Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-14T07:08:49.993Z Has data issue: false hasContentIssue false

Parametric decay of parallel and oblique Alfvén waves in the expanding solar wind

Published online by Cambridge University Press:  19 August 2014

L. Del Zanna*
Affiliation:
Dipartimento di Fisica e Astronomia, Università degli Studi di Firenze, Italy INAF - Osservatorio Astrofisico di Arcetri, Firenze, Italy INFN - Sezione di Firenze, Italy
L. Matteini
Affiliation:
Dipartimento di Fisica e Astronomia, Università degli Studi di Firenze, Italy Space and Atmospheric Physics Group, Imperial College London, UK
S. Landi
Affiliation:
Dipartimento di Fisica e Astronomia, Università degli Studi di Firenze, Italy INAF - Osservatorio Astrofisico di Arcetri, Firenze, Italy
A. Verdini
Affiliation:
Dipartimento di Fisica e Astronomia, Università degli Studi di Firenze, Italy Solar-Terrestrial Center of Excellence, Royal Observatory of Belgium, Brussels, Belgium
M. Velli
Affiliation:
Dipartimento di Fisica e Astronomia, Università degli Studi di Firenze, Italy Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California, USA
*
Email address for correspondence: luca.delzanna@unifi.it

Abstract

The long-term evolution of large-amplitude Alfvén waves propagating in the solar wind is investigated by performing two-dimensional MHD simulations within the expanding box model. The linear and nonlinear phases of the parametric decay instability are studied for both circularly polarized waves in parallel propagation and for arc-polarized waves in oblique propagation. The non-monochromatic case is also considered. In the oblique case, the direct excitation of daughter modes transverse to the local background field is found for the first time in an expanding environment, and this transverse cascade seems to be favored for monochromatic mother waves. The expansion effect reduces the instability growth rate, and it can even suppress its onset for the lowest frequency modes considered here, possibly explaining the persistence of these outgoing waves in the solar wind.

Type
Research Article
Copyright
Copyright © Cambridge University Press 2014 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Araneda, J. A., Marsch, E. and F.-Viñas, A. 2008 Proton core heating and beam formation via parametrically unstable Alfvén-Cyclotron waves. Phys. Rev. Lett. 100 (12), 125003.Google Scholar
Barnes, A. and Hollweg, J. V. 1974 Large-amplitude hydromagnetic waves. J. Geophys. Res. 79, 2302.Google Scholar
Bavassano, B., Pietropaolo, E. and Bruno, R. 2000 On the evolution of outward and inward Alfvénic fluctuations in the polar wind. J. Geophys. Res. 105, 1595915964.Google Scholar
Belcher, J. W. and Jr.Davis, L. 1971 Large-amplitude Alfvén waves in the interplanetary medium, 2. J. Geophys. Res. 76, 3534.Google Scholar
Breech, B., Matthaeus, W. H., Minnie, J., Oughton, S., Parhi, S., Bieber, J. W. and Bavassano, B. 2005 Radial evolution of cross helicity in high-latitude solar wind. Geophys. Res. Lett. 32, 6103.Google Scholar
Bruno, R., Bavassano, B. and Villante, U. 1985 Evidence for long period Alfven waves in the inner solar system. J. Geophys. Res. 90, 43734377.Google Scholar
Bruno, R. and Carbone, V. 2013 The solar wind as a turbulence laboratory. Living Rev. Sol. Phys. 10, 2.Google Scholar
Del Zanna, L. 2001 Parametric decay of oblique arc-polarized Alfvén waves. Geophys. Res. Lett. 28, 2585–+.Google Scholar
Del Zanna, L. 2009 The ECHO code for classical and relativistic MHD. In: Numerical Modeling of Space Plasma Flows: ASTRONUM-2008 (eds. Pogorelov, N. V., Audit, E., Colella, P. and Zank, G. P.), Astronomical Society of the Pacific Conference Series, St, John, USVI, Vol. 406, pp. 217.Google Scholar
Del Zanna, L., Landi, S., Matteini, L. and Velli, M. 2012a The expanding box model in ECHO: application to the parametric decay of Alfvén Waves in the fast solar wind. In: Numerical Modeling of Space Plasma Slows (ASTRONUM 2011) (eds. Pogorelov, N. V., Font, J. A., Audit, E. and Zank, G. P.), Astronomical Society of the Pacific Conference Series, Valencia, Spain, Vol. 459, pp. 196.Google Scholar
Del Zanna, L., Matteini, L., Landi, S. and Velli, M. 2012b Parametric decay of large-amplitude Alfvén waves: MHD and hybrid simulations. In: American Institute of Physics Conference Series (eds. Heerikhuisen, J., Li, G., Pogorelov, N. and Zank, G.), American Institute of Physics Conference Series, Maui, Hawaii, US, Vol. 1436, pp. 1217.Google Scholar
Del Zanna, L. and Velli, M. 2002 Coronal heating through Alfven waves. Adv. Space Res. 30, 471480.Google Scholar
Del Zanna, L., Velli, M. and Londrillo, P. 2001 Parametric decay of circularly polarized Alfvén waves: Multidimensional simulations in periodic and open domains. Astron. Astrophys. 367, 705718.Google Scholar
Del Zanna, L., Zanotti, O., Bucciantini, N. and Londrillo, P. 2007 ECHO: a Eulerian conservative high-order scheme for general relativistic magnetohydrodynamics and magnetodynamics. Astron. Astrophys. 473, 1130.Google Scholar
Jr.Derby, N. F. 1978 Modulational instability of finite-amplitude, circularly polarized Alfven waves. Astrophys. J. 224, 10131016.Google Scholar
Dobrowolny, M., Mangeney, A. and Veltri, P. 1980 Fully developed anisotropic hydromagnetic turbulence in interplanetary space. Phys. Rev. Lett. 45, 144147.Google Scholar
Dong, Y., Verdini, A. and Grappin, R. 2014 Evolution of turbulence in the expanding solar wind: a numerical stuty. Astrophys. J. submitted.Google Scholar
Galeev, A. A. and Oraevskii, V. N. 1963 The stability of Alfvén Waves. Sov. Phys. Dokl. 7, 988.Google Scholar
Ghosh, S., Vinas, A. F. and Goldstein, M. L. 1993 Parametric instabilities of a large-amplitude circularly polarized Alfven wave - Linear growth in two-dimensional geometries. J. Geophys. Res. 98, 15561.Google Scholar
Goldstein, M. L. 1978 An instability of finite amplitude circularly polarized Alfven waves. Astrophys. J. 219, 700704.Google Scholar
Goldstein, M. L., Roberts, D. A. and Matthaeus, W. H. 1995 Magnetohydrodynamic turbulence in the solar wind. Annu. Rev. Astron. Astrophys. 33, 283326.CrossRefGoogle Scholar
Grappin, R., Mangeney, A. and Marsch, E. 1990 On the origin of solar wind MHD turbulence - HELIOS data revisited. J. Geophys. Res. 95, 81978209.Google Scholar
Grappin, R. and Velli, M. 1996 Waves and streams in the expanding solar wind. J. Geophys. Res. 101, 425444.Google Scholar
Grappin, R., Velli, M. and Mangeney, A. 1993 Nonlinear wave evolution in the expanding solar wind. Phys. Rev. Lett. 70, 21902193.Google Scholar
Hellinger, P., Velli, M., TráVníčEk, P., Gary, S. P., Goldstein, B. E. and Liewer, P. C. 2005 Alfvén wave heating of heavy ions in the expanding solar wind: Hybrid simulations. J. Geophys. Res. (Space Physics) 110, 12109.Google Scholar
Hollweg, J. V. 1994 Beat, modulational, and decay instabilities of a circularly polarized Alfven wave. J. Geophys. Res. 99, 23431.Google Scholar
Horbury, T. S., Forman, M. A. and Oughton, S. 2005 Spacecraft observations of solar wind turbulence: an overview. Plasma Phys. Control. Fusion 47, B703B717.Google Scholar
Hoshino, M. and Goldstein, M. L. 1989 Time evolution from linear to nonlinear stages in magnetohydrodynamic parametric instabilities. Phys. Fluids 1, 14051415.Google Scholar
Inhester, B. 1990 A drift-kinetic treatment of the parametric decay of large-amplitude Alfven waves. J. Geophys. Res. 95, 1052510539.Google Scholar
Landi, S., Londrillo, P., Velli, M. and Bettarini, L. 2008 Three-dimensional simulations of compressible tearing instability. Phys. Plasmas 15 (1), 012302–+.Google Scholar
Liewer, P. C., Velli, M. and Goldstein, B. E. 2001 Alfvén wave propagation and ion cyclotron interactions in the expanding solar wind: One-dimensional hybrid simulations. J. Geophys. Res. 106, 2926129282.Google Scholar
Lionello, R., Velli, M., Downs, C., Linker, J. A., Mikić, Z. and Verdini, A. 2014 Validating a time-dependent turbulence-driven model of the solar wind. Astrophys. J. 784, 120.CrossRefGoogle Scholar
Londrillo, P. and Del Zanna, L. 2004 On the divergence-free condition in Godunov-type schemes for ideal magnetohydrodynamics: the upwind constrained transport method. J. Comput. Phys. 195, 1748.Google Scholar
Malara, F., Primavera, L. and Veltri, P. 2000 Nonlinear evolution of parametric instability of a large-amplitude nonmonochromatic Alfvén wave. Phys. Plasmas 7, 28662877.Google Scholar
Malara, F. and Velli, M. 1996 Parametric instability of a large-amplitude nonmonochromatic Alfvén wave. Phys. Plasmas 3, 44274433.Google Scholar
Marsch, E. and Tu, C.-Y. 1990 On the radial evolution of MHD turbulence in the inner heliosphere. J. Geophys. Res. 95, 82118229.Google Scholar
Matteini, L. 2012 Parametric decay of Alfvén waves at parallel and oblique propagation: kinetic effects and transverse couplings. In American Institute of Physics Conference Series (eds. Sulem, P.-L. and Mond, M.), American Institute of Physics Conference Series, Eilat, Israel, Vol. 1439, pp. 8393.Google Scholar
Matteini, L., Horbury, T. S., Neugebauer, M. and Goldstein, B. E. 2014 Dependence of solar wind speed on the local magnetic field orientation: Role of Alfvénic fluctuations. Geophys. Res. Lett. 41, 259265.Google Scholar
Matteini, L., Landi, S., Del Zanna, L., Velli, M. and Hellinger, P. 2010a Parametric decay of linearly polarized shear Alfvén waves in oblique propagation: one and two-dimensional hybrid simulations. Geophys. Res. Lett. 37, 20101.Google Scholar
Matteini, L., Landi, S., Hellinger, P. and Velli, M. 2006 Parallel proton fire hose instability in the expanding solar wind: Hybrid simulations. J. Geophys. Res. (Space Physics) 111, 10101.Google Scholar
Matteini, L., Landi, S., Velli, M. and Hellinger, P. 2010b Kinetics of parametric instabilities of Alfvén waves: Evolution of ion distribution functions. J. Geophys. Res. (Space Physics) 115, 9106.Google Scholar
Nariyuki, Y. and Hada, T. 2006 Kinetically modified parametric instabilities of circularly polarized Alfvén waves: Ion kinetic effects. Phys. Plasmas 13 (12), 124501.Google Scholar
Nariyuki, Y., Hada, T. and Tsubouchi, K. 2007 Parametric instabilities of parallel propagating incoherent Alfvén waves in a finite ion beta plasma. Phys. Plasmas 14 (12), 122110.Google Scholar
Riley, P., Sonett, C. P., Tsurutani, B. T., Balogh, A., Forsyth, R. J. and Hoogeveen, G. W. 1996 Properties of arc-polarized Alfvén waves in the ecliptic plane: ulysses observations. J. Geophys. Res. 101, 1998719994.Google Scholar
Roberts, D. A., Goldstein, M. L., Klein, L. W. and Matthaeus, W. H. 1987 Origin and evolution of fluctuations in the solar wind - HELIOS observations and Helios-Voyager comparisons. J. Geophys. Res. 92, 1202312035.Google Scholar
Sagdeev, R. Z. and Galeev, A. A. 1969 Nonlinear Plasma Theory. Benjamin, New York.Google Scholar
Tenerani, A. and Velli, M. 2013 Parametric decay of radial Alfvén waves in the expanding accelerating solar wind. J. Geophys. Res. (Space Physics) 118, 75077516.Google Scholar
Tsurutani, B. T. and Ho, C. M. 1999 A review of discontinuities and Alfvén waves in interplanetary space: Ulysses results. Rev. Geophys. 37, 517524.Google Scholar
Tu, C.-Y. and Marsch, E. 1990 Evidence for a ‘background’ spectrum of solar wind turbulence in the inner heliosphere. J. Geophys. Res. 95, 43374341.Google Scholar
Umeki, H. and Terasawa, T. 1992 Decay instability of incoherent Alfven waves in the solar wind. J. Geophys. Res. 97, 31133119.Google Scholar
Vasquez, B. J. and Hollweg, J. V. 1996 Formation of arc-shaped Alfvén waves and rotational discontinuities from oblique linearly polarized wave trains. J. Geophys. Res. 101, 1352713540.Google Scholar
Velli, M., Grappin, R. and Mangeney, A. 1992 MHD turbulence in an expanding atmosphere. In: Electromechanical Coupling of the Solar Atmosphere (ed. Spicer, D. S. and MacNeice, P.), American Institute of Physics Conference Series, In: Electromechanical coupling of the solar atmosphere; Proceedings of the OSL Workshop, Capri, Italy, May 27–31, 1991 (A93-39876 15-92), Vol. 267, pp. 154159.Google Scholar
Verdini, A., Grappin, R., Pinto, R. and Velli, M. 2012 On the Origin of the 1/f Spectrum in the Solar Wind Magnetic Field. ApJLett 750, L33.Google Scholar
Verdini, A. and Velli, M. 2007 Alfvén Waves and Turbulence in the Solar Atmosphere and Solar Wind. Astrophys. J. 662, 669676.Google Scholar
Verdini, A., Velli, M., Matthaeus, W. H., Oughton, S. and Dmitruk, P. 2010 A Turbulence-Driven Model for Heating and Acceleration of the Fast Wind in Coronal Holes. ApJLett 708, L116L120.Google Scholar
Viñas, A. F. and Goldstein, M. L. 1991 Parametric instabilities of circularly polarized large-amplitude dispersive Alfvén waves: excitation of parallel-propagating electromagnetic daughter waves. J. Plasma Phys. 46, 107.Google Scholar