbulence. II. Numerical solution,” Phys. Plasmas 20, 072303 (2013).
http://dx.doi.org/10.1063/1.4812807
61.
61. W. M. Elsasser, “The hydromagnetic equations,” Phys. Rev. 79, 183 (1950).
http://dx.doi.org/10.1103/PhysRev.79.183
62.
62. G. G. Howes, S. D. Bale, K. G. Klein, C. H. K. Chen, C. S. Salem, and J. M. TenBarge, “The slow-mode nature of compressible wave power in solar wind turbulence,” Astrophys. J. Lett. 753, L19 (2012); e-print arXiv:1106.4327 [astro-ph.SR].
http://dx.doi.org/10.1088/2041-8205/753/1/L19
63.
63. J. Cho, A. Lazarian, and E. T. Vishniac, “Simulations of magnetohydrodynamic turbulence in a strongly magnetized medium,” Astrophys. J. 564, 291301 (2002).
http://dx.doi.org/10.1086/324186
64.
64. J. Cho and A. Lazarian, “Compressible magnetohydrodynamic turbulence: Mode coupling, scaling relations, anisotropy, viscosity-damped regime and astrophysical implications,” Mon. Not. Roy. Astron. Soc. 345, 325339 (2003).
http://dx.doi.org/10.1046/j.1365-8711.2003.06941.x
65.
65. G. G. Howes, J. M. TenBarge, W. Dorland, E. Quataert, A. A. Schekochihin, R. Numata, and T. Tatsuno, “Gyrokinetic simulations of solar wind turbulence from ion to electron scales,” Phys. Rev. Lett. 107, 035004 (2011).
http://dx.doi.org/10.1103/PhysRevLett.107.035004
66.
66. G. I. Taylor, “The spectrum of turbulence,” Proc. Roy. Soc. A 164, 476490 (1938).
http://dx.doi.org/10.1098/rspa.1938.0032
67.
67. W. H. Matthaeus and M. L. Goldstein, “Measurement of the rugged invariants of magnetohydrodynamic turbulence in the solar wind,” J. Geophys. Res. 87, 60116028, doi:10.1029/JA087iA08p06011 (1982).
http://dx.doi.org/10.1029/JA087iA08p06011
68.
68. D. A. Roberts, L. W. Klein, M. L. Goldstein, and W. H. Matthaeus, “The nature and evolution of magnetohydrodynamic fluctuations in the solar wind—Voyager observations,” J. Geophys. Res. 92, 1102111040, doi:10.1029/JA092iA10p11021 (1987).
http://dx.doi.org/10.1029/JA092iA10p11021
69.
69. R. Bruno, B. Bavassano, and U. Villante, “Evidence for long period Alfven waves in the inner solar system,” J. Geophys. Res. 90, 43734377, doi:10.1029/JA090iA05p04373 (1985).
http://dx.doi.org/10.1029/JA090iA05p04373
70.
70. M. L. Goldstein, D. A. Roberts, and W. H. Matthaeus, “Magnetohydrodynamic turbulence in the solar wind,” Ann. Rev. Astron. Astrophys. 33, 283326 (1995).
http://dx.doi.org/10.1146/annurev.aa.33.090195.001435
71.
71. C.-Y. Tu and E. Marsch, “MHD structures, waves and turbulence in the solar wind: Observations and theories,” Space Sci. Rev. 73, 12 (1995).
http://dx.doi.org/10.1007/BF00748891
72.
72. B. Bavassano, E. Pietropaolo, and R. Bruno, “Cross-helicity and residual energy in solar wind turbulence—Radial evolution and latitudinal dependence in the region from 1 to 5 AU,” J. Geophys. Res. 103, 6521, doi:10.1029/97JA03029 (1998).
http://dx.doi.org/10.1029/97JA03029
73.
73. B. Bavassano, E. Pietropaolo, and R. Bruno, “Alfvénic turbulence in the polar wind: A statistical study on cross helicity and residual energy variations,” J. Geophys. Res. 105, 1269712704, doi:10.1029/2000JA900004 (2000).
http://dx.doi.org/10.1029/2000JA900004
74.
74. R. Bruno and V. Carbone, “The solar wind as a turbulence laboratory,” Living Rev. Solar Phys. 2, 4 (2005).
http://dx.doi.org/10.12942/lrsp-2005-4
75.
75. J. J. Podesta, D. A. Roberts, and M. L. Goldstein, “Spectral exponents of kinetic and magnetic energy spectra in solar wind turbulence,” Astrophys. J. 664, 543548 (2007).
http://dx.doi.org/10.1086/519211
76.
76. C. S. Salem, D. J. Sundkvist, and S. Bale, “Wavemode identification in the dissipation/dispersion range of solar wind turbulence: Kinetic Alfvén Waves and/or Whistlers? (Invited),” AGU Fall Meeting Abstracts, A4+ (Dec. 2009).
77.
77. S. Boldyrev and J. C. Perez, “Spectrum of weak magnetohydrodynamic turbulence,” Phys. Rev. Lett. 103, 225001 (2009); e-print arXiv:0907.4475 [astro-ph.GA].
http://dx.doi.org/10.1103/PhysRevLett.103.225001
78.
78. W.-C. Müller and R. Grappin, “Spectral energy dynamics in magnetohydrodynamic turbulence,” Phys. Rev. Lett. 95, 114502 (2005).
http://dx.doi.org/10.1103/PhysRevLett.95.114502
79.
79. Y. Wang, S. Boldyrev, and J. C. Perez, “Residual energy in magnetohydrodynamic turbulence,” Astrophys. J. Lett. 740, L36 (2011); e-print arXiv:1106.2238 [astro-ph.GA].
http://dx.doi.org/10.1088/2041-8205/740/2/L36
80.
80. N. Tronko, S. V. Nazarenko, and S. Galtier, “Weak turbulence in two-dimensional magnetohydrodynamics,” Phys. Rev. E 87(3), 033103 (2013).
http://dx.doi.org/10.1103/PhysRevE.87.033103
81.
81. P. Dmitruk and W. H. Matthaeus, “Waves and turbulence in magnetohydrodynamic direct numerical simulations,” Phys. Plasmas 16, 062304 (2009).
http://dx.doi.org/10.1063/1.3148335
82.
82. S. Boldyrev, J. Mason, and F. Cattaneo, “Dynamic alignment and exact scaling laws in magnetohydrodynamic turbulence,” Astrophys. J. Lett. 699, L39L42 (2009).
http://dx.doi.org/10.1088/0004-637X/699/1/L39
83.
83. T. N. Parashar, M. A. Shay, P. A. Cassak, and W. H. Matthaeus, “Kinetic dissipation and anisotropic heating in a turbulent collisionless plasma,” Phys. Plasmas 16, 032310 (2009).
http://dx.doi.org/10.1063/1.3094062
84.
84. S. Servidio, W. H. Matthaeus, M. A. Shay, P. A. Cassak, and P. Dmitruk, “Magnetic reconnection in two-dimensional magnetohydrodynamic turbulence,” Phys. Rev. Lett. 102, 115003 (2009).
http://dx.doi.org/10.1103/PhysRevLett.102.115003
85.
85. T. N. Parashar, S. Servidio, B. Breech, M. A. Shay, and W. H. Matthaeus, “Kinetic driven turbulence: Structure in space and time,” Phys. Plasmas 17, 102304 (2010).
http://dx.doi.org/10.1063/1.3486537
86.
86. S. Servidio, W. H. Matthaeus, M. A. Shay, P. Dmitruk, P. A. Cassak, and M. Wan, “Statistics of magnetic reconnection in two-dimensional magnetohydrodynamic turbulence,” Phys. Plasmas 17, 032315 (2010).
http://dx.doi.org/10.1063/1.3368798
87.
87. S. Servidio, P. Dmitruk, A. Greco, M. Wan, S. Donato, P. A. Cassak, M. A. Shay, V. Carbone, and W. H. Matthaeus, “Magnetic reconnection as an element of turbulence,” Nonlin. Proc. Geophys. 18, 675695 (2011).
http://dx.doi.org/10.5194/npg-18-675-2011
88.
88. S. A. Markovskii and B. J. Vasquez, “A short-timescale channel of dissipation of the strong solar wind turbulence,” Astrophys. J. 739, 22 (2011).
http://dx.doi.org/10.1088/0004-637X/739/1/22
89.
89. T. N. Parashar, S. Servidio, M. A. Shay, B. Breech, and W. H. Matthaeus, “Effect of driving frequency on excitation of turbulence in a kinetic plasma,” Phys. Plasmas 18, 092302 (2011).
http://dx.doi.org/10.1063/1.3630926
90.
90. S. Servidio, F. Valentini, F. Califano, and P. Veltri, “Local kinetic effects in two-dimensional plasma turbulence,” Phys. Rev. Lett. 108, 045001 (2012).
http://dx.doi.org/10.1103/PhysRevLett.108.045001
91.
91. B. J. Vasquez and S. A. Markovskii, “Velocity power spectra from cross-field turbulence in the proton kinetic regime,” Astrophys. J. 747, 19 (2012).
http://dx.doi.org/10.1088/0004-637X/747/1/19
92.
92. V. A. Svidzinski, H. Li, H. A. Rose, B. J. Albright, and K. J. Bowers, “Particle in cell simulations of fast magnetosonic wave turbulence in the ion cyclotron frequency range,” Phys. Plasmas 16, 122310(2009).
http://dx.doi.org/10.1063/1.3274559
93.
93. P. Hunana, D. Laveder, T. Passot, P. L. Sulem, and D. Borgogno, “Reduction of compressibility and parallel transfer by landau damping in turbulent magnetized plasmas,” Astrophys. J. 743, 128 (2011); e-print arXiv:1109.2636 [physics.plasm-ph].
http://dx.doi.org/10.1088/0004-637X/743/2/128
94.
94. C. S. Salem, G. G. Howes, D. Sundkvist, S. D. Bale, C. C. Chaston, C. H. K. Chen, and F. S. Mozer, “Identification of kinetic Alfvén wave turbulence in the solar wind,” Astrophys. J. Lett. 745, L9 (2012).
http://dx.doi.org/10.1088/2041-8205/745/1/L9
95.
95. K. G. Klein, G. G. Howes, J. M. TenBarge, S. D. Bale, C. H. K. Chen, and C. S. Salem, “Using synthetic spacecraft data to interpret compressible fluctuations in solar wind turbulence,” Astrophys. J. 755, 159 (2012), e-print arXiv:1206.6564 [physics.space-ph].
http://dx.doi.org/10.1088/0004-637X/755/2/159
96.
96. G. G. Howes, D. J. Drake, K. D. Nielson, T. A. Carter, C. A. Kletzing, and F. Skiff, “Toward astrophysical turbulence in the laboratory,” Phys. Rev. Lett. 109, 255001 (2012); e-print arXiv:1210.4568 [physics.plasm-ph].
http://dx.doi.org/10.1103/PhysRevLett.109.255001
97.
97. G. G. Howes, K. D. Nielson, D. J. Drake, J. W. R. Schroeder, C. A. Skiff, F. Kletzing, and T. A. Carter, “Alfvén wave collisions, the fundamental building block of plasma turbulence. III. Theory for experimental design,” Phys. Plasmas 20, 072304 (2013).
http://dx.doi.org/10.1063/1.4812808
98.
98. D. J. Drake, J. W. R. Schroeder, G. G. Howes, C. A. Skiff, F. Kletzing, T. A. Carter, and D. W. Auerbach, “Alfvén wave collisions, the fundamental building block of plasma turbulence. IV. Laboratory experiment,” Phys. Plasmas 20, 072305 (2013).
http://dx.doi.org/10.1063/1.4813242
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FIG. 1.

Schematic of the initial conditions specifying two perpendicularly polarized, counterpropagating Alfvén waves overlapping within a periodic domain.

Image of FIG. 2.

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FIG. 2.

Schematic diagram of the Fourier modes in the perpendicular plane arising in the asymptotic solution. The Fourier modes depicted are the primary modes (circles), secondary modes (triangles), and tertiary modes (squares). Filled symbols denote the key Fourier modes that play a role in the secular transfer of energy to small scales in the Alfvén wave collision. The parallel wavenumber for each of the modes is indicated by the diagonal grey lines, a consequence of the resonance conditions for the wavevector.

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/content/aip/journal/pop/20/7/10.1063/1.4812805
2013-07-15
2014-04-20

Abstract

The nonlinear interaction between counterpropagating Alfvén waves is the physical mechanism underlying the cascade of energy to small scales in astrophysical plasma turbulence. Beginning with the equations for incompressible MHD, an asymptotic analytical solution for the nonlinear evolution of these Alfvén wave collisions is derived in the weakly nonlinear limit. The resulting qualitative picture of nonlinear energy transfer due to this mechanism involves two steps: first, the primary counterpropagating Alfvén waves interact to generate an inherently nonlinear, purely magnetic secondary fluctuation with no parallel variation; second, the two primary waves each interact with this secondary fluctuation to transfer energy secularly to two tertiary Alfvén waves. These tertiary modes are linear Alfvén waves with the same parallel wavenumber as the primary waves, indicating the lack of a parallel cascade. The amplitude of these tertiary modes increases linearly with time due to the coherent nature of the resonant four-wave interaction responsible for the nonlinear energy transfer. The implications of this analytical solution for turbulence in astrophysical plasmas are discussed. The solution presented here provides valuable intuition about the nonlinear interactions underlying magnetized plasma turbulence, in support of an experimental program to verify in the laboratory the nature of this fundamental building block of astrophysical plasma turbulence.

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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Alfvén wave collisions, the fundamental building block of plasma turbulence. I. Asymptotic solution
http://aip.metastore.ingenta.com/content/aip/journal/pop/20/7/10.1063/1.4812805
10.1063/1.4812805
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