We present a statistical study of the magnetosheath plasma fluctuation spectra at a high-frequency range (with frequencies from 0.01 to 10 Hz). Variations of ion flux value and its direction are considered. The direction of ion flux is characterized by a polar angle – the deviation of the ion flux vector from the Sun–Earth line. We consider 290 Fourier's spectra that can be described by two power laws with a break, i.e., a change of slope. The ion flux fluctuation spectra are shown to have breaks at higher frequencies compared to the polar angle spectra. We compare the frequency of the break with the gyrostructure frequency for a number of cases. We show the polar angle break frequency to usually be smaller than the gyrostructure frequency. The dependencies of spectrum parameters such as the slopes and the break frequency on plasma parameters are also considered.
Space plasma is often in a turbulent state and can serve as a natural laboratory for turbulence exploration. Nowadays a number of spacecraft scanning the solar wind (SW) and the Earth's magnetosheath (MSH) provide large data sets of in situ measurements for the exploration of turbulence in these two regions. Solar wind turbulence has been studied for the past several decades. The results of the investigation are summarized in Alexandrova et al. (2013). Thus, the solar wind turbulence cascade was well discussed at the MHD scales and around the ion characteristic scales (e.g., Markovskii et al., 2008; Riazantseva et al., 2015; Šafránková et al., 2013a, 2015, 2016) as well as between the ion and electron scales (e.g., Chen et al., 2012, 2013a, b; Sahraoui et al., 2013).
The magnetosheath turbulence is less well studied. Unlike the solar wind turbulence, it evolves between two boundaries – the magnetopause and the bow shock. The main feature of the magnetosheath is the ion temperature anisotropy that results from the presence of the boundaries and is also a source of free energy that leads to wave generation. A variety of wave modes and instabilities observed in the MSH is described in Lacombe et Belmont (1995) and Schwartz et al. (1996). Spectra of the magnetic fluctuations in the MSH in a large frequency range were discussed by a number of researchers (e.g., Anderson et al., 1994; Czaykowska et al., 2001; Sahraoui et al., 2006, 2013; Alexandrova, 2008; Alexandrova et al., 2008; Huang et al., 2014). These spectra exhibit the presence of several scales, as it was shown for solar wind spectra. As far as we are aware, spectra of plasma (i.e., ion flux or ion density) fluctuations in the magnetosheath are described for frequencies as small as 1 Hz (e.g., Shevyrev et al., 2003) for the lack of direct plasma measurements with better temporal resolution. A statistical analysis of the ion flux fluctuation spectra together with a comparison between the solar wind and magnetosheath spectra was discussed in Riazantseva et al. (2016). The present study continues the study of Riazantseva et al. (2016). We deal with the enlarged statistics and consider fluctuations of both ion flux value and its direction. We present a statistical analysis of spectral properties of the magnetosheath plasma fluctuations with frequencies up to 10 Hz. We consider a set of the spectrum indexes and break frequencies and compare them to those obtained previously for the solar wind plasma fluctuations as well as magnetosheath magnetic field fluctuations. Also, we compare the frequency of the break to various plasma and magnetic field parameters in order to uncover the processes that are responsible for the change in slope.
Note that ion cyclotron waves and mirror waves are supposed to be dominant in the MSH at the frequencies explored in the present study (e.g., Alexandrova et al., 2004; Sahraoui et al., 2003; Anderson et al., 1994). However, the identification of wave modes requires magnetic field measurements unavailable on Spektr-R. For this reason, we do not distinguish wave modes affecting the plasma fluctuation spectra in the present paper.
Our study is based on data of the BMSW (fast solar wind monitor) instrument
(Zastenker et al., 2013; Šafránková et al., 2013b) on board the
Spektr-R spacecraft. Though Spektr-R was designed for astrophysical purposes,
its orbit (apogee
An example of the BMSW measurements in the MSH is shown in Fig. 1. The
spacecraft location for the analyzed case is
An example of the magnetosheath ion flux value (top panel) and polar angle (bottom panel) measurements by BMSW during period 11:40–12:40 on 13 October 2011.
A comparison of the ion flux value and polar angle measurements with the help of the BMSW instrument in the SW was discussed by Zastenker et al. (2015). The authors showed these two quantities to be non-correlated with each other in the majority of cases. Both quantities demonstrated rapid variations with the level of polar angle variations being higher (in a statistical sense) than the level of the flux value variations. We suppose that the ion flux value fluctuations represent fluctuations of ion number density (see Pitňa et al., 2016, for a comparison between the density and ion flux fluctuation spectra by using BMSW data), whereas the polar angle fluctuations represent predominantly the plasma bulk velocity variations.
In the example presented in Fig. 1, the polar angle seems to vary stronger
than the flux value. However, to compare levels of fluctuations themselves,
one should deal with normalized quantities. Before calculation of the
spectra, we normalized data to the mean value for the interval. Examples of
the spectra are presented in Fig. 2. The spectra are calculated at
Example of normalized ion flux (black curves) and polar angle (red curves) fluctuation spectra. Vertical dashed lines denote frequencies of the breaks. The dotted line denotes the frequency of the noise beginning at the polar angle fluctuations. Straight lines represent linear approximations of every part of the spectra. The values of the spectral slopes are given next to each line.
The spectra of the ion flux as well as of the polar angle fluctuations
exhibit two power laws separated with breaks. Below the break (at MHD
scales), the slope of the ion flux fluctuation spectra is
Altogether, we managed to find
Spektr-R positions during the analyzed intervals. Dotted lines denote the average location of the magnetopause (MP) and the bow shock (BS).
For further study, we use
We compare PSD for both quantities in the MSH. We calculate PSD on two
scales: 2
Histograms of PSD values for high-frequency (HF, top panel) and low-frequency (LF, bottom panel) fluctuations of ion flux value (black columns) and polar angle (grey columns) in the MSH. Gauss fits and their parameters for each distribution are shown.
Histograms of the slopes
Figure 5a–d show the spectral indexes for all intervals. The slope values
below (
For the ion flux value, the slopes above the spectral break also show a broad
distribution peaked at
The spectral break of the ion flux fluctuations ranges from 0.08 to 3.8.
However, the number of spectra with
To make sure that the difference between the break frequencies of different
parameters takes place, we present the distribution of the frequency ratio –
The slopes of the ion flux fluctuation spectra were shown to be nearly the
same in the SW and MSH in both frequency ranges under study (Riazantseva et
al., 2016). Figure 5 demonstrates that the slopes of the ion flux value and
polar angle fluctuation spectra in the MSH are roughly equal. Thus, one can
suppose the ion flux value and polar angle spectral slopes to also be roughly
equal in the SW. This hypothesis was verified. The mean values of the polar
angle spectral slopes are
Since we have observed the difference in the break frequencies of the flux
value and polar angle fluctuations in the MSH, a comparison between these
quantities in the SW is required. Figure 5e presents histograms of the break
frequencies of the flux value and polar angle fluctuation spectra in the SW.
Figure 5f represents the distribution of the frequency ratio calculated for
each spectra in the SW. The distribution of the break frequencies of the ion
flux fluctuation spectra show a clear two-peak structure with peaks at
0.8
Thus, the spectra of the ion flux value fluctuations usually have the break at frequencies 2–2.5 times higher than those of the polar angle fluctuations in the MSH as well as in the SW. Ion flux fluctuations seem to have spectra of two types with the break frequencies differing by a factor of 2–2.5 in both regions.
To find out if there are some factors influencing the spectral indexes we
calculate a correlation coefficient between the spectral indexes and plasma
parameters – density, bulk velocity and the inertial length frequency. The
latter was chosen following Šafránková et al. (2015). The
inertial length frequency is defined as
Break frequency of the polar angle spectra as a function of the
inertial length frequency (
Another characteristic scale supposedly related to the break between MHD and
kinetic scales is the thermal gyroradius,
Ion flux measured by Spektr-R (black line) and by Themis-B (red line) on 1 December 2012. Themis-B data are shifted back by 12.5 min to match Spektr-R data.
Themis-B data are shifted by
We calculate the frequency spectra with a 1 min step for this case. Figure 8 presents the break frequencies for the ion flux value (black triangles) and for the polar angle (red dots) fluctuations vs. the gyrostructure frequency. Šafránková et al. (2015) reported the high correlation between the break frequency of the ion density fluctuation spectra and the gyrostructure frequency. Šafránková et al. (2016) showed that the break frequency of the density as well as the bulk velocity fluctuations is always lower than the gyrostructure frequency. According to Fig. 8 the break frequency of the ion flux fluctuations does not exhibit any dependence on the gyrostructure frequency, though these frequencies are of the same order of magnitude. The polar angle fluctuation spectra have the break at frequencies lower than the gyrostructure frequency. Similar dependence was shown for the bulk velocity spectra.
The break frequencies of the ion flux (black triangles) and polar
angle (red dots) fluctuation spectra vs. the gyrostructure frequency
(
We have presented a statistical study of the frequency spectral indexes for
the ion flux value and polar angle high-frequency fluctuations in the Earth's
magnetosheath. Our results can be summarized as follows:
Below the break, the spectral slopes of both quantities' fluctuations
correspond to those predicted by Kolmogorov's theory, Above the break the ion flux value fluctuation spectra have slopes of
For both frequency ranges and for both quantities, the values of the
spectral slopes in the MSH match the values of those in the SW (taking into
account standard deviations). Spectra of the plasma fluctuations in the MSH have breaks at smaller
frequencies compared to those in the SW. In the MSH, the spectra of the ion
flux value fluctuations exhibit two different groups with break frequencies
of 0.45 The polar angle fluctuation spectra have the break at frequencies 2–2.5
times smaller than the ion flux value fluctuation spectra: at frequencies
0.36 The correlation between the spectral indexes and ambient plasma parameters
seems to be small. The only significant dependence (
The data set is available on request from the Plasma-F team, at the Experiment BMSW web page:
The reported study was funded by RFBR according to the research project nos. 16-32-00818, 16-02-00669 and 16-02-00125, and by program no. 7 of Fundamental Research of the Russian Academy of Sciences. The topical editor, C. Owen, thanks the two anonymous referees for help in evaluating this paper.