1. Исследование широкополосной ELF турбулентности по данным спутника FAST И.В. Головчанская, Б.В. Козелов, И.В. Дэспирак Полярный геофизический институт

2. The Fast Auroral SnapshoT Launched 21 August 1996 into a 4175 × 350 km orbit with 83° inclination. FAST was equipped with a complete instrument suite for high- resolution in situ studies of auroral physics, including electron and ion electrostatic analyzers, ion mass spectrometer, and electric and magnetic field sensors. dc electric fields were sampled with a rate 125 s -1 in the survey mode, 500-2000 s -1 in the normal mode, and 2·10 6 s -1 in the burst mode..

3. Event of the BBELF turbulence observed by FAST in the morning side cleft Figure 1 (from [Chaston et al., 1999]) 1: detrended E  to B 0 and  to sc trajectory; 2: magnetic field (f > 1Hz)  to B 0,  to E from the fluxgate magnetometer; 3: electric field PSD up to 16 kHz; 4: n e from the Langmuir probe; 5: field-aligned Poynting flux from 3D E, B (positive downward). Overplotted is electron energy downward flux *10; 6: electron energy flux versus energy; 7: electron energy flux versus pitch-angle; 8: ion energy flux versus energy; 9: ion energy flux versus pitch-angle;

4. Event of the BBELF turbulence observed by FAST in the near-midnight auroral zone Figure 2 (from [Ergun et al., 1998]) 1: E (nearly S-N) in the band 1 Hz < f < 10 Hz; 2: E (nearly S-N) in the band 1 Hz < f < 4 kHz; 3: B (nearly E-W); the negative/positive slope indicates j || up/down; 4: high-frequency PSD of the electric field; the white line is the electron cyclotron frequency; 5: low-frequency PSD of the electric field; the white line is the H + cyclotron frequency; 6: electron energy flux versus energy; 7: electron energy flux versus pitch-angle; fluxes near 180° are up-going; those near 0° and 360 ° are down-going; 8: ion energy flux versus energy; 9: ion energy flux versus pitch-angle;

5. Figure 3 BUT: application of standard spectral methods (FFT, windowed FFT) to strongly non- stationary BBELF signals resulted in diverse spectra and biased spectral indices. BBELF emissions were called ‘turbulence’ based on power law distributions in frequency, E 2 ~ f - 

6. Early attempts to interpret the BBELF spectra in terms of Iroshnikov-Kraichnen model of 2D hydrodynamic turbulence Figure 4 (from [Kintner and Seyler, 1985]) Interpretation of the two-slope power law spectrum of the ionospheric electric fields by the direct enstrophy cascade and inverse energy cascade in the early works, where α 1 was expected to be ~ -3. Later, α 1 = -3 was not confirmed. Extrapolation of the two curves suggests the scale of energy pumping into the system of a few tens of km.

7. Application of wavelet analysis and larger statistics allowed more reliable estimating of turbulence scaling indices Figure 5 (from [Golovchanskaya and Kozelov, 2010]) Scaling indices α 1 and α 2 of the BB ULF-ELF turbulence derived by Abry et al. [2000] technique from Dynamics Explorer 2 electric field measurements in the auroral zone (a) and polar cap (b). Confidence intervals are estimated with a bootstrap procedure. BUT: low sampling rate of DE2 (16 s -1 or 500 m) did not enable to determine the lower bound of the scaling regime with α 1 ~ 2.

8. We have done this by FAST electric field measurements sampled at 500 s -1 (14 m). Figure 6. Samples of despun electric fields (middle) observed by FAST in the passes through the auroral region (left) and their logscale diagrams (right).

9. The results of the analysis over 16 events at altitudes 700-2500 km indicate α ~ 2 down to scales 100-900 m Figure 7. Comparison of the scaling regime over 100 m to 2 km derived from FAST observations (a) and over 1-32 km obtained from DE-2 data (b).

10. Now a prevailing view is that the BBELF turbulence is somehow related to the inertial Alfvén waves (IAWs) [Goertz and Boswell, 1979]. In the linear description of the IAWs: - the dispersion relation is - the ratio of the perpendicular to B 0 electric and magnetic perturbations is - the ratio of the parallel and perpendicular electric perturbations is - this yields the purely electrostatic wave for k  λ e >>1 The characteristic scale length for the IAWs is the electron inertial length, where the electron plasma frequency is In calculations we used, where n e is in cm -3

11. We tested the behavior of LDs around λ e and found some relationship between the scale length λ break, where the α 1 ~ 2 scaling regime terminates, and λ e. Figure 8. λ break versus λ e for sixteen events of BBELF turbulence observed by FAST.

12. If one considers the α 1 ~ 2 scaling regime to indicate the direct cascade of Alfvén wave energy to smaller scales, the dissipation scale could be expected near ~ λ e, meaning the parallel electron heating at λ e as a dissipation mechanism [e.g., Kletzing, 1994]. But: in no case an expected steepening in LDs around λ e was found. On the contrary, starting from λ e toward smaller scales we could always see shallowing in LDs. Previously, from rocket data, Earle and Kelly [1993] reported on the plateau in the spectra of turbulent electric fields at scale ~ 100 m and identified it as the scale of energy pumping into the system. Figure 9 Shallowing of the LD slope at scales smaller than λ e.

13. We note that the leading theories also predict the inverse cascade of energy in the considered range of scales. The cascade is related to the interaction of coherent (i.e., non-propagating) structures that form in result of non-linear dynamics of the inertial Alfvén waves. The coherent structures may be of electrostatic type, such as convective cells proposed by Dubinin et al., 1988; Volokitin and Dubinin, 1989; Pokhotelov et al., 2003 for interpretation of the observed vortex patterns [e.g., Chmyrev et al., 1988]. Figure 10 Vortex patterns of the perturbations on different scales observed by ICB-1300 (from [Dubinin et al., 1988]).

14. Or magnetostatic type (current filaments) [e.g., Chang et al., 2004]

15. Conclusions By FAST high-resolution measurements of dc electric fields in sixteen events of the BBELF turbulence it is demonstrated that 1.BBELF turbulence at scales < 2 km is characterized by scaling index α = 1.9 ±0.3. 2.Within the confidence interval this value of α is coincident with that reported for scales 1-32 km from Dynamics Explorer 2 observations. 3.The α ~ 2 scaling regime extends down to scales the order of λ e. 4.At scales smaller than λ e, shallowing of LDs is observed. This implies that λ e is not the dissipation scale for the BBELF turbulence. This is also an indirect evidence for the inverse turbulent cascade in the considered range of scales.