(1) Institute for Space Sciences, Bucharest, Romania(2) Jacobs University Bremen, Bremen, Germany

Costel Bunescu (1, 2), Octav Marghitu (1), Joachim Vogt (2), Adrian Blagau (1)Costel Bunescu (1, 2), Octav Marghitu (1), Joachim Vogt (2), Adrian Blagau (1)

Field-aligned Current Dynamics above the Auroral oval: Method and Cluster Events

MPE Symposium on Auroral Physics and Plasma Boundary Analysis  Garching, 1 – 5 July 2013

Can we use better the 12 years database of Cluster perigee passes in order to study Can we use better the 12 years database of Cluster perigee passes in order to study FAC dynamics?FAC dynamics?

• In particular, make use of the multi-point capabilities of Cluster, used e. g. to In particular, make use of the multi-point capabilities of Cluster, used e. g. to check the AAR potential structure, though not so much to investigate FAC check the AAR potential structure, though not so much to investigate FAC dynamicsdynamics

Proper evaluation of the FAC dynamics may result in better estimates of key Proper evaluation of the FAC dynamics may result in better estimates of key parameters, like Poynting flux, current density, potential drop, field-aligned parameters, like Poynting flux, current density, potential drop, field-aligned conductance / current-voltage relationship.conductance / current-voltage relationship.

FAC dynamics above the AAR is directly related to the generator region in the FAC dynamics above the AAR is directly related to the generator region in the plasma sheet.plasma sheet.

Techniques developed for analyzing FAC structures with Cluster may help multi-Techniques developed for analyzing FAC structures with Cluster may help multi-point investigations with different data sets, like those of the upcoming Swarm point investigations with different data sets, like those of the upcoming Swarm mission.mission.

Motivation

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A.A. Continuous and multi-scale evaluation of key quantites:Continuous and multi-scale evaluation of key quantites:

Time lag (2 satellites)Time lag (2 satellites)

Orientation (MVA, 1 satellite)Orientation (MVA, 1 satellite)

Speed (requires time lag, orientation AND planar structures)Speed (requires time lag, orientation AND planar structures)

B.B. Event study – 1D arcEvent study – 1D arc

Satellite configurationSatellite configuration

Spacecraft and ground dataSpacecraft and ground data

Time lag, orientation and velocityTime lag, orientation and velocity

C.C. Event study – 2D structureEvent study – 2D structure

Satellite configurationSatellite configuration

Spacecraft and ground dataSpacecraft and ground data

Spectral analysisSpectral analysis

Time lag, orientation and velocity derived from Cluster dataTime lag, orientation and velocity derived from Cluster data

Doppler analysis of Cluster and ground dataDoppler analysis of Cluster and ground data

Examination of Cluster 3 / FAST conjunctionExamination of Cluster 3 / FAST conjunction

D.D. Summary and prospectsSummary and prospects

Outline

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Method

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A. Method: Intro

For ideal, planar FAC sheets, the time-lag (2 satellites) and orientation (MVA, 1 satellite) are enough to determine velocity. For locally planar FAC structures one can still derive the normal velocity.

• Locally planar => local radius of curvature (significantly) larger than FAC structure scale.

In order to fully characterize the motion of a 2D FAC structure one needs additional information, e.g. by Doppler analysis of spacecraft and ground data, or by analysis of conjugate satellite data. 5

=t1-t4; l=r1-r4

A. Method: Intro

A typical Cluster crossing above the auroral oval take 0.5–1 h. During this time FACs are, in general, not stationary.

At the same time, magnetic field perturbation, B, includes contributions from a wide range of scales, from very small to very large.

• Also, a specific scale range, like meso-scale (a few 100 km), often includes a set of contributions, as revealed e. g. by the spectral peaks of B.

Challenge: Develop a continuous and multi-scale analysis method, to be used for deriving the time lag, orientation, and velocity of FAC structures.

Inspiration in Soucek et al. (Ann. Geophys., 2004), who developed a two-satellite technique and applied it to magnetopause crossings (~1 min intervals).

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A. Method: Time Lag

Non-stationary, one scale:

• Compute cross-correlation over a sliding window of given width / scale, C (t, ), and take 0 that maximizes C.

Maximum correlation at each tk

Time

Tim

e la

g

Time

Tim

e la

g

Time

Tim

e la

g

Time

Tim

e la

g

Scal

e Non-stationary, multi-scale:

• Compute cross-correlation over a set of sliding windows, covering a range of widths / scales, C (t, , w), and at each time show the histogram over scales, N (t, ).

• The peak value of the histogram, 0, provides a proxy for the time lag.

• The standard deviation provides a proxy for the time lag error. 7

A. Method: Time Lag

Synthetic signals S1, S2:

• S1: 1.5 mHz + 9/10 3.5 mHz

• S2: 1.5 mHz + 2/5 3.5 mHz

• Time shift in phase of 40 s

Time lag of 40 s correctly reproduced.

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A. Method: Time Lag

Synthetic signals S1, S2:

• S1: 1.5 mHz + ½ 3.5 mHz

• S2: 1.5 mHz + ½ 3.2 mHz

• Time shift in phase of 40 s

Narrow peak of the histogram => ‘structure’ behaviour. The time varying time lag changes with a period of ~3300 s, consistent with the beats of S1 and S2, =0.3 mHz.

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A. Method: Orientation Orientation can be investigated similar to the time lag, by computing the minimum variance direction, , over a set of sliding windows, (t, w), and then showing at each time the histogram over scales, N (t, ).

B for a current filament, R=10. White = satellite crossing at 0.5 R. MVA over scale from 0.5R to R.

-40 -20 0 20 40

40

20

0

-20

-40

At distances where the curvature radius becomes larger than the range of scales, MVA provides a locally planar signature.

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Event study -1D arc

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B. Event - 1D: Spacecraft Configuration

Cluster at 3.4 – 3.7 RE altitude, 2-3 MLT 12

FSIM

FSMI

FSIM

B. Event - 1D: Ground / Cluster Magnetic Field

Cluster magnetic data show an upward current region of 5min width observed with time lags of: 3min between C2-C3, 8min between C2-C4 and 5min between C3-C4Ground magnetic data show oscillating B, mainly in N-S component, with periods of ~10min and 6–7 min

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B. Event - 1D: Magnetic Field Spectra

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FSIM

FSMI

C2

C3

C4

Ground: -two peaks at ~10-11 min and ~6-7 min -decrease in peaks intensity towards East (from FSIM to FSMI)

Cluster: - scale range ~1–10 mHz covers all the relevant ULF peaks. - progressive evolution to more intense peaks .

B. Event - 1D: Time Lag

Time lags: t3–t2=2.8min, t4-t2=8min and t4-t3=5.1min

histogram over scales,w=1.7–10 mindt_step= 0.4s1313 scales

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B. Event - 1D: Orientation

High eigenvalue ratio=> planar FAC structures Small eigenvalue ratio => NOT planar FAC structures

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histogram over scales,w=1.7–10 mindt_step= 2s263 scales

B. Event - 1D: Velocity

Small velocity of the planar FAC structure consistent with optical data

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Event -2D structure

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C. Event - 2D: Spacecraft Configuration

Cluster at 3.2 – 3.8 RE altitude, 2–3 MLT C3 / FAST conjunction, FAST at ~2000 km altitude

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Jan. 30, 2005

C1/C4: 00:33–01:18C2: 00:41–01:26C3: 00:49–01:34FAST: 01:12–01:18

TRO = TromsoBJN = Bear IslandHRN = Hornsund

No optical data!

HRN

BJN

TRO

C. Event - 2D: Spacecraft Configuration

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Cluster/Ground conjunction

C4/C1 – KIL 00:45C4/C1 – TRO 00:47 C2 – KIR 00:47 C2 – ABK 00:51

C. Event - 2D: Substorm Context

Observations during late recovery phase. 21

C4/C1 00:47

C4/C1 00:45

C2 00:47

C2 00:51

x, y, z

C. Event - 2D: Ground / Cluster Magnetic Field

B oscillations from sub-auroral latitudes to the polar cap boundary, with period of 4–5 min and amplitude of ~20 nT. The number of oscillations appears to decrease with time. What can this be? 22

x, y, z

C. Event - 2D: Ground / Cluster Magnetic Field

Ground magnetic data show as well oscillating B, in all three components, with period of 7–8 min and amplitude from ~10 nT to ~60nT. Corroborated with the substorm recovery phase, this suggests that at least part of the oscillatory motion is related to omega band like undulations. 23

x, y, z

C. Event - 2D: Particle Data Cluster 1

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C. Event - 2D: Electron Data and Magnetic Field

Upward current regions (negative slope in By) rather well correlated with missing low energy upgoing electrons – reflected by the potential barrier below Cluster.

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C. Event – 2D: Cluster Magnetic Field Spectra

Scale range ~1–7 mHz covers all the relevant ULF peaks. Progressive ‘relaxation’ from several spectral peaks (C4/C1, C2) to one intense peak (C3).

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00:33 – 01:18C1

00:33 – 01:18C4 00:41 – 01:26C2

00:49 – 01:34C3

x, y

C. Event - 2D: Ground spectral analysis

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X

Y

Z

C. Event - 2D: Ground spectral analysis

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X

Y

Z

C. Event – 2D: C4 /ground spectral analysis

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00:45/00:47

00:45 00:47

C. Event – 2D: C2 /ground spectral analysis

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00:47

00:47/00:51

00:51

C. Event – 2D: Cluster /ground spectral analysis

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C4

C1

C2

C3

HOR

BJN

SOR

MAS

C. Event – 2D: Time Lag C4-C1

Negative/positive time lag, = t1–t4, until/after ~00:49, while C1 was ahead / behind, indicates a (small) equatorward component of the motion.

RMS corr.,w = 4.5 min

histogram over scales,w=2.5–10 mindt_step=0.4s1191 scales

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C4C1

C. Event – 2D: Orientation

Small eigenvalue ratio most of the time => NOT planar FAC structures

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histogram over scales,w=2.5–10 mindt_step=2s239 scales

C. Event -2D: Orientation

Eigenvalue ratio increases, on average, with time => the FAC structures become more and more planar with the progress of the recovery phase.

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histogram over scales,w=2.5–10 mindt_step=2s239 scales

C. Event – 2D: Velocity, Planar Assumption

Small equatorward velocity over the auroral oval => errors because of planar assumption difficult to quantify. Additional information is needed in order to investigate the azimuthal motion.

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Two spectral components (?)• Lower frequency decreases abruptly poleward• Higher frequency has much less variation• Doppler shift Cluster / ground (?)

Lower frequency = FLR (?) Higher frequency = omega band undulations (?)

x, y, z

?

C. Event - 2D: Doppler Analysis B

2.5 mHz 3.5 mHz

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HOR

BJN

SOR

MAS

C4

C1

With 20o – 40o, the motion has a moderate equatorward component and 100 – 300 km is reasonably consistent with omega band length scales. In this case the velocity observed on ground is v = gr 0.25 – 0.75 km/s,

consistent as well with typical omega band velocities.

B. Event – 2D: Doppler Analysis

East

sc – gr = 1 mHzVgr = 0.14 km/svC = 15o

mC = 9.7

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C. Event - 2D: C3/FAST Conjunction

The most intense FAC structure observed by C3 => (almost) conjugate with a meso-scale FAC structure observed by FAST. 38

B. Event – 2D: C3/FAST Conjunction

Geometry

• d 100 km; F 0o (Bx By); C –30o (MVA).

• R = d / [2 sin(F – C) / 2] 190 km.

• 0.03 – 0.36 for = 100 – 300 km.39

B. Event - 2D: C3/FAST Conjunction

Velocity

• Assuming equal ionospheric footprints of the FAC sheet thickness:

one obtains for the sheet velocity at Cluster:

• With F 0o, C –30o, vC = 4.7 km/s , vF = 6.6 km/s, vC = 15o, vF = 45o, mC=9.7,

mF = 1.5, TC=100 s, TF = 20 s, =1 (perfect M – I coupling) =>

=> vsh = 2.7 / sin(+30o) = 2.9–5.4 km/s for = 0o – 40o

=> ~0.15 – 0.4 km/s mapped, = 75 – 200 km40

Summary and Prospects

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D. Summary and Prospects

Continuous, multi-scale FAC analysis method, providing time lag and orientation information. For planar structures the method provides also a normal velocity proxy. For 2-D structures additional information is needed in order to derive the velocity, to be obtained e.g. by Doppler analysis of ground data or by conjugate data from another satellite. For the explored event, observed during the late recovery phase of a substorm, omega band like structures appear to ‘relax’ to an undulated FAC sheet on a time scale of ~15 min. Future work could address the mechanism(s) behind the omega bands like structures / auroral undulations (drifting mirror instability?, Kelvin-Helmholtz instability?, electrostatic interchange instability?, relationship to BBF?, …) The method could be used to analyse other Cluster events, ideally also in conjunction with optical data. Swarm data could be analysed as well, once the s/c are launched – perhaps some events conjugate with Cluster.

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Thank youThank you

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A. Method: Orientation Orientation can be investigated similar to the time lag, by computing the minimum variance direction, , over a set of sliding windows, (t, w), and then showing at each time the histogram over scales, N (t, ).

B for a current filament, R=10. White = satellite crossing at 0.5 R. MVA over scale from 0.5R to R.

-40 -20 0 20 40

40

20

0

-20

-40

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