1. Contact person Maria Riazantseva: orearm@gmail.com
Space Research Institute
High - frequency plasma turbulence observed on SPECTR-R in the solar wind and in the magnetosheath
M. O. Riazantseva1, V.P. Budaev1,2, G. N. Zastenker1,
L. S. Rakhmanova1, J. Safrankova3, Z. Nemecek3, L. Prech3
1 Space Research Institute (IKI) Russian Academy of Science, Moscow, Russia
2 National research centre “Kurchatov Institute”, Moscow, Russia
3Charles University in Prague, Czech Republic
Contact person Maria Riazantseva:

2. BMSW instrument (experiment PLASMA-F)
on board of spacecraft SPECTR-R
Experiment PLASMA-F :
BMSW – measurements of Solar wind (SW) and Magnetosheath (MSH) ion flow parameters (faraday cups)
MEP – energetic particles(Si-detectors keV) BS MP
The main objectives:
Turbulence in the solar wind and the magnetosheath
Fine structure of energetic particle acceleration
SPECTR-R: Launched 18 July 2011 on highly elliptical orbit
period of revolution 8.3 days
Perigee 576 km; 
apogee km = 53 Re; 
inclination 51.3 deg.
BMSW:
- ion flux value and direction (time resolution 30 ms)
plasma parameters in sweeping mode (most of the time): proton density , bulk speed, temperature, alpha particles/proton ratio ( resolution 3 s)
plasma parameters in adaptive mode (separate time intervals): proton density, bulk speed and temperature (resolution 30 ms)
BMSW instrument

3. The main principle of the BMSW instrument
and features of the «new» BMSW
laboratory sample of the
new sensor DP
idea of the two part collectors
Sensor – Faraday cap
C2, C4 – grounding grid; C3 – control grid; C1 – suppressor grid
Collector
All the sensors are identical and directed along the axis of the device oriented to the sun.
Sensors have collectors cut into two parts (one sensor can measure the direction of the flux in one plane). It provides flexibility, reservation and possibility to intercalibrate sensors in flight.
Sensors are united in pairs (one pair - for measuring ion flux vector (magnitude and two angles with time resolution 30 ms), the second - for sweeping mode (measurements of full energetic spectrum, and Np, Vp, Tp, Na/Np with time resolution 1.5 s), the third - for adaptive mode (measurements of Np, Vp, Tp with the highest time resolution 30 ms)).
Sensors will have wider angle diagrams ± 60.
new BMSW will consist of two types of blocks – main and additional (to have the possibility to measure the particle from the direction not to the Sun ).
new BMSW will be almost identical for all projects.

4. Strannik “Piligrim” - the nearest mission (launch ~2022):
Outer magnetosphere orbit
apogee Re
Perigee Re
inclination 51.8˚ deg.
Launch ~
combination of PLASMA-F and Resonance instruments
fast plasma and energetic particle measurements (BMSW-S, TOTEM-I, KAMERA-OV, TOTEM-E, TDK-S, DOC-MS,);
3D electric and magnetic field measurements (instruments FM-PS, AMEF-WB, LEMI, HFA, RZ, ELMAVAN)
Objectives:
Thin boundaries, small scale structures and transient processes in critical points of energy transformation in magnetosphere (sub solar point of magnetopause, day cusps, plasmasheath in night tail), and also in the solar wind and magnetosheath
Plasma turbulence up to electron scales

5. Main objectives of investigation of turbulent characteristics in the solar wind and in the flank magnetosheath:
to study properties of frequency spectra of the ion flux fluctuations on scales Hz and to show a variability of kinds of spectra (more than 1500 of spectra in SW and MSH).
to analyze properties of probability distributions functions of the small-scale ion flux fluctuations and to explore the degree and nature of the differences between the experimental distribution functions from the standard (Gaussian) distribution functions.
to compare the turbulent properties in the SW and in the flank MSH.
to determine scaling characteristics of high order structure functions of ion flux fluctuations, to demonstrate their variability and to compare them with predictions of different models.
to produce parameterization of scaling of the structure functions with log-Poisson model and to investigate the contribution of different geometry of dissipative structures.

6. Turbulent ion flux fluctuations on different scales
Multiscale process :
(Zeleniy & Milovanov, 2004)
An example of typical turbulent ion flux fluctuations in the SW /07/15 (high resolution BMSW measurements 32 Hz) on interval of 8 hours (a), 20 min (b), 40 sec (c) .
The high level of variations is observed on all scales  multiscale SW structure

7. Spectra with two characteristic slopes
-5/3
Fb=2.4
P2= -2.85
Spectra with two characteristic slopes and the break point between them are repeatedly discussed both for the interplanetary magnetic field and for the SW plasma fluctuations ( see, for example, the review of Bruno, Living Rev. Solar Phys., 2013; and the review of Alexandrova et.al.,Space Sci. Rev.,2013)
inertial range SW
dissipation range
Spectrum of the interplanetary magnetic field fluctuations (CLUSTER). Alexandrova et. al.,2013 SpaceScienceRev
Spectrum of ion flux fluctuations
in the SW 12/07/15 00:23-00:40
P1= -1.95
P2= -3.36
Fb=0.45
MSH
inertial scale
Also using BMSW measurements: Safrankova et.al., PRL 2013 – for ion density, velocity and temperature fluctuations in the SW ; Riazantseva et al., Phil. Trans – for ion flux fluctuations in the SW ; Riazantseva et. al., Adv.Sp.Res 2016 – for ion flux fluctuations in the SW and MSH
dissipation range
Spectra with two characteristic slopes observed in ~ 50% in the SW and in ~ 47% in the MSH
Spectrum of ion flux fluctuatuations
in the MSH 11/10/30 09:23-09:40

8. <P1SW>=-1.6±0.2 <P2SW>=-2.9±0.5 <FbSW>=1.9±0.8 Hz
The comparison of ion flux spectra with two characteristic slopes in the SW and MSH
Ion flux fluctuation spectra in the MSH 24/10/ :41 – 08:58 UT and in the SW 28/09/ :30-09:20 UT
Slopes of the spectrum in the MSH seems to be practically the same as in the SW . The break frequency changes in a wide ranges, but in a whole the Fb in MSH is usually more than twice less than in the SW ; In average on statistic in the SW (Riazantseva et.al., Adv.Sp.Res.2016):
<P1SW>=-1.6±0.2 <P2SW>=-2.9±0.5 <FbSW>=1.9±0.8 Hz
<P1MSH>=-1.75±0.2 <P2MSH>=-3.0±0.4 <FbMSH>=0.9±0.5 Hz
Statistics: in the SW 363 spectra (calculated on17 min. intervals) in the MSH 427 spectra
The distribution of spectra indexes

9. Spectra with flattening around the break
Pp= - 1.1
P2= - 2.9
Fb1= 0.08
Fb2= 2.4 SW
Spectrum of electron density fluctuations in the SW on ISEE1-2 (Celnikier et al., Sp. Sci. Rev.,1983)
Spectrum of ion flux fluctuations in the SW 11/09/29 03:08-03:25
Spectrum with flattening observed in ~ 32% the SW intervals and in ~ 18% in the MSH). The flattening in the MSH is observed at lower frequencies.
P2= -3.6
Pp= -0.7
P1= -2.3
Fb2=0.35
Fb1=0.02
MSH
Plasma fluctuation spectra with flattening between low and high frequency parts of them are observed also in: Unti et.al., Astrophys. J ; Celnikier et.al., Astron. Astrophys., 1987; Chen et.al., Phys. Rev. Lett )
Also using BMSW measurements: Safrankova et.al., Astrophys. J for ion density in the SW
Spectrum of ion flux fluctuations in the MSH 12/10/31 15:42-15:59

10. Spectra with peak around the break
F=0.4 SW
Spectrum of ion flux fluctuations
in the SW 12/04/05 11:16-11:33
Spectrum of magnetic field fluctuations in the MSH (CLUSTER). (Alexandrova et. al.,2006 JGR)
MSH
F=0.13
Spectra with peak around the break observed in ~ 19 % in the MSH and in ~ 3 % in the SW.
Peaks around the break on spectra of the magnetic field fluctuations in the MSH were investigated in Alexandrova et. al., JGR, 2004 and It was shown that they are the sign of Alfven vortices
Spectrum of ion flux fluctuations
in the MSH 12/02/09 11:29-11:46

11. Dynamic of ion flux fluctuation spectra
in MSH 12/02/09 10:29-12:02

12. Spectra with nonlinear descent on high frequenciesSW
Spectrum of ion flux fluctuations
in the SW 1109/29 01:51-02:08
Spectrum of magnetic field fluctuation in the SW (CLUSTER). (Alexandrova et. al., 2012 APJ)
MSH
High frequency part of the ion flux fluctuation spectra can not be approximated by linear fashion in ~ 6 % in the SW and in ~ 11 % in the MSH.
In Alexandrova et al. Astrophys. Journ the exponential character of such descent for spectra of the interplanetary magnetic field fluctuations was demonstrated.
Spectrum of ion flux fluctuations
in the MSH 11/11/29 03:58-04:15

13. Variability of ion flux fluctuation spectra
spectra with two characteristic slopes
spectra with flattening
around the break
spectra with peak around the break
spectra with nonlinear descent on high frequencies
Other types of spectra SW
50%
32% 3% 6% 9%
MSH
47%
18%
19%
11% 5%

14. Variability of probability distribution functions on small time scales
Experimental
distribution
(BMSW)
Experimental
distribution
(BMSW)
Gaussian
distribution
Gaussian
distribution
An example of PDF of ion flux fluctuations on scale 0.1 s in the SW 28/09/ :59-04:16 UT - symmetric view
An example of PDF of ion flux fluctuations on scale 0.1 s in the SW 28/09/2011 3:16-03:33 UT - asymmetric view
No Gaussian PDF’s of different forms is the result of intermittency in the turbulent SW flow

15. Variability of probability distribution functions for different time scales
An example os PDFs of ion flux fluctuations in the MSH (solid line) on scales of 1/8 s (a); 1 s (b); 64 s (c); and 2048 s (d), and corresponding Gaussian distributions (dashed line) for period of 2011/10/13 15:11-18:35 UT.
PDFs strongly differ from Gaussian distribution on scales less than 1 s, this difference disappears toward large scales.
Also using BMSW measurements: Chen et.al., Astrophys. J.let,. 2014;
Riazantseva, Phil. Trans
By previous results: see for example (Bruno et al., JGR 2003; Alexandrova et al., Phys Rev. Let. 2009) by magnetic field measurements, and (Bruno et al., JGR, 2003, Riazantseva, AIP Conf. Proc. 2010) for plasma measurements.

16. The variability of flatness value in the SW and in the MSH
structure function of q order ( - scale parameter) :
Sq()~ q/3 – for Gaussian PDF
Sq()~  (q) – no Gaussian PDF
MSH
Flatness (4th-order of moment) :
Flatness coeficients are strongly different for various intervals. In average a tendency of flatness increasing from large to smaller scales are observed and (according to the approach of Bruno et al., JGR, 2003 ) demonstrate the multifractal signal and high level of intermittency.
The dependence of flatness coefficient from the time scale parameter  for different time intervals in the SW and MSH. Solid line – an average flatness. Green line F = 3 for Gaussian distribution

17. The analysis of high order structure function in the SW and in the MSH
The dependence of structure functions of high orders q from time scale parameter  on interval in the SW :39 – 03:05 UT and on interval in the MSH :15 – 12:45 UT
The dependence of high orders structure functions from structure function for q= 3 on interval :39 – 03:05 UT on interval in the MSH :15 – 12:45 UT
In accordance with Benzi et al., Phys. Rev. 1993, linear dependence of the structure function of q-th order from the structure function of 3-th order in wide range of scales demonstrate the extended self similarity and generalized multi-scale invariance at time scales >> linear correlations

18. The comparison of experimental scaling of the structure functions for ion flux fluctuations in the SW and in the MSH with model scaling SW
MSH
The experimental scaling ζ(q)/ ζ(3)-q/3 for several 26 min intervals (different colors for different intervals) vs order q in the SW during the period 09/10/2011, 08:02-18:53 UT (left panel) and in the MSH during the period 07/10/2011,04:37-09:06 UT (right panel), scaling for Kolmogorov model (K41) (dashed line– q/3) , log-Poisson model of She –Leveque (solid line Δ= β=2/3), and Biskamp and Mueller model (dashed dotted line).
Non-linear scaling of the structure functions is strongly differed from Kolmogorov model scaling and it is predominantly close to the log-Poisson model

19. Parameterization of the structure functions by the log-Poisson model.
Intermittent turbulence
Scaling of the structure function according to She –Leveque - Dubrulle model (She & Leveque, Phys.Rev. Let., 1994; Dubrulle, Phys.Rev. Let., 1994):
Non intermittent turbulence
β – characteristic of the intermittency (β=1 → (q)=q/3 Kolmogorov model without intermittency), Δ - parameters related to geometry of dissipation structure and edge effects, scaling of most intermittent dissipative structure l ~ l - Δ. For isotropic 3D (She -Leveque model) Δ= β=2/3
The high level of intermittency is observed for ion flux flow in the SW and in the MSH. Non intermittent flow is observed only in 10% of intervals.
The distributions of β and Δ parameterization coefficient for ion flux fluctuations in the SW and in the MSH

20. Parameterization of the structure functions by the log-Poisson model.
Scaling of the structure function according to Biskamp and Mueller model for two-dimensional dissipative structures (Biskamp and Mueller, Phys Plasmas, 2000) :
Scaling of the structure function according to model for 1-D filament-like dissipative structures ( Budaev, Phys.Lett. A, 2009 ) :
gf is close to 3 – the filament structure dominate in the process.
The analysis of structure function scaling according to log-Poisson model show the dominant contribution of filament structures in turbulent processes in the SW and in the MSH.
The distributions of g and gf parameterization coefficient for ion flux fluctuations in the SW and in the MSH

21. Conclusions:
Different shapes of spectra of ion flux fluctuations in the SW and the MSH can be observed. Spectra with two characteristic slopes are observed in near to 50% of cases both for the SW and the MSH , spectra with flattening around the break - in 30% for the SW and in 20% for the MSH , spectra with peak - in 3% for the SW and in 20% for the MSH , spectra with nonlinear descent on high frequencies -in 6% for the SW and in 10% for the MSH . This is the demonstration of the nonstationary character of SW turbulence.
The observations in the SW and in the flank MSH demonstrate practically the same mean value of characteristics slopes, whereas the break frequency in the MSH is twice less than in the SW .
PDF’s of ion flux fluctuations in the SW and the MSH strongly differ from Gaussian distribution on scales ~ Hz. In average the flatness grow towards the small scale and demonstrate the multifractal signal and high level of intermittency. The flow in the MSH is usually less intermittent than one in the SW .
The analysis of high order structure functions show the nonlinear dependence from scale parameters, in this way the trivial self similarity is not satisfied, but the extended self similarity in plasma turbulence both in the SW and MSH can be observed.
Statistical characteristics of ion flux fluctuations in the SW and the magnetoshath can vary significantly for different intervals, however for the most part of cases they can be described by Log-Poisson model. The analysis of structure functions scaling in the frame of log-Poisson approach has shown the observation of intermittent character of flow with dominant contribution of filament-like structures.