36. Observations of Alfvén Vortices in the fast solar wind

Author: Owen Wyn Roberts1, Xing Li1, and Bo Li2
1Institute of Mathematics and Physics, Aberystwyth University, UK
2School of Space Science and Physics, Shandong University, China

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Introduction

The solar wind is a turbulent medium, with structure at all scales. The character of the turbulence at length scales comparable to the ion gyroradius or the ion inertial length d=vA/Ω0 (where vA and Ω0 are the Alfvén speed and proton gyro-frequency)  -the so-called ion kinetic scales  – is not understood. Two current ideas are that the turbulence is carried by a superposition of plane plasma waves, with the two most prominent candidates being whistler waves [1] and kinetic Alfvén waves (KAWs) [2]. The other idea is that the turbulent fluctuations are populated by 2-D coherent structures such as current sheets or magnetic vortices. In this nugget we will discuss the latter.

In this nugget we present a model of structure called an Alfvén vortex, and compare its predictions to data obtained from the Cluster mission in situ in the fast solar wind [3]. These vortices are solitary waves, and they take the form of tubular structures, aligned with the background magnetic field in the case of monopolar vortices, or making a small angle with it in the case of dipolar vortices. Mathematically, they appear as nonlinear solutions of MHD equations [4,5] when the magnetic field fluctuation along B0 vanishes, δB∥=0 and they are thus incompressible. They have been observed in the Earth’s magnetosheath [6] and Saturn’s magnetosheath [7]. Here we present evidence that Alfvén vortices also exist in the fast solar wind at ion kinetic scales.

Alfvén dipole vortex model

We focus here on dipolar vortices. We have constructed a mathematical model of such a vortex, and in Figure 1. we show the predicted parameters that would be observed by a spacecraft passing through a vortex (or the vortex moving relative to the spacecraft), and the 2D representations of the magnetic field and fluctuations. Figure 1a shows the field perturbations in the plane perpendicular to the background magnetic field B0 (along the z axis), representing a changing polarization. Figure 1b shows, as a function of position x in the structure, the rate of change of the angle φ that the magnetic field vector makes with the x axis. A positive (negative) dφ/dt  signifies right (left) handed polarization.  Figure 1c displays the fluctuations in the perpendicular directions, and Figure 1d shows the direction and strength of the field vector, with blue indicating that left-handed rotations are predicted (this plot is known as a hodogram). Clear coherent rotations are seen in Figure 1d, from the crossing.


Figure 1: Polarizations in the plane perpendicular to B0  of the crossing of a model dipolar vortex inclined at 4˚ to B0 . (a) Shows the hodograph, (b) dφ/dt, the direction of polarization as a function of distance x, (c) Perpendicular fluctuations δB⊥x and  δB⊥y,  (d) Hodograms of the crossing.

 Observations

Using magnetic field data from the Cluster mission, the polarization in the plane perpendicular to B0 is investigated and compared to the theoretical models of Alfvén vortices. The raw magnetic field data which is in the Geocentric Solar Ecliptic (GSE) coordinates, was quite stable and there were no obvious discontinuities as shown in Figure 2a. Figure 2b shows the Fourier power spectra of the three magnetic field components from the fluxgate magnetometer on spacecraft C4. The spectra are typical of the turbulent magnetic field fluctuations in the solar wind. At relatively low frequencies (0.007–0.4 Hz), the fluctuations have a Kolmogorov power law dependence on the frequency measured in the frame of reference of the spacecraft fsc with a power-law index -5/3 (the Kolmogorov power law frequency range is often called the turbulence  inertial range).   At a break point fsc ∼ 0.4–0.5 Hz, the spectra steepen to a spectral index of about −3.5. The spectra become flattened again at the second break point roughly at 2.4 Hz due to the magnetometer reaching its noise floor [8].

Figure 2: Spectra of typical magnetic field components Bx, By, and Bz measured by the Cluster C4 fluxgate magnetometer from 04:10 UT to 04:35 UT on 2004 February 29. The vertical dashed lines denote the frequency range to which a k-filtering technique (which is able to determine the wave number and maximum power of magnetic field fluctuations in the wave number space) has been applied in Roberts et al. (2013).

The polarization of the magnetic field fluctuations is investigated in the plane perpendicular to B0. Time series of the two magnetic field components are filtered and reconstructed, so that signals including only a small frequency range are present in the time series. This is achieved by using a wavelet transform as a natural bandpass filter.

Several representations of the polarization for the measured data are shown in Figure 3 which is similar to Figures 1a-1d. Figures 3a-3d show the analysis for a filtered frequency at 0.74Hz, which is located in the frequency range often called the dissipation range. This is above the frequencies of the inertial range plasma turbulence  . Figure 3c shows the filtered time series and the vertical lines denote the period that Figure 3d  covers. Here red and blue denote right- and left- handed polarization, and ‘C’s denote times when Cluster went through a region of shear in the magnetic field. The polarization can be either positive or negative in this plane as can be seen in Figures 3a and 3b. This is as expected, since the polarization depends on the type of vortex as well as the spacecraft’s trajectory through the vortex. Figure 3d shows different representation of the polarization and some coherent rotations are present, similar to those shown in Figure 1 for the solitary dipolar vortex model. We think that these rotations are a signature of coherent Alfvén vortices.  At 0.74Hz, the wave packet typically lasts for 6-8s which corresponds to a diameter of around 3400∼5300km.


Figure 3 Polarization analysis in the plane perpendicular to B0 at fsc = 0.74 Hz for the data taken between 04:10-04:20 on the 29th of February 2004. (a) δB⊥x − δB⊥y hodograph, (b)  dφ/dt , (c) representative waveforms, magnetic field hodograms for the region between the two vertical lines are shown in (d). Blue and red denote right- and left-handed polarization. The wave vector determined by the k-filtering is kvA/Ω0 = 0.981 and the wave vector k is nearly perpendicular to B0. The data are taken from C4.

Conclusions

Observations of Alfvén vortices are presented for an interval of undisturbed fast solar wind. Theoretical models for dipolar vortices are presented and the polarization is shown for spacecraft trajectory. We have shown evidence of the existence of these coherent structures at ion kinetic scales in the fast solar wind. However, there are still questions to be answered: how frequently do they occur in the solar wind, and what are the implications for particle heating?  For more details, readers may refer to our recent publication [3].

References

  • [1] Gary, S.P., & Smith, C.W. 2009, J. Geophys. Res., 114, A12105.
  • [2] Salem, C.S., Howes, G.G., et al. 2012, ApJL, 745, L9.
  • [3] Roberts,O.W., Li, X, Li B., Astrophysical Journal, 769, 58, 2013
  • [4] Petviashvili, V., & Pokhotelov, O. 1992, Solitary Waves in Plasmas and in the Atmosphere
  • [5] Verkhoglyadova, O. P., Dasgupta, B., & Tsurutani, B. T. 2003, Nonlinear  Proc. in Geophy., 10, 335
  • [6] Alexandrova, O., Mangeney, A., Maksimovic, M., et al. 2006, JGRA, 111, 12208
  • [7] Alexandrova, O., & Saur, J. 2008, Geophys. Res. Lett., 35, 15102
  • [8] Balogh, A., Carr, C. M., Acuña, M. H., et al. 2001, AnGeo, 19, 1207