Nonlinear Processes in Geophysics www.nonlin-processes-geophys.net 1023-5809 1607-7946 17 5 2010 10.5194/npg-17-383-2010 http://www.nonlin-processes-geophys.net/17/383/2010/ http://www.nonlin-processes-geophys.net/17/383/2010/npg-17-383-2010.html http://www.nonlin-processes-geophys.net/17/383/2010/npg-17-383-2010.pdf 383 394 2010-09-01 Wave vector analysis methods using multi-point measurements Y. Narita y.narita@tu-bs.de K.-H. Glassmeier U. Motschmann Institut für Geophysik und extraterrestrische Physik, Technische Universität Braunschweig, Mendelssohnstr. 3, 38106 Braunschweig, Germany Max-Planck-Institut für Sonnensystemforschung, Max-Planck-Str. 2, 37191 Katlenburg-Lindau, Germany Institut für Theoretische Physik, Technische Universität Braunschweig, Mendelssohnstr. 3, 38106 Braunschweig, Germany DLR-Institut für Planetenforschung, Rutherfordstr. 2, 12489 Berlin, Germany Recent developments of multi-point measurements in space provide a means to analyze spacecraft data directly in the wave vector domain. For turbulence study this means that we are able to estimate energy, helicity, and higher order moments in the wave vector domain without assuming Taylor's hypothesis or axisymmetry around the mean magnetic field. The methods of the wave vector analysis are presented and applied to four-point data of Cluster in the solar wind. Balogh, A., Carr, C. M., Acuña, M. H., Dunlop, M. W., Beek, T. J., Brown, P., Fornacon, K.-H., Georgescu, E., Glassmeier, K.-H., Harris, J., Musmann, G., Oddy, T., and Schwingenschuh, K.: The Cluster Magnetic Field Investigation: overview of in-flight performance and initial results, Ann. Geophys., 19, 1207–1217, doi:10.5194/angeo-19-1207-2001, 2001. Biskamp,~D.: Magnetohydrodynamic Turbulence, Cambridge University Press, Cambridge, 2003. Capon,~J.: High resolution frequency-wavenumber spectrum analysis, Proc. IEEE, 57, 1408–1418, 1969. Carbone, V., Malara,~F., and Veltri,~P.: A model for the three-dimensional magnetic field correlation spectra of low-frequency solar wind fluctuations during Alfvénic periods, J. Geophys. Res., 100, 1763–1778, 1995. Chanteur, G.: Spatial interpolation for four spacecraft: Theory, in Analysis Methods for Multi-Spacecraft Data, G. Paschmann and P. Daly (eds.), ISSI Scientific Reports Series, ESA/ISSI, 1, 349–370, 1998. Choi,~J., Song,~I., and Kim,~H M.: On estimating the direction of arrival when the number of signal sources is unknown, Signal Process., 34, 193–205, 1993. Coleman~Jr.,~P J.: Turbulence, viscosity, and dissipation in the solar-wind plasma, Astrophys. J., 153, 371–388, 1968. Constantinescu,~O D., Glassmeier,~K.-H., Motschmann,~U., Treumann,~R A., Fornaçon,~K.-H., and Fränz,~M.: Plasma wave source location using CLUSTER as a spherical wave telescope, J. Geophys. Res., 111, A09221, doi:10.1029/2005JA011550, 2006. Constantinescu, O. D., Glassmeier, K.-H., Décréau, P. M. E., Fränz, M., and Fornaçon, K.-H.: Low frequency wave sources in the outer magnetosphere, magnetosheath, and near Earth solar wind, Ann. Geophys., 25, 2217–2228, doi:10.5194/angeo-25-2217-2007, 2007. Constantinescu,~O D.: Wave sources and structures in the Earth's magnetosheath and adjacent regions, Ph.D thesis, Copernicus GmbH, Katlenburg-Lindau, 2007. Dasso, S., Milano,~L J., Matthaeus,~W H., and Smith,~C W.: Anisotropy in fast and slow solar wind fluctuations, Astrophys. J., 635, L181–L184, 2005. Derby~Jr.,~N F.: Modulational instability of finite-amplitude, circularly polarized Alfvén waves, Astrophys. J., 224, 1013–1016, 1978. Escoubet, C. P., Fehringer, M., and Goldstein, M.: \textitIntroduction The Cluster mission, Ann. Geophys., 19, 1197–1200, doi:10.5194/angeo-19-1197-2001, 2001. Gary, S P.: Theory of space plasma microinstabilities. Cambridge Atmos, Space Science Series, Cambridge, 1993. Glassmeier,~K.-H., Coates,~A J., Acuña,~M H., Goldstein,~M L., Johnstone,~A D., Neubauer,~F M., and Rème,~H.: Spectral characteristics of low-frequency plasma turbulence upstream of Comet P/Halley, J. Geophys. Res., 94, 37–48, 1989. Glassmeier, K.-H., Motschmann, U., Dunlop, M., Balogh, A., Acuña, M. H., Carr, C., Musmann, G., Fornaçon, K.-H., Schweda, K., Vogt, J., Georgescu, E., and Buchert, S.: Cluster as a wave telescope - first results from the fluxgate magnetometer, Ann. Geophys., 19, 1439–1447, doi:10.5194/angeo-19-1439-2001, 2001 (correction in 21, p 1071, 2003). Goldstein,~M L.: An instability of finite amplitude circularly polarized Alfvén waves, Astrophys. J., 219, 700–704, 1978. Harjes,~H P. and Henger,~M.: Array Seismologie, Zeitschrift f. Geophys., 39, 865–905, 1973. Haykin,~S.: Adaptive filter theory, 2nd edn., Prentice Hall information and system science series, Prentice-Hall Inc., New Jersey, USA, 1991. Longtin,~M. and Sonnerup,~B.: Modulational instability of circularly polarized Alfvén waves, J. Geophys. Res., 91, 798–801, 1986. Marsch,~E. and Tu,~C.-Y.: On the radial evolution of MHD turbulence in the inner heliosphere, J. Geophys. Res., 95, 8211–8229, 1990. Marsch,~E.: MHD turbulence in the solar wind, Physics of the Inner Heliosphere, Vol. II, edited by: Schwenn, R. and Marsch, E., Springer Verlag, Heidelberg, 159–241, 1995. Matthaeus,~W H. and Goldstein, M L.: Measurement of the rugged invariants of magnetohydrodynamic turbulence in the solar wind, J. Geophys. Res., 87, 6011–6028, 1982. Matthaeus,~W H., Goldstein, M L., and Smith,~C.: Evaluation of magnetic helicity in homogeneous turbulence, Phys. Rev. Lett., 48, 1256–1259, 1982. Matthaeus, W H., Goldstein,~M L., and Roberts,~D A.: Evidence for the presence of quasi-two-dimensional nearly incompressible fluctuations in the solar wind, J. Geophys. Res., 95, 20673–20683, 1990. Mjølhus,~E.: On the modulational instability of hydromagnetic waves parallel to the magnetic field, J. Plasma Phys., 16, 321–334, 1976. Motschmann,~U., Woodward,~T I., Glassmeier,~K.-H., Southwood,~D J., and Pin\c con,~J L.: Wavelength and direction filtering by magnetic measurements at satellite arrays: generalized minimum variance analysis, J. Geophys. Res., 101, 4961–4965, 1996. Musmann,~G., Beinroth,~H J., Denskat,~U., Hente,~B., Theile,~B., and Neubauer,~F.: Proposal for a plasma wave array experiment to be flown on the ESA Spacelab, European Space Agency, submitted, 1974. Narita,~Y., Glassmeier,~K.-H., and Treumann,~R A.: Magnetic turbulence spectra in the high-beta plasma upstream of the terrestrial bow shock, Phys. Rev. Lett., 97, 191101, 2006. Narita, Y., Glassmeier, K.-H., Fränz, M., Nariyuki, Y., and Hada, T.: Observations of linear and nonlinear processes in the foreshock wave evolution, Nonlin. Processes Geophys., 14, 361–371, doi:10.5194/npg-14-361-2007, 2007. Narita, Y., Glassmeier, K.-H., Décréau, P. M. E., Hada, T., Motschmann, U., and Nariyuki, Y.: Evaluation of bispectrum in the wave number domain based on multi-point measurements, Ann. Geophys., 26, 3389–3393, doi:10.5194/angeo-26-3389-2008, 2008. Narita, Y. and Glassmeier, K.-H.: Spatial aliasing and distortion of energy distribution in the wave vector domain under multi-spacecraft measurements, Ann. Geophys., 27, 3031–3042, doi:10.5194/angeo-27-3031-2009, 2009a. Narita, Y., Kleindienst, G., and Glassmeier, K.-H.: Evaluation of magnetic helicity density in the wave number domain using multi-point measurements in space, Ann. Geophys., 27, 3967–3976, doi:10.5194/angeo-27-3967-2009, 2009. b. Narita,~Y., Sahraoui,~F., Goldstein,~M L., and Glassmeier,~K.-H.: Magnetic energy distribution in the four-dimensional frequency and wave vector domain in the solar wind, J. Geophys. Res., 115, A04101, doi:10.1029/2009JA014742, 2010a. Narita,~Y., Glassmeier,~K.-H., and Motschmann,~U.: High-resolution wave number spectrum using multi-point measurements in space – the multi-point signal resonator (MSR) technique, Ann. Geophys., in review, 2010b. Narita,~Y., Glassmeier,~K.-H., Goldstein,~M L., and Sahraoui,~F.: Wave-vector dependence of magnetic-turbulence spectra in the solar wind, Phys. Rev. Lett., 104, 171101, doi:10.1103/PhysRevLett.104.171101, 2010c. Narita,~Y. and Glassmeier,~K.-H.: Anisotropy evolution of magnetic field fluctuation through the bow shock, Earth Planets Space, 62, e1–e4, 2010d. Neubauer,~F M. and Glassmeier,~K.-H.: Use of an array of satellites as a wave telescope, J. Geophys. Res., 95, 19115–19122, 1990. Pin\c con,~J L. and Lefeuvre,~F.: Local characterization of homogeneous turbulence in a space plasma from simultaneous measurement of field components at several points in space, J. Geophys. Res., 96, 1789–1802, 1991. Pin\c con,~J.-L. and Motschmann,~U.: Multi-Spacecraft Filtering: General Framework, Analysis methods for multi-spacecraft data, edited by: Paschmann, G. and Daly, P W., ISSI Scientific Report, SR-001, Bern, 1998. Pinçon,~J.-L. and Glassmeier,~K.-H.: Multi-spacecraft methods of wave field characterization, Multi-Spacecraft Analysis Methods Revisited, edited by: Paschmann, G. and Daly, P W., ISSI Scientific Report, SR-008, ISSI/ESA, Noordwijk, 2008. Plaschke, F., Glassmeier, K.-H., Constantinescu, O. D., Mann, I. R., Milling, D. K., Motschmann, U., and Rae, I. J.: Statistical analysis of ground based magnetic field measurements with the field line resonance detector, Ann. Geophys., 26, 3477–3489, doi:10.5194/angeo-26-3477-2008, 2008. Podesta,~J J., Roberts,~D A., and Goldstein,~M L.: Spectral exponents of kinetic and magnetic energy spectra in solar wind turbulence, Astrophys. J., 664, 543–548, 2007. Sahraoui,~F., Pinçon,~J L., Belmont,~G., Rezeau,~L., Cornilleau-Wehrlin,~N., Robert,~P., Mellul,~L., Bosqued,~J M., Balogh,~A., Canu,~P., and Chanteur,~G.: ULF wave identification in the magnetosheath: The k-filtering technique applied to Cluster II data, J. Geophys. Res., 108, SMP1-1, 1335, doi:10.1029/2002JA009587, 2003 (correction in 109, A04222, doi10.1029/2004JA010469, 2004). Sahraoui,~F., Belmont,~G., Rezeau,~L., Cornilleau-Wehrlin,~N., Pin\con,~J L., and Balogh,~A.: Anisotropic turbulent spectra in the terrestrial magnetosheath as seen by the Cluster spacecraft, Phys. Rev. Lett., 96, 075002, PMID:16606099, 2006. Sahraoui,~F., Belmont,~G., Goldstein~M., and Rezeau,~L.: Limitations of multi-spacecraft data techniques in measuring wavenumber spectra of space plasma turbulence, J. Geophys. Res., in press, doi:10.1029/2009JA014724, 2010. Schmidt,~R O.: Multiple emitter location and signal parameter estimation, IEEE T. Antenn., Propag., AP-34, 276–280, 1986. Spangler,~S R.: Two-dimensional magnetohydrodynamics and interstellar plasma turbulence, Astrophys. J., 522, 879–896, 1999. Stix, T. H.: Waves in plasmas, Springer-Verlag, New York, 1992. Taylor,~G I.: The spectrum of turbulence, P. Roy. Soc. Lond A, 164, 476–490, 1938. Terasawa,~T., Hoshino,~M., Sakai,~J.-I., and Hada,~T.: Decay instability of finite-amplitude circularly polarized Alfvén waves: A numerical simulation of stimulated brillouin scattering, J. Geophys. Res., 91, 4171–4187, 1986. Tu,~C.-Y. and Marsch,~E.: MHD structures, waves, and turbulence in the solar wind: observations and theories, Space Sci. Rev., 73, 1–210, 1995. Vogt, J., Narita, Y., and Constantinescu, O. D.: The wave surveyor technique for fast plasma wave detection in multi-spacecraft data, Ann. Geophys., 26, 1699–1710, doi:10.5194/angeo-26-1699-2008, 2008. Wong,~H K. and Goldstein,~M L.: Parametric instabilities of circularly polarized Alfvén waves including dispersion, J. Geophys. Res., 91, 5617–5628, 1986.