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A New Method For Investigating Reconnection At A Current Sheet

by F.S. Mozer1 and A. Retino2

1. Physics Department and Space Sciences Laboratory, University of California,

Berkeley, Ca. 94720, USA2. Swedish Institute of Space Physics, Uppsala, Sweden

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SPATIAL SCALES ASSOCIATED WITH RECONNECTION• MHD SCALE

Paschmann, G. et al, (1979), Nature, 282:243–246. Sonnerup, B.U.O. et al, (1981), J. Geophys. Res., 86, 10,049

Compared plasma changes with B changes

• ION SCALE (c/ωpI ~ 100 km) Mozer F.S. et al, (2002), Phys. Rev. Lett., 89(1), 015002-1 Vaivads A. et al, (2004), Phys. Rev. Lett., 93(10):105001. Wygant, J. R., et al. (2005), J. Geophys. Res., 110, A09206, doi:10.1029/2004JA010708

Electric and magnetic fields at individual crossings

• ELECTRON SCALE (c/ωpe ~ 2 km) Mozer, F.S., (2004), J. Geophys. Res., 110, A12222, doi:10.1029/2005JA011258

Observations and statistics of parallel electric fields

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POLAR OBSERVATION OF THE ELECTRON DIFFUSION REGION

• Reconnection magnetic field changes in steps• Current filamentary

• At largest filament, see 60 mV/m electric field lasting for ~75 msec (width ~c/ωpe).

• Ell ~ 8 mV/m• jperp·Eperp/n >100 keV per particle per second

• Major density change at this time.• Electron beta < 1

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LET X = normal to the current sheet Y = out-of-plane direction Z = direction of reconnecting component of B EX, BY, BZ = the large fields in a reconnecting current sheet eY, eZ, bX = the small fields in a reconnecting current sheet

The most important field components are: bX because a normal magnetic field is required for the field lines on the two sides to be connected

eY and eZ

because a tangential electric field is required for (EXB/B2)X = (eYBZ – eZBY)/B2 to be inward from both sides

RECONNECTION ON THE ION SCALE

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PROBLEM

The most important fields (eY, eZ, bX), being the smallest fields, are contaminated by the largest fields when the normal to the current sheet is inaccurate.

The analysis assumes a normal direction that is constant, whereas the normal oscillates ~5 degrees due to surface waves on the magnetopause. These produce error signals ~ (Big Field)*sin5o which are comparable to the (Small Field).

CONCLUSION

The parameters that determine that reconnection is occurring and what its magnitude is, are poorly measured.

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IN THIS TALK

1. Two Polar satellite magnetopause crossings, of two second and six minute durations, are analyzed to show that reconnection was occurring but that the reconnection rate was uncertain due to oscillations of the normal direction.

2. A method is described for minimizing this uncertainty by using measurements of only the three large field components to obtain the three small components from correlations that result from the parallel electric field being zero on ion scales.

3. Of >100 sub-solar magnetopause crossings, about 40% had correlations that suggest a constant reconnection rate. Detailed statistics are presented for 20 of these crossings.

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7.52 RE, 1130 MLT, 22.30 MLAT

S/C crosses current sheet in ~2 seconds

Thickness = 300 km =2 c/ωpI

Density (panel a)), BZ (panel e)) show passage from sphere to sheath through magnetopause.

<bX> <0 (panel c)) NECESSARY CONDITION FOR RECONNECTIONMagnitude uncertain due to oscillations

<eY>, <eZ> >0 (panels g), h)) NECESSARY AND SUFFICIENT FOR RECONNECTION. Magnitude uncertain due to oscillations

(EXB/B2)X inward from both sides (panel i))

<bX> < 0 requires outflow in +Z direction. It is (panel k)). Outflow speed of 500 km/sec agrees with vALFVEN = 340 km/sec (sheath) = 830 km/sec (sphere)

BG ~0.2, Btotal ~ constantUnipolar out-of-plane B with parallel j.

EX CORRELATES WITH BY (panels d) and f)

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9.2 RE, 1225 MLT, 22.70 MLAT

S/C crosses current sheet in ~ 6 minutes.

Density (panel a)), BZ (panel e)) show passage from sphere to sheath through magnetopause.

<bX> <0 (panel c)) NECESSARY CONDITION FOR RECONNECTIONMagnitude uncertain due to oscillations

<eY>, <eZ> >0 (panels g), h)) NECESSARY AND SUFFICIENT FOR RECONNECTION. Magnitude uncertain due to oscillations

(EXB/B2)X inward from both sides (panel i))

<bX> < 0 requires outflow in +Z direction. It is (panel k)). Outflow speed of 400 km/sec agrees with vALFVEN = 500 km/sec (sheath) = 630 km/sec (sphere)

BG ~ 1, Btotal ~ constantUnstructured out-of-plane B.

EX CORRELATES WITH BZ (panels d) and f)

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REASON THAT EX CORRELATES WITH BY AND/OR BZ

ASSUME THAT Ell = 0 ON THE ION SCALE

EXbX + eYBY + eZBZ = 0

If bX = eY = eZ = 0 because there is no reconnection, then EX, BY, and BZ have no necessary relationship to each other.

If there is reconnection, bX, eY, and/or eZ ≠ 0 and

EX = – (eY/bX)BY – (eZ/bX)BZ

= – aBY – bBZ where a = (eY/bX) and b = (eZ/bX) IF a and b are constant and EX correlates with BY and/or BZ

THEN The small fields that determine reconnection may be obtained from the large and easily measured fields, by least-squares fits.

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LEAST SQUARES FIT TO APRIL 3, 2002 DATA

R2 = 0.94 (94% of the variation of EX is accounted for by (–aBY –bBZ)

a = eY/bX = -0.41

b = eZ/bX = -0.005

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LEAST SQUARES FIT TO MARCH 20, 2001 DATA

R2 = 0.93

a = eY/bX = -0.32

b = eZ/bX = -0.20

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SUMMARY OF OBSERVATIONS:

1. Because constant a and b fit the data so well, reconnection must have been occurring at a constant rate during these crossings.

2. To the eye, about 40 of 120 sub-solar magnetopause crossings had apparent correlations between EX and the combination of BY and/or BZ. So reconnection at a constant rate may occur for more than 40% of sub-solar magnetopause crossings.

3. Twenty of these crossings were analyzed quantitatively.

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SUMMARY

1. On the ion scale, reconnection can be directly observed by measuring the normal magnetic field and tangential electric field components.

2. These measurements are uncertain due to the uncorrected oscillation of the magnetopause normal.

3. In many cases, the normal magnetic field and tangential electric field can be obtained by analyses of the correlations between the normal electric field and tangential magnetic field that arise from the parallel electric field being zero.

4. These analyses show that reconnection at a constant rate may occur at the sub-solar magnetopause more than 40% of the time.

5. They suggest that reconnection at the sub-solar magnetopause may not depend on the guide magnetic field strength (the clock angle between the reconnecting fields) but that the reconnection rate may decrease with increasing guide magnetic field.