Flow driven instabilities in the Earth's Magnetotail

1. Flow driven instabilities in the Earth's Magnetotail Including an IntroductiontoMagnetospheresandMagnetotails Martin Volwerk Space Research Institute Austrian AcademyofSciences

2. All you need to know in 45 min. • Introduction to magnetospheres • Solar wind – Earth magnetic field interaction • Generation of magnetotail • Magnetosphere dynamics • Reconnection and magnetic field transport • Magnetic flow cycles • The Cluster mission • Instabilities in the magnetotail • A zoo of large scale instabilities • Plasma dynamics in fast flows • Small scale instabilities

3. Let‘sgetstarted! 让我们开始！

4. Introduction to Magnetospheres Water flow around a rock

5. Closed Magnetosphere • Schematic view of a magnetically closed magnetosphere, cut in the noon-midnight meridian plane • The solar wind plasma has no magnetic field • A sharp boundary between the different plasmas

6. Earth's Magnetosphere • Solar wind/IMF cannot enter magnetosphere • Supersonic stream decelerated at bow shock • Magnetopause is boundary between two plasma populations • Magnetosheath: solar wind plasma behind the bow shock

7. Open Magnetosphere • Schematic representation of a magnetically open magnetosphere cut in noon-midnight meridian plane • Solar wind is magnetized and can enter the magnetosphere • Reconnection at the nose connects dipole with solar wind field lines • Tailward transport builds up the magnetotail

8. The Dungey Cycle • Magnetospheric dynamics associated with the Dungey cycle driven by the solar wind. • The numbers show the time sequence for a flux tube being reconnected at the dayside magnetopause and convected through the magnetosphere. Bottom: view in the equatorial plane.

9. Magnetospheric convection magnetic reconnection magnetotail nightside dayside

10. Plasma Sources for the M’sphere • The shaded, dotted area illustrates the boundary layer through which solar wind plasma enters the magnetosphere. • The largest component is H+ which can come from ionosphere or solar wind • The O+ component comes from the ionosphere • He is + in ionosphere but ++ in solar wind

11. Aurora observation Space Shuttle (Height: 380 km) Ground-based observation • Auroral substorm: consist of complex transient and localized structures • Auroraprecipitation caused by energy conversion process in the night-side magnetosphere (magnetotail) Satellite image (Height: >40000 km)

12. Recent Magnetotail Missions • Geotail (1995 – present) • EquatorS (1997-1998) • Cluster (2001- present)4-spacecraft separation 200 ~10000km • Double Star (2004-2007)1-equator, 1-polar • THEMIS (2007-present)5-spacecraft separation > 6,000km • MMS (to be launched 2014)4-spacecraftseparation few10s~1000km Magnetotail Cluster THEMIS 2001- 2006 2007-

13. Multi-point observation (two-points) • Difference in observed parameter at A & B In linear case: For steady state, ∂/∂t=0 (& 1D structure) : • Simultaneous observations at different point (t=0)  spatial gradient (Gradient analysis) • Same values at different points at different times (Dt=0)  motion (v) of the signatures (Timing analysis)

14. Multi-point observation (two-points) • Difference in observed parameter at A & B In linear case: For steady state, ∂/∂t=0 (& 1D structure) : • Simultaneous observations at different point (t=0)  spatial gradient (Gradient analysis) • Same values at different points at different times (Dt=0)  motion (v) of the signatures (Timing analysis)

15. Multi-point observation (two-points) • Difference in observed parameter at A & B In linear case: For steady state, ∂/∂t=0 (& 1D structure) : • Simultaneous observations at different points (t=0)  spatial gradient (Gradient analysis) • Same values at different points at different times (Dt=0)  motion (v) of the signatures (Timing analysis)

16. Cluster: Why four spacecraft ? • Spatial gradient: • Current density (∇xB; ‘curlometer’) • Magnetic field curvature, b·∇b • Plasma (flow) structure • Characterization of a planar boundary • Orientation & motion of boundary • Thickness & internal structure • Four single-point observations(in four different plasma domains) Minimum number of spacecraft required to determine spatial gradient or velocity vector of a planar structure in 3D space is four

17. Transient thin current sheet (Nakamura et al., 2006) Current sheet thickness determined sequentially from model fitting (Harris current sheet) Bx = B0tanh{(z-z0)/L} Sudden thinning (L: 5000⇨500 km) associated with fast flows Off-equator peaked (bifurcated) current sheet Bifurcated thin current sheetnear reconnection region and more often during fast flows

18. Near-Earth tail dynamics field-alignedcurrent near-Earth reconnection Fast plasma flow Aurora ? ? Key process: Reconnection at near-Earth thin current sheet Localized & bursty plasma flows Interaction of the plasma flows with Earth’s dipole field field aligned current & aurora

19. PossibleOscillationsoftheTail Sausage Mode Kink Mode Flapping Mode Large Scale Mode

20. Which Instabilities? • Eigenoscillations of the plasma sheet: • Roberts, 1981a, 1981b Wave propagation in a magnetically structured atmosphere, I, Surface waves at a magnetic interface; II, Waves in a magnetic slab • Lee et al., 1988Streaming sausage, kink and tearing instabilities in a current sheet with applications to the Earth’s magnetotail • Seboldt, 1990Nonlocal analysis of low-frequency waves in the plasma sheet • Smith et al., 1997Magnetoacoustic wave propagation in current sheets • Louarn et al., 2004On the propagation of low-frequency fluctuations in the plasma sheet: 1. Cluster observations and magnetohydrodynamic analysis • Fruit et al., 2004On the propagation of low-frequency fluctuations in the plasma sheet: 2. Characterization of the MHD eigenmodes and physical implications • Erkaev et al., 2009MDH model of the flapping motions in the magnetotail current sheet • In the next part we will look at: • Kink I • Sausage - Large scale • KHI • Flapping • Wavy current sheet • Dipolarization and plasma heating

21. Kink-mode Oscillation I 22 August 2001 • Oscillations of the current sheet observed by Cluster [Volwerk et al., 2003] • Before substorm onset, a thin current sheet moves with a velocity of 10 km/s in Z • After substorm onset the current sheet thickens and moves with greater velocity, 25 km/s in Z • Driven magnetoacoustic wave, different values for current sheet half thickness and velocity before and after substorm onset [Smith et al., 1997]

22. Kink-mode Oscillation II • One significant difference with Smith et al.: • ω = 2.5 × 10-3 s-1 is smaller than the limit set on the frequency for an eigenmode oscillation • fmin ≈ 0.462 vA,e/λ ≈ 0.29 s-1vA,e is the Alfvén velocity in the lobe • not dealing with an eigenmode of the current sheet, but with an oscillation driven by the strong flow in the current sheet. • Indeed, when we compare the oscillation and the strong earthward flow we find that both span the same time period. • The damping of the kink mode is over a timescale of the observed oscillation itself • The mean period of oscillation ~ 800 sec. • In model we have used γ = 1/800 s-1 • The current sheet half thickness λ changes on the damping time with exponential growth rate of ~1 RE in 13 minutes (780 sec.).

23. Large-Scale Oscillation I 12 August 2001 • A different kind of flow-driven event • A strong Earthward flow burst • Strong increase in T at flow start • Followed by a strong decrease in B for ~15 min • Then a slow “oscillatory” recovery of the tail takes place

24. Large-Scale Oscillation II • Seboldt [1990]: low-frequency wave modes using the basic MHD equations with a polytropic pressure • Symmetric mode: • period of oscillation: Tosc ≈ 20 min → fosc ≈ 0.8 mHz • close to frequency of first harmonic f1 ≈ 0.5 mHz, finetuning gives ~0.8 • Rapid flux transport event measured by Cluster • The signatures of the flow vx and the magnetic field Bz are in agreement with flux transport calculated with Maxwell’s equations and with the drop in Bx resulting from it • After flux transfer event, Cluster in a magnetic field evacuated region of the magnetotail, where the surrounding magnetic field is held off by the large plasma pressure • transient situation of the tail, in which the plasma pressure keeps off the magnetic field of the lobe • magnetic field returns to the evacuated region and tries to establish a new stable configuration, which results in a damped oscillating motion of the magnetic field. The period of this oscillating motion fits well with the periods obtained in theory by Seboldt [1990].

25. Kelvin-Helmholtz Oscillation I 14 August 2004 • Cluster and DoubleStar in the current sheet • A strong flow burst observed (differently) at both spacecraft • Large oscillations in the magnetic field appear at start of flow • Timing analysis gives phase velocity of ~250 km/s, half the flow velocity

26. Kelvin-Helmholtz Oscillation II • Observation of KH waves in the current sheet proper • Cluster moves into the current sheet, increasing amplitude [Ferrari et al., 1981] • TC1 observes same waves at higher amplitude, exponential growth • Works well for amplitude • Energy conversion gives ∆vflow ≈ 60 km/s • With amplitude in current sheet larger (Cluster), KHI could be a significant source of flow braking • Unfortunately no TC1 data deeper in current sheet

27. Magnetotail Flapping I • Sergeev et al. [1998,2004] and Runov et al. [2005] • large-scale kink-like waves propagating from the tail center toward flanks • Propagation velocities are in the range of several tens km/s for the locally quiet sheets, and up to 200 km/s during fast flows • Of internal origin and that kink-like waves are emitted in the central part of the tail by some impulsive source • The wave properties do not match any local excitation mechanism previously discussed so far in the literature

28. Magnetotail Flapping II • Zhang et al. [2005] found a wavy-twisted current sheet and strong flapping motion • Combining Cluster and DS data, flapping fits well • Volwerk et al. [2008] showed: • Cross-correlating C&TC1 shows best time-shift: 78 s. • Phase differencing k ≈ (1.05;1,17; 0,40)RE-1 • αfront-CTC ≈ 7.5˚ • ∆ ≈ 0.62RE • With 78 s → v ≈ 50 km/s • slightly higher than Zhang et al.’s average 36 km/s. • Double-gradient model [Erkaev et al., 2009] seems to work

29. New kindofflapping? • Wavycurrentsheet • Veryharmonicwaves • Movingtowardsthecentreofthetail

30. Fast Flow & Dipolarization I • Fast flows (BBFs) dipolarize the tail • Is there a difference in the plasma before and after? • Fast flows develop as they travel along the tail • Is there a difference in the plasma before and after? • Dipolarization: • Field turns from x in z • Assumed: • T increases • n decreases • Two great PhD students! • Schmid et al. [2011, 2014] • Wu et al [2013a,b]

31. Fast Flow & Dipolarization II • Behind DF • Fermi acceleration for T↓ and n↑ • Different categories of DF • For β > 1 • T↑ and n↓ • T↓ and n↑ • Behind DF • Betatron acceleration for T↑ and n↓

32. Fast Flow & Dipolarization III • Electron energization at the dipolarization • In the far tail, Themis B (-20 Re) and C (-17 Re) • Betatron acceleration most important • Cigar like distribution • In the near tail, Themis D & E (-11 Re) • Fermi acceleration most important • Pancake distribution • No contradiction with Schmid et al. • Both kinds are present

33. Fast Flow & Plasma Temperature I • Quiescent magnetotail plasma is basically isotropic • T⊥≈ T∥ • Plasma during BBF is strongly anisotropic • T⊥>T∥ >1 • Mirror mode instability • Proton Cyclotron instability • T⊥>T∥< 1 • Parallel fire hose • Oblique fire hose

34. Fast Flow & Plasma Temperature II • Near Earth X< 14 Re • Tail

35. Conclusions • The interactionbetweenthe solar wind andtheEarth‘sinternalmagneticfieldcreates a (dynamic) magnetotail • Manyofthetheoreticallyproposedoscillationscanactuallybefound in e.g. the Cluster data • Some „unexpected“ behaviour (e.g. theflapping) ledtomoretheoreticalmodelingand subsequent testingofthemodels • Simultaneous multi-pointmeasurements in spacephysicsarenow „a must.“ • Manymorepearlsaretobefound in the Cluster data: • Both in eventstudies • And in statisticalstudies • http://caa.estec.esa.int/caa/home.xml • http://www.iwf.oeaw.ac.at/eclat/

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