Observational signatures of ULF turbulence

L. RezeauCETP/IPSL/Université Pierre et Marie Curie

F. Sahraoui, D. AttiéCETP/IPSL/CNRS

Question : How ULF turbulence can influence energy and mass

transfers at the magnetopause ?

v

It can create the small scales where micro-physical processes occur potential role for driving reconnection.

~104km

~10 km

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 ?

• 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

Role of the multi-point measurements made by Cluster and Double Star Probe

CLUSTER

Turbulence is very similar in the magnetosheath and at the magnetopause

Cluster 1-STAFF/SC-2002/02/18- 04:58 Cluster 1-STAFF/SC-2001/01/14- 15:05

magnetosheath

magnetopause

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

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

ULF fluctuations in the magnetopause are correlated to upstream activity

DSP

CLUSTER

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

DSP ULF wave power at the magnetopause

1,00E-03

1,00E-02

1,00E-01

1,00E+00

8,00 9,00 10,00 11,00 12,00

Calculated subsolar distance (Re)

Pz

po

wer

at

2 H

z (n

T2/

Hz)

Double Star Probe

Pmsh(nT2)

Solar wind dynamic pressure(nPa)

10-3

10-2

10-1

100

101

102

1 10

CLUSTERThe ULF power is higher when the magnetosphere is compressed

Turbulence in magnetosheath can be an external source of the high wave activity at the magnetopause.

10-6

10-5

10-4

10-3

10-2

10-1

100

10-5 10-4 10-3 10-2 10-1

P*msh

P*max

Wave power normalized to the local magnetic field

•amplification •strong correlation

Magnetopause

Magnetosheath

CLUSTER data

0.0001

0.001

0.01

0.1

1

0.0001 0.001 0.01 0.1 1

power (nT 2̂/Hz) CLUSTER 1 - DSP1 , 2Hz

Pto

t DS

P

Ptot Cluster

Each point is an observation by CLUSTER and DSP at the same time

More power near the front of the magnetopause than on the flanks

DSP

CLUSTER

Interaction of ULF waves coming from the magnetosheath with the magnetopause

Incident fast magnetosonic wave

Trapping of an incident magnetosheath wave [Belmont&Rezeau , 2001]

n

y

z

MAGNETOPAUSE

MAGNETOSPHEREMAGNETOGAINE

kT

2

1

BokikT

nT2

(deg)

x

kt

IncidentFMS

ReflectedAlfven

magnetosheath magnetosphereMP density gradient

Evanescent waves

ReflectedFMS

IncidentFMS

ReflectedAlfvén

The power in the boundary should be higher when the rotation angle is large

Small scales created in the gradient

10-6

10-5

10-4

10-3

10-2

10-1

100

101

0 20 40 60 80 100 120 140 160

(deg)

Strong correlation between wave power and rotation of B at the magnetopause.

•Wave power

•Amplification into the boundary

Amplification of the magnetosheath turbulence increasing with rotation of B

0,1

1

10

100

0 30 60 90 120 150 180

PP

msh

*

*

max

P*max

(deg)

Statistics

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

• 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

Role of the multi-point measurements made by Cluster and Double Star Probe

CLUSTER

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 ?

Turbulence in the solar wind : Data from HEOS in the solar wind (Tu and Marsch, 1995)

k-5/3 law

How can you transform temporal signals in a wave number spectrum ?

In the solar wind : the Taylor’s hypothesis is valid

Fast plasma velocity strong Doppler effect

The calculation of a k spectrum is possible with one spacecraft

VkVplasmaspacecraft k.Vk.V

But spectrum along one single direction

In the magnetosheath

phase velocity of the modes plasma velocity

One must understand better the structure of turbulence to de-Dopplerize the signal

The calculation of a k spectrum from an spectrum is impossible

Two methods : phase differencing, k-filtering

Frequency (Hz)

Phase differencing method (2 spacecraft)

Assuming the wave is mono-k for each Each correlation of two components of the analyzed vector field at two spacecraft brings one informationFor Bx1 and Bx2 : xi

xx

xx eBB

BB 21

*21

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

).( 12 rrk xGives the projection of k along the separation vector

K-filtering techniqueCLUSTER

B1

B2

B3

B4

(Pinçon and Lefeuvre, 1991)

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

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)

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 :

Identification of wave modes

kz

kx

ky

kz1

kz2 kz23. for each kz plane containing a

significant maximum, the (kx,ky) isocontours of P(sc,kx,ky,kz) and f(sc,kx,ky,kz)=0 are then superimposed

1. the spatial energy distribution is calculated: P(sc,kx,ky,kz)

2. the theoretical linear dispersion relations are calculated and Doppler shifted: f(sc,kx,ky,kz)=0

Ex: Alfvén mode: sc-kz VA=k.v

For each sc:

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:

1. Relative homogeneity /Stationarity

2. Spatial Aliasing effect ( > spacecraft separation)

(Neubauer & Glassmeier, 1990)

Two satellites cannot distinguish between k1 and k2 if : k.r12= 2n

Application to Cluster magnetic data

Magnetosheath (FGM-18/02/2002)

Limit imposed by the Cluster minimum separation d~100 km:

max~kmaxv ~ 2 v /min~ 2 v /d

In the magnetosheath: v ~200 km/s

fmax ~ 2Hz !

cpthkv //

cp

k(max)

instability

(Sahraoui et al., Ann., 2004)

Mirror mode identification

Mirror : fsat~ 0.3fci ; fplasma~ 0

ko~0.0039 rd/km; (ko,Bo) = 81°

The energy of the spectrum is injected by a mirror instability well described by the linear kinetic theory

ko~0.3~ k(max)

Linear kinetic theory instability if

11

//TT

measurements: 4;28.01//

T

T

f0 = 0.11Hz

fci=0.33Hz

fci~0.33Hz

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.

Mirror: f1~ fci; fplasma~ 0

k1 ~ 3ko ; (k1,Bo) = 82°

f1=0.37Hzfo=0.11Hz

Mirror : fo= 0.11Hz ; fplasma~ 0

ko~0.3~ k(max); (ko,Bo) = 81°

Mirror: f2~ 4 fci; fplasma~ 0

k2 ~ 10ko ; (k2,Bo) = 86°

f2 = 1.32Hz

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

v

nB0

Calculation of integrated k-spectra

First direct determination of a fully 3-D k-spectra in space: it evidences an anistropic behaviour

(v,n) ~ 104° (v,Bo,) ~ 110° (n,Bo) ~ 81°

Energy distribution of the identified mirror structures along :

B0 n v

),k,kP(k)P(k,knk

nvv //

//

Integration over the spectra:

• Over frequencies :

• Over directions :

scf

sc,fPP )()( kk

Li~1800km Ls~150km

We observe a cascade along v on the mirror mode :

B2~kv-8/3

Steeper slope than in all MHD theories

(Sahraoui et al., submitted to PRL)

fsc-7/3 temporal signature in the satellite frame of kv

-8/3 spatial cascade

Comparison of temporal and spatial spectra

• 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

Main results of the analysis of magnetosheath turbulence :

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 (Lv~1800 km) up to 150 km with a new law kv-8/3

Conclusion : towards a model ?

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 …

Magnetosheath Magnetopause

?