1. Flow driven instabilities in the Earth's Magnetotail Martin Volwerk Space Research Institute Austrian Academy of Sciences Including an Introduction to Magnetospheres and Magnetotails

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‘s get started! 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. dayside nightside magnetic reconnection Magnetospheric convection magnetotail

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  Auroral substorm: consist of complex transient and localized structures  Aurora precipitation caused by energy conversion process in the night-side magnetosphere (magnetotail) Ground-based observation Satellite image (Height: >40000 km) Space Shuttle (Height: 380 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-spacecraft separation few10s~1000km Magnetotail 2007- 2001- 2006 Cluster THEMIS

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

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

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

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  Current sheet thickness determined sequentially from model fitting (Harris current sheet)  B x = B 0 tanh{(z-z 0 )/L}  Sudden thinning (L: 5000⇨500 km) associated with fast flows  Off-equator peaked (bifurcated) current sheet  Bifurcated thin current sheet near reconnection region and more often during fast flows (Nakamura et al., 2006)

18. Thin current sheet in ion diffusion region  First curlometer measurement of Hall current & its closure current detected at ion scale (0.9-1.1) c/ω pi current sheet  Hall-effect well resolved by Cluster multi-point measurements  Reconnection current sheet with guide field  Electron distribution and remote obs. of Hall current system J V ion V elec. electron demagnetized (electron diffusion) ion demagnetized (ion diffusion) ? c/  p i V i =0.5 V Ai, j x =34nA/m 2  V e =1.7V Ai Cluster Fast crossing  s

19. Near-Earth tail dynamics 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 ? field-aligned current Fast plasma flow near-Earth reconnection ? Aurora

20. Possible Oscillations of the Tail Kink Mode Sausage Mode Large Scale Mode Flapping Mode

21. 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., 1988 Streaming sausage, kink and tearing instabilities in a current sheet with applications to the Earth’s magnetotail  Seboldt, 1990 Nonlocal analysis of low-frequency waves in the plasma sheet  Smith et al., 1997 Magnetoacoustic wave propagation in current sheets  Louarn et al., 2004 On the propagation of low-frequency fluctuations in the plasma sheet: 1. Cluster observations and magnetohydrodynamic analysis  Fruit et al., 2004 On the propagation of low-frequency fluctuations in the plasma sheet: 2. Characterization of the MHD eigenmodes and physical implications  Erkaev et al., 2009 MDH 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

22. Kink-mode Oscillation I  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 August 2001

23. 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  f min ≈ 0.462 v A,e /λ ≈ 0.29 s -1 v A,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 R E in 13 minutes (780 sec.).

24. Large-Scale Oscillation I  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 12 August 2001

25. Large-Scale Oscillation II  Seboldt [1990]: low-frequency wave modes using the basic MHD equations with a polytropic pressure  Symmetric mode:  period of oscillation: T osc ≈ 20 min → f osc ≈ 0.8 mHz  close to frequency of first harmonic f 1 ≈ 0.5 mHz, finetuning gives ~0.8  Rapid flux transport event measured by Cluster  The signatures of the flow v x and the magnetic field Bz are in agreement with flux transport calculated with Maxwell’s equations and with the drop in B x 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].

26. Kelvin-Helmholtz Oscillation I  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 14 August 2004

27. 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 ∆v flow ≈ 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

28. Another Kink Mode I  Nakamura et al. [2009]  Evolution of dipolarization and associated disturbances  Multiple intensifications in electrojet and Pi2  Multiple Bz enhancements, dipolarizations at onsets  During the strong flows between 0906 and 0909 UT strong oscillation of the current sheet  A closer look: 2007 so spacecraft separation is large 10000 km (C3-C4 tens of km) 27 October 2007

29. Another Kink Mode II  Bx oscillations at T~15 sec  Duration of oscillation equal to C2 negative Bx excursion  C2 remains at the border of the oscillation indicating thin current sheet  C3/4 is proxy for current, large currents at both sides of the CS, but one nice crossing  Oscillations in Y-direction consistent, both hemispheres same direction → kink mode  Flapping exclusively during flow, wave propagates perpendicular to field along current direction

30. 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

31. 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)R E -1  α front-CTC ≈ 7.5˚  ∆ ≈ 0.62R E  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

32. New kind of flapping?  Wavy current sheet  Very harmonic waves  Moving towards the centre of the tail

33. 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]

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

35. 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

36. 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

37. Fast Flow & Plasma Temperature II  Near Earth X< 14 Re  Tail

38. Conclusions  The interaction between the solar wind and the Earth‘s internal magnetic field creates a (dynamic) magnetotail  Many of the theoretically proposed oscillations can actually be found in e.g. the Cluster data  Some „unexpected“ behaviour (e.g. the flapping) led to more theoretical modeling and subsequent testing of the models  Simultaneous multi-point measurements in space physics are now „a must.“  Many more pearls are to be found in the Cluster data:  Both in event studies  And in statistical studies  http://caa.estec.esa.int/caa/home.xml http://caa.estec.esa.int/caa/home.xml  http://www.iwf.oeaw.ac.at/eclat/ http://www.iwf.oeaw.ac.at/eclat/

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