Walen and Slow-mode Shock Analyses Walen and Slow-mode Shock Analyses Applied to High-Speed Flows of Applied to High-Speed Flows of

the Near-Earth Magnetotail the Near-Earth Magnetotail

S. ErikssonS. Eriksson11, C. Mouikis, C. Mouikis22, M. W. Dunlop, M. W. Dunlop33, , M. OierosetM. Oieroset44, ,

D. N. BakerD. N. Baker11, C. Cully, C. Cully11, H. Reme, H. Reme55, and A. , and A. BaloghBalogh66

11 Laboratory for Atmospheric and Space Physics, University of Laboratory for Atmospheric and Space Physics, University of Colorado, Boulder, USAColorado, Boulder, USA22 Space Science Center, University of New Hampshire, Durham, Space Science Center, University of New Hampshire, Durham, USAUSA33 Rutherford Appleton Laboratory, Chilton, UK Rutherford Appleton Laboratory, Chilton, UK44 Space Sciences Laboratory, University of California, Berkeley, Space Sciences Laboratory, University of California, Berkeley, USAUSA55 Centre d’Etude Spatiale des Rayonnements, Toulouse, France Centre d’Etude Spatiale des Rayonnements, Toulouse, France66 Imperial College, London, UK Imperial College, London, UK

Contact information:

eriksson@lasp.colorado.edu

OutlineOutline

IntroductionIntroduction1.1. Tail reconnection and slow-mode Tail reconnection and slow-mode

shocksshocks2.2. deHoffmann-Teller and Walen analysesdeHoffmann-Teller and Walen analyses3.3. Slow-mode shock criteriaSlow-mode shock criteria Cluster observationsCluster observations

2001-08-27 from 03:50 UT to 04:35 UT2001-09-15 from 03:55 UT to 05:20 UT2002-08-21 from 07:50 UT to 08:40 UT

SummarySummary

Tail Reconnection and Slow-mode Tail Reconnection and Slow-mode ShocksShocks

[Hill, T.W., JGR, 80, 4689, 1975][Feldman et al., JGR, 92, 83, 1987]

• Acceleration in tail reconnection is assumed to take place across a slow-mode shock (SS) connected to the diffusion region.

• SS generated due to near-symmetric conditions (comparable plasma density and magnetic field strength) on either side of the current layer.

• Configuration essentially that of Petschek [1964] (above right).

Tail Reconnection and Slow-mode Tail Reconnection and Slow-mode ShocksShocks

[Hill, T.W., JGR, 80, 4689, 1975][Feldman et al., JGR, 92, 83, 1987]

• Slow-mode shocks were first observed in the tail by e.g. Feldman et al. [1984, 1987] using the Rankine-Hugoniot (RH) jump conditions on ISEE 2 data.

• Later confirmed by Geotail RH observations [e.g. Saito et al., 1995; Seon et al., 1996] and by Wind data [Oieroset et al., 2000] using the shear-stress balance test on Wind data 60 Re downtail.

M

m

mm BvvM

vD

D(v)V

V

v,v

BB

n

1

2)()(

HT

HT

(2)(1)

)2()1(

1)(

: minimizingby obtained

velocityframeTeller deHoffmann:

velocitymeasured :

field magnetic measured:,

normalshock :ˆ

deHoffmann-Teller AnalysisdeHoffmann-Teller Analysis

[Khrabrov and Sonnerup, ISSI Sci.rep., 1998]

• The existence of an HT frame indicates the presence of a quasi-stationary coherent pattern of magnetic field and plasma velocity.

Shear-Stress Balance (Walen) TestShear-Stress Balance (Walen) Test

• Disturbance generated by reconnection propagates away from the diffusion region at a field-aligned phase speed in the HT shock frame determined by the type and strength of the shock.

1A*A2A

0

*A

A

HT

shock) mode(slow '

use)(magnetopa '

'

'

MMM

BMv

vv

BB

vvv

Shear-Stress Balance (Walen) TestShear-Stress Balance (Walen) Test

1A*A2A

0

*A

A

HT

shock) mode(slow '

use)(magnetopa '

'

'

MMM

BMv

vv

BB

vvv

• The sign of the Walen slope depends on whether the B-field is parallel or antiparallel to the flow direction.

Walen Analysis in the MagnetotailWalen Analysis in the Magnetotail

Walen slope

Oieroset et al., JGR, 105, 25,247, 2000.

Walen Analyses at Wind (x= -60 Walen Analyses at Wind (x= -60 Re)Re)

Oieroset et al., JGR, 105, 25,247, 2000.

(Note that there is no ion composition in the Wind data set and that these slopes were derived assuming 100% H+.)

• Earthward jet

• Negative Bx

• Walen slope

should be positive

Slow-mode Shock CriteriaSlow-mode Shock Criteria

0.1 (8)

24)()( ; 0.1 (7)

cos ; 0.1 (6)

)ˆarccos( (5)

2 (4)

(3)

)25)ln()2ln23( (2)

satisfied conditions jumpshock

Hugoniot- Rankine(1)

downstream :

upstream:

*

22222222**

**

02

2

dSM

ISASASSMSMnSMuSM

AIInIuI

ud

bub

db

Bpup

dp

BpBud

M

VVVVVVVVVMM

VVVVMM

BnB

BPPP

TnkPPP

nhTkm(kSSS

d

u

Cluster Cluster Observations on Observations on

2001-08-272001-08-27

A B C

Walen Analyses 2001-08-27Walen Analyses 2001-08-27

A: Tailward flows in Northern Hemisphere

Walen Analyses 2001-08-27Walen Analyses 2001-08-27

B: Earthward flows in Northern Hemisphere

Walen Analyses 2001-08-27Walen Analyses 2001-08-27

C: Earthward flows in Northern Hemisphere

Shock Shock Analysis on Analysis on 2001-08-272001-08-27

up1up1 downdown11

up2up2 downdown22

PPpp 0.200.20 0.240.24 0.010.01 0.030.03

PPbb 0.180.18 0.150.15 0.090.09 0.060.06

thetatheta 2828oo 1111oo 4040oo 1010oo

NNpp 0.280.28 0.300.30 0.020.02 0.040.04

TTpp 4.54.5 5.15.1 2.42.4 5.65.6

SSpp 1.051.05 1.061.06 1.201.20 1.251.25

MMAA 0.760.76 0.800.80 0.310.31 0.330.33

MMII 0.860.86 0.820.82 0.400.40 0.340.34

MMSMSM 1.071.07 0.850.85 1.761.76 0.500.50

A CA B C

Shock Normal Optimization Shock Normal Optimization 2001-08-272001-08-27

Cluster Cluster Observations on Observations on

2001-09-152001-09-15

A B C

Walen Analyses 2001-09-15Walen Analyses 2001-09-15

A: Tailward flows in Northern Hemisphere

Walen Analyses 2001-09-15Walen Analyses 2001-09-15

B: Tailward flows in Northern Hemisphere

Walen Analyses 2001-09-15Walen Analyses 2001-09-15

C: Tailward flows in Southern Hemisphere

Shock Shock Analysis on Analysis on 2001-09-152001-09-15

up1up1 downdown11

up2up2 downdown22

PPpp 0.150.15 0.300.30 0.250.25 0.290.29

PPbb 0.220.22 0.040.04 0.110.11 0.050.05

thetatheta 7171oo 4242oo 5757oo 3636oo

NNpp 0.420.42 0.520.52 0.620.62 0.560.56

TTpp 2.22.2 3.43.4 2.42.4 2.82.8

SSpp 0.930.93 0.960.96 0.900.90 0.930.93

MMAA 0.330.33 0.670.67 0.560.56 0.760.76

MMII 1.011.01 0.900.90 1.041.04 0.940.94

MMSMSM 1.661.66 0.930.93 1.251.25 0.980.98

A B

BA C

Cluster Cluster Observations on Observations on

2002-08-212002-08-21

A B C

Walen Analyses 2002-08-21Walen Analyses 2002-08-21

A: Tailward flows in Northern Hemisphere

Walen Analyses 2002-08-21Walen Analyses 2002-08-21

B: Tailward flows in Northern Hemisphere

Walen Analyses 2002-08-21Walen Analyses 2002-08-21

C: Tailward flows in Southern Hemisphere

Shock Shock Analysis on Analysis on 2002-08-212002-08-21

up1up1 downdown11

PPpp 0.140.14 0.240.24

PPbb 0.370.37 0.130.13

thetatheta 6363oo 4040oo

NNpp 0.150.15 0.190.19

TTpp 5.05.0 7.07.0

SSpp 1.121.12 1.141.14

MMAA 0.370.37 0.510.51

MMII 0.810.81 0.670.67

MMSMSM 1.631.63 0.770.77

B

BA C

SummarySummary The Walen test together with the location of The Walen test together with the location of

Cluster suggest the presence of slow-mode Cluster suggest the presence of slow-mode shocks on the tailward sides of near-Earth X-shocks on the tailward sides of near-Earth X-lines (X>-19 Re) for three events: lines (X>-19 Re) for three events: 2001-08-27, 2001-08-27, 2001-09-15, 2002-08-21 2001-09-15, 2002-08-21..

Earthward jets seemingly fail the Walen test Earthward jets seemingly fail the Walen test more readily than tailward jets.more readily than tailward jets.

Joint Walen and RH analyses generally confirm Joint Walen and RH analyses generally confirm the presence of slow-mode shocks during the presence of slow-mode shocks during accelerated tailward flows. Based on three accelerated tailward flows. Based on three events and several jets.events and several jets.

Shock-normal analyses suggest that magnetic Shock-normal analyses suggest that magnetic coplanarity theorem results in a normal near coplanarity theorem results in a normal near the optimized (minimum RH deviations) the optimized (minimum RH deviations) direction.direction.