Transcript Golovchanskaya

Исследование широкополосной ELF турбулентности
по данным спутника FAST
И.В. Головчанская, Б.В. Козелов, И.В. Дэспирак
Полярный геофизический институт
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 highresolution 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 2·106 s-1 in the burst
mode..
Event of the BBELF turbulence observed by FAST in the morning side cleft
Figure 1 (from [Chaston et al., 1999])
1: detrended E to B0
and  to sc trajectory;
2: magnetic field (f > 1Hz)  to B0,  to E
from the fluxgate magnetometer;
3: electric field PSD up to 16 kHz;
4: ne 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;
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;
BBELF emissions were called ‘turbulence’ based on power law distributions in frequency,
E2 ~ f -
Figure 3
BUT: application of standard spectral methods (FFT, windowed FFT) to strongly nonstationary BBELF signals resulted in diverse spectra and biased spectral indices.
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 α1 was expected to be
~ -3. Later, α1 = -3 was not
confirmed.
Extrapolation of the two curves
suggests the scale of energy
pumping into the system of a few
tens of km.
Application of wavelet analysis and larger statistics allowed more reliable
estimating of turbulence scaling indices
Figure 5 (from [Golovchanskaya and Kozelov, 2010])
Scaling indices α1 and α2 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 α1 ~ 2.
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).
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).
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 B0 electric and magnetic perturbations is
- the ratio of the parallel and perpendicular
electric perturbations is
- this yields the purely electrostatic wave
for k λe>>1
2 
k||2v A2
1  k2 2e
E
 vA (1  k22e )1 / 2
B
E||
k||k  2e

E 1  k 2 2e
E|| k||

E  k 
The characteristic scale length for the IAWs is the electron inertial length
1/ 2
c
 4ne e 2 
e 

, where the electron plasma frequency is  pe  
 pe
In calculations we used
 me 
5km
e  1 / 2 , where ne is in cm-3
ne
We tested the behavior of LDs around λe and found some relationship between
the scale length λbreak, where the α1 ~ 2 scaling regime terminates, and λe.
Figure 8. λbreak versus λe for sixteen events of BBELF turbulence observed by FAST.
If one considers the α1 ~ 2 scaling regime to indicate the direct cascade of Alfvén wave
energy to smaller scales, the dissipation scale could be expected near ~ λe, meaning
the parallel electron heating at λe as a dissipation mechanism [e.g., Kletzing, 1994].
But: in no case an expected steepening in LDs around λe was found. On the contrary,
starting from λe toward smaller scales we could always see shallowing in LDs.
Figure 9 Shallowing of the LD slope at scales smaller than λe.
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.
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]).
Or magnetostatic type (current filaments) [e.g., Chang et al., 2004]
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 λe.
4.
At scales smaller than λe, shallowing of LDs is observed. This implies that λe 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.