Observational signatures of ULF turbulence

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Observational signatures of ULF turbulence

• L. RezeauCETP/IPSL/Université Pierre et Marie
  CurieF. Sahraoui, D. Attié
• CETP/IPSL/CNRS

2
Question How ULF turbulence can influence
energy and mass transfers at the magnetopause ?
104km
10 km
It can create the small scales where
micro-physical processes occur ? potential role
for driving reconnection.
3
ULF turbulence is also observed in the nearby
magnetosheath
Is the ULF turbulence observed at the
magnetopause generated locally or is it a product
of the magnetoseath turbulence ?

• Local instability ?
• External source ?

What do we know about its role for driving
reconnection ?
4

• Observational arguments in favor of an external
  source
• Analysis of the magnetosheath turbulence
• Mode identification
• Integrated k-spectra
• Role of the Doppler shift
• Possible model

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Turbulence is very similar in the magnetosheath
and at the magnetopause
Cluster 1-STAFF/SC-2002/02/18- 0458
Cluster 1-STAFF/SC-2001/01/14- 1505
magnetopause
magnetosheath

• Power higher at the magnetopause
• Similar specral law
• Less steep slope at the magnetopause

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The magnetic spectrum goes down with a similar
slope to a frequency around low-hybrid frequency

• FGM
• Staff SC
• Staff SA

Sensitivity of magnetic antenna
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ULF fluctuations in the magnetopause are
correlated to upstream activity
DSP
CLUSTER

• DSP near the subsolar point
• CLUSTER far from the subsolar point

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Double Star Probe
The ULF power is higher when the magnetosphere is
compressed
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Wave power normalized to the local magnetic field
CLUSTER data
Magnetopause

• amplification
• strong correlation

Magnetosheath
Turbulence in magnetosheath can be an external
source of the high wave activity at the
magnetopause.
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More power near the front of the magnetopause
than on the flanks
DSP
Each point is an observation by CLUSTER and DSP
at the same time
CLUSTER
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Interaction of ULF waves coming from the
magnetosheath with the magnetopause
Trapping of an incident magnetosheath wave
BelmontRezeau , 2001
z
y
ki
kT
kT
n
MAGNETOSPHERE
MAGNETOGAINE
MAGNETOPAUSE
Incident fast magnetosonic wave
The power in the boundary should be higher when
the rotation angle is large
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Statistics

• Wave power

Strong correlation between wave power and
rotation of B at the magnetopause.
Pmax
? (deg)

• Amplification into the boundary

Amplification of the magnetosheath turbulence
increasing with rotation of B
? (deg)
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ULF large scale fluctuations observed in the
magnetosheath could

• Be the source of the turbulence observed at the
  magnetopause
• Cascade to small scale fluctuations when trapped
  in the magnetopause

The model is not fully realistic and should be
adapted to the observations made by Cluster
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• Observational arguments in favor of an external
  source
• Analysis of the magnetosheath turbulence
• Mode identification
• Integrated k-spectra
• Role of the Doppler shift
• Possible model

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Analysis of the turbulence observed in the
magnetosheath by CLUSTER
Measurements provide temporal spectra
B2?sc-7/3
Is it possible to obtain a wave-number spectrum
from this frequency spectrum ?
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Turbulence in the solar wind Data from HEOS in
the solar wind (Tu and Marsch, 1995)
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In the solar wind the Taylors hypothesis is
valid

• Fast plasma velocity ? strong Doppler effect

• The calculation of a k spectrum is possible with
  one spacecraft

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In the magnetosheath

• phase velocity of the modes ? plasma velocity

? The calculation of a k spectrum from an w
spectrum is impossible
Frequency (Hz)
? One must understand better the structure of
turbulence to de-Dopplerize the signal
Two methods phase differencing, k-filtering
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Phase differencing method (2 spacecraft)
Assuming the wave is mono-k for each w Each
correlation of two components of the analyzed
vector field at two spacecraft brings one
information For Bx1 and Bx2

• No test of the mono-k hypothesis from this only
  correlation
• Different k obtained from different correlations
• No use of cross-correlations

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Estimation of the energy distribution function of
the waves in (w,k) space
P(w,k)

• Use of the global correlation matrix
• Allows to take into account theoretical
  constraints

Only hypothesis the analyzed fluctuations are
sufficiently homogeneous and stationary ? can
be applied to magnetosheath not to magnetopause
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Non linear method of the maximum likelihood
type, based on filters depending on the data (but
transparent for mono-k waves)
More numerous the correlations are, more
trustable is the estimate of the energy
distribution in k space

• Works quite well with the 3 component B field
  (with constraint ?.(B)0)
• Is improved when including the two components of
  E (and the corresponding Faraday law as an
  extra-constraint). (Tjulin et al, 2005)

• Has been validated by numerical simulations
  (Pinçon et al, 1991)
• Applied for the first time to real data with
  CLUSTER (Sahraoui et al., 2003)

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Identification of wave modes
For each wsc

• the spatial energy distribution is calculated
  P(wsc,kx,ky,kz)

• the theoretical linear dispersion relations are
  calculated and Doppler shifted f(wsc,kx,ky,kz)0
• Ex Alfvén mode wsc-kz VAk.v

• for each kz plane containing a significant
  maximum, the (kx,ky) isocontours of
  P(wsc,kx,ky,kz) and f(wsc,kx,ky,kz)0 are then
  superimposed

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Limits of validity of the k-filtering method
Generic to all techniques intending to correlate
fluctuations from a finite number of points.
Two main points to be careful with

• Relative homogeneity /Stationarity
• Spatial Aliasing effect (l gt spacecraft
  separation)

Two satellites cannot distinguish between k1 and
k2 if ?k.r12 2?n
(Neubauer Glassmeier, 1990)
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Application to Cluster magnetic data
Magnetosheath (FGM-18/02/2002)
?
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Mirror mode identification
The energy of the spectrum is injected by a
mirror instability well described by the linear
kinetic theory
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Study of higher frequencies
Observation of mirror structures over a wide
range of frequencies in the satellite frame, but
all are stationary in the plasma frame.
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Role of Doppler shift

• All the observed mirror modes have different
  (low) frequencies in the spacecraft frame but
  they have a zero frequency in the plasma frame.
• A statistical study performed by Lacombe et al
  shows that the power at 11 Hz is correlated to
  the plasma velocity in the magnetosheath. It is
  an indication that the fluctuations observed at
  11Hz are also Doppler-shifted waves.
• The limitation in the frequencies that can be
  studied by Cluster prevents from testing directly
  this result. MMS

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Calculation of integrated k-spectra
(v,n) 104 (v,Bo,) 110 (n,Bo) 81
Energy distribution of the identified mirror
structures along
B0
n
v
First direct determination of a fully 3-D
k-spectra in space it evidences an anistropic
behaviour
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Integration over the spectra

• Over frequencies
• Over directions

(Sahraoui et al., submitted to PRL)
We observe a cascade along v on the mirror mode
B2kv-8/3 Steeper slope than in all MHD theories
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Comparison of temporal and spatial spectra
fsc-7/3 temporal signature in the satellite frame
of kv-8/3 spatial cascade
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Main results of the analysis of magnetosheath
turbulence

• Linear mirror modes have been identified in the
  magnetosheath turbulence
• They are likely to cascade to smaller scales
• Doppler shift has a significant contribution in
  the resulting slope of the spectra

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Conclusion towards a model ?

• The magnetosheath is likely to be the source of
  the magnetopause turbulence
• First 3-D k-spectrum evidence of strong
  anisotropies (Bo, v, n)
• Evidence of a 1-D direct cascade of mirror
  structures from an injection scale (Lv1800 km)
  up to 150 km with a new law kv-8/3

• Main consequences
• A Turbulence theory is necessary to understand
  the non-linear cascade.
• Necessity to explore much smaller scales to reach
  the reconnection scales? MMS (2010?)

• Open questions
• How are the magnetopause small scales generated ?
  Do they result of local cascade or are they
  coming from the magnetosheath
• How can the new law be used in reconnection
  models ? open

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Magnetosheath
Magnetopause
?