Z. Nemecek, J. Safrankova, L. Prech, O. Goncharov, F. Nemec, A. Pitna, A. University, Faculty of Mathematics and Physics, Prague, Czech Republic G. Zastenker, M. Riazantseva IKI RAN, Moscow, Russia Fast measurements of solar wind parameters: Contribution to turbulence and IP shock structure investigations Moscow, February 16–20, 2015

Bright Monitor of the Solar Wind (BMSW) Developed by Charles University in Prague and Space Research Institute in Moscow for Spektr-R  Three Faraday cups for determination of the speed and temperature - 0, 1, 2  Three declined Faraday cups for determination of the density and velocity direction – 3, 4, 5  LaunchJuly 18, 2011  Apogee~50 R E  Inclination65 o  Orbital period~8.5 days  Time resolution31 ms  Three axis stabilized Safrankova et al. (SSR, 2013) Zastenker et al. (Cos. Res., 2013)

How to reach the ion kinetic scale ?  Three identical FCs  Voltages on deceleration grids of FC1 and FC2 set by a feedback to obtain ~ 50% and 30% of the FC0 current  3 points of the distribution are enough to calculate basic plasma moments  Maximum time resolution is given by a telemetry bit rate FC current FC2 FC1

Outline The contribution deals with:  Turbulence in a quiet solar wind  Evolution of turbulence across IP shocks  Interplanetary shock scales  Wave packets associated with IP shocks  Future plans

Expectation on solar wind turbulence  Power law frequency spectrum with several segments  -1 slope on large scale determined by the solar activity  -5/3 (Kolgomorov) slope at the MHD scale (MHD waves)  -7/3 slope at the ion kinetic scale (KAW, ion cyclotron waves)  A steeper slope at the electron scale -? -7/3 -5/3 Years to days MHD kinetic ionelectron Power spectral density ωcωc  The spectral slope at the upper end of the MHD range is often lower  The plateau would be more distinct for low beta and for low level of density fluctuations (Chandran et al., 2009) General view Present knowledge

Spectrum of solar wind density fluctuations Ion inertial length -5/3  An example of precise processing of density fluctuations  This example is taken from June 2, 2012, UT (5 hours)  FFT is computed on ~20-min time intervals with shift of ~1 minute  The median of ~280 spectra is shown  Three different spectral slopes divided by two breaks are clearly revealed  This shape of the frequency spectrum is typical for the density; exceptionally, it can be find for the magnetic field Break 2 MHD range Slope 1 kinetic range Slope 2 plateau Break 1

Scaling of the spectra  Gyro-structure frequency, Fg computed as a solar wind speed divided by proton thermal gyroradius  This frequency corresponds to a model in which turbulent eddies with dimensions proportional to the proton gyroradius are blown along the spacecraft  The frequency of the Break 2 frequency between MHD and kinetic scales in the quiet solar wind is proportional to Fg  The same holds for the magnetic field fluctuations (calculated from data of Bruno and Trenchi, 2014)  Does this relation conserve in disturbed conditions? green points from Bruno and Trenchi, 2014 Safrankova et al. (ApJ, 2015)

Spectral slopes  A slope of the density spectrum is not universal  This slope is determined (among other parameters) by the density fluctuation level  Larger fluctuations – steeper slopes in both MHD and kinetic ranges  A possible explanation – if the forcing from larger scales exceeds the dissipation rate, the spectrum becomes steeper  Do we see this effect across the interplanetary shocks? Safrankova et al. (ApJ, 2015) Slope 1 Slope 3

Evolution of the spectra across IP shocks Two examples: θ Bn = 67°, Ma = 5,2, β = 0.55, V sh = 704 km/s Δ V = 210 km/s θ Bn = 59°, Ma = 4.5, β = 0.19, V sh = 770 km/s Δ V = 220 km/s October 2, 2013 September 12, 2014  The increase of a fluctuation level by an order of magnitude is very typical but the steepenig of the spectra is not observed or it is weak in the MHD range  Although both shocks are very similar, they affect the spectrum of solar wind turbulence by different ways, especially in the kinetic range  An exponential decay of the spectrum was reported on electron scales in the solar wind (Alexandrova et al., 2012) or on ion scales in the inter-stellar medium (Haverkorn and Spangler, 2013)  Which of these two features are typical for interplanetary shocks?  How the exponential decay can be described?

Mean spectra at IP shocks  Only fast forward shocks were considered!  Although a fluctuation level increases by an order of magnitude, the spectral slope in the MHD scale is conserved – why?  The shift of the spectral break is consistent with changes of the gyro-structure frequency  The exponential decay in the kinetic range is typical in the sheath of the IP shocks – what mechanism can lead to this shape?  This spectral feature lasts for more than 1 hour – what the relaxation time is?  No significant dependence on the shock parameters was found Four randomly chosen shocks (the shock with exponential decay in the upstream region was preceded by another shock ~1 hour before) Mean spectra (all 36 registered shocks) upstream downstream

Analytical description of the exponential decay  The power-law fit is more appropriate in the upstream region, whereas the formula suggested by Spangler and Gwinn (1990) often describes the downstream spectrum well  What mechanism can lead to this shape?  Two different interpretation can be found:  Exponential decay is natural and the linear shape is due to experimental insufficiencies (Howes et al., 2008)  Power law decay is natural and the exponential shape is a consequence of changes of mean parameters during the interval used for spectrum computations (Sahraoui, 2014, AGU Fall Meeting) Pitna et al. (AJ, 2015)

Definition of slopes and breaks  A slope in the MHD range of frequencies is well defined because this part exhibits power- law decay.  For its determination in the kinetic range, we have defined the peak frequency, f p  f p corresponds to the spectral break frequency if the bi-linear fit can be used; we use it as a proxy of the break for spectra with the exponential decay  The slope in the downstream region is calculated in the range 1.3 – 2.6 f p to account for the spectrum curvature Pitna et al. (AJ, 2015)

Scaling of the spectra  All spectra were fitted by bi-power and exponential fits and the errors were estimated for each fit  A majority of the spectra can be fitted by one from these two functions with a reasonable error  If the spectrum can be fitted with a reasonable error either by the bi- linear or by exponential fit, the spectral break follows the dependence that was found in the quiet solar wind  Note that f p refers to the break in the downstream spectrum f g ~ 6.2 f p

Spectral slopes  No clear dependence of the slope 1 (MHD scale) on the magnetic field, plasma parameters and/or their combinations was found, similarly to the solar wind  The decreasing trend of the spectral index with the amplitude of variations is the same as that found in the solar wind in both upstream and downstream regions  Our set of IP shocks suggests that the slope in the kinetic scale is about proportional (?determined) by the gyrostructure frequency, i.e., by the frequency of the spectral break. Pitna et al. (AJ, 2015)

Conclusion - turbulence  The description of the spectral shape with a “plateau”  The spectral slopes are highly variable  A mean slope of ~1.95 (i.e., much steeper than 5/3) was found for the MHD scale, a mean value of 2.5 at the kinetic scale is close to 7/3  The break frequency between a plateau and the kinetic scale increases linearly with the gyrostructure frequency in the solar wind as well as downstream of IP shocks  The same is true for the first break frequency  Frequency spectra downstream of IP shocks exhibit “exponential decay” in the ion kinetic range that was earlier reported at electron scales in the solar wind or at ion scales in the interstellar medium (similarity with our observations).

Ion scales of IP shocks  The ramp width varies by an order of magnitude – from 50 to 400 km  The ramp width is proportional to the ion thermal gyroradius  The suggested scaling with the bulk speed gyroradius corrected to θ BN cannot be applied for subcritical shocks - there are no reflected ions  Shock ramp duration s  Shock speed – 704 km/s  Ramp thickness – 338 km  Ion inertial length – 99.6 km  M A =3.8; M MS =2.4; θ BN =70 o ; β=1.3 Nemecek et al. (GRL, 2013)

Waves associated with the shock ramp  Wave packets adjacent to the IP shock ramp are very typical feature  They are observed in magnetic field as well as in plasma parameters  Their amplitudes can be as high as the shock jump (left) or very small (right) Goncharov et al. (GRL, 2014)

Presence of wave packets Goncharov et al. (GRL, 2014)  In spite of a large separation, the waves observed in Wind magnetic field and Spektr R plasma data are vey similar  The waves are not observed at quasiparallel shocks  Mach number is not important for the wave packet presence

Scaling of wave packets  Wavelengths of waves in upstream and downstream packets are well correlated  Both wave packets would be of the same origin  Wavelengths are correlated with the shock ramp thickness Goncharov et al. (GRL, 2014)

Phase shift of ion moments  Fast measurements of plasma moments facilitate the determination of phase shifts between various quantities  Our analysis reveals that whereas the density and speed vary in phase, the phase shift between density and temperature is about 90 o  MHD approach predicts either positive or negative correlations  It confirms a kinetic origin of these waves Goncharov et al. (GRL, 2014)

Conclusion - shocks  Conclusions are valid for subcritical quasi-perpendicular shocks  The shock ion ramp thickness is directly proportional to the proton thermal gyroradius  The proportionality constant is about 3.9  What is the mechanism of the proton heating on such a small scale?  Our analysis of high-frequency wave packets upstream and downstream of IP shocks shows their direct proportionality to the IP shock ramp thickness, i.e., to the proton thermal gyroradius.  The constants are ~ 2.1 for upstream and ~ 3.6 for downstream  It suggests a kinetic origin of these features  No clear correlation of the wave presence with the Mach number and/or BN angle was found  Phase shift between the density and temperature is ~ 90 o

 Collection of a significantly larger data set  Continuation of the statistical analysis of spectral slopes and investigation of dependences of slopes and break frequencies on other parameters  A deeper study of turbulence in disturbed regions  A further analysis of IP shock (and bow shock) ramps and waves connected with them Directions of further investigations Thank you for your attention

Call for papers Based on very successful session on boundary layers that was held in COSPAR 2014 meeting, the special issue of Advances in Space Research is announced. Short title: Magnetospheric boundaries Submission deadline: March 31, 2015 Acceptance of papers: no later than August 31 Editor: Z. Nemecek No submission fee except for color figures in printed version!