Flow driven instabilities in the Earth's Magnetotail

Martin Volwerk

Space Research Institute

Austrian Academy of Sciences

Including an Introduction to Magnetospheres and Magnetotails

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

Let‘s get started!

让我们开始！

Introduction to Magnetospheres

Water flow around a rock

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

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

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

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.

dayside

nightside

magnetic reconnection

Magnetospheric convection

magnetotail

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

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)

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

2007-

2001- 2006

Cluster

THEMIS

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)

Multi-point observation (two-points)

( , ) ( , )

AB

B A

Q

Q t Q t

Dt

r L v r

v L

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)

Multi-point observation (two-points)

( , ) ( , )

AB

B A

Q

Q t Q t

Dt

r L v r

v L

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)

Multi-point observation (two-points)

( , ) ( , )

AB

B A

Q

Q t Q t

Dt

r L v r

v L

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

Transient thin current sheet

Current sheet thickness determined sequentially from model fitting (Harris current sheet)

Bx = B0 tanh{(z-z0)/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)

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-alignedcurrent

Fast plasma flow near-Earth reconnection

?Aurora

Possible Oscillations of the Tail

Kink ModeSausage ModeLarge Scale ModeFlapping Mode

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

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]

zBBBzB

a

zvzv

etvdz

dBB

dz

dvvb

e

z

tz

zAm

tanh

exp5.05.0

2cos

11

2

2

0

21

22 August 2001

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-1

vA,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.).

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

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].

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

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

CDSCDS xkBB ,Imexp

bflowpik W

bvmNW

0

22

22

1

With amplitude in current sheet larger (Cluster), KHI could be a significant source of flow braking

Unfortunately no TC1 data deeper in current sheet

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

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

New kind of flapping?

Wavy current sheet

Very harmonic waves

Moving towards the centre of the tail

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]

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↑

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

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

20||

|| 1

a

T

T

Fast Flow & Plasma Temperature II

Near Earth X< 14 Re Tail

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://www.iwf.oeaw.ac.at/eclat/

谢谢您们