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CO-WORKERS Jim Drake, Jim McFadden, Phil Pritchett, Ilan Roth, David Sundkvist

I SCALING MAGNETIC FIELD RECONNECTION TO OTHER BODIES II WAVES AND ANOMALOUS DRAG AT THE SUB-SOLAR MAGNETOPAUSE Professor Forrest Mozer Physics Department and Space Sciences Laboratory University of California, Berkeley, CA 94720, USA forrest.mozer@gmail.com. CO-WORKERS

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CO-WORKERS Jim Drake, Jim McFadden, Phil Pritchett, Ilan Roth, David Sundkvist

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  1. I SCALING MAGNETIC FIELD RECONNECTION TO OTHER BODIES II WAVES AND ANOMALOUS DRAG AT THE SUB-SOLAR MAGNETOPAUSE Professor Forrest Mozer Physics Department and Space Sciences Laboratory University of California, Berkeley, CA 94720, USA forrest.mozer@gmail.com CO-WORKERS Jim Drake, Jim McFadden, Phil Pritchett, Ilan Roth, David Sundkvist

  2. I SCALING RECONNECTION TO OTHER BODIES • Because these results were recently published, they will only be summarized here • Published in Phys. Plasmas, 17, 102906, 2010 • Conjecture that energy conversion in reconnection α B3/n0.5 • Polar satellite sub-solar reconnection data confirmed this conjecture. • Application to planets to explain large reconnection rate at Mercury and little or no reconnection at Jupiter and Saturn. • Application to Sun increases energy release by ~ 1010 compared to reconnection at the terrestrial magnetopause. Makes reconnection explanation of solar flares much more plausible. • Application to astrophysics?

  3. II WAVES AND ANOMALOUS DRAG AT THE SUB-SOLAR MAGNETOPAUSE Some theories assume that the drag = η*j is caused by the anomalous resistivity, η* produced by waves. This is an ad hoc assumption that will be replaced by deriving the anomalous drag from first principles and applying it to space data to estimate the effect of wave processes on reconnection. Newton’s second law for a unit volume of electrons in a collisionless plasma is: -neE = nm(∂Ue/∂t + Ue·Ue) + neUexB) + ·Pe EY AND DENSITY ARE COMPOSED OF AVERAGE VALUES AND FLUCTUATIONS EY = <EY> + δEY and n = <n> + δn So nEY = <n><EY> + <n>δEY + <EY>δn + δnδEY Averaging over many cycles of the fluctuating wave gives <nEY> = <n><EY> + <δnδEY> Substituting this into the time average of Newton’s second law gives <EY> = <nm(∂Ue/∂t + Ue·Ue)Y>/e<n>  <nUexB)Y>/<n>  <(·Pe)Y >/e<n> + DY where DY = ANOMALOUS DRAG ≡ – <δnδEY>/<n>

  4. COMMENTS • Ninety crossings of sub-solar magnetopauses having wave turbulence on THEMIS D were studied. • 90% had wave turbulence near the magnetospheric separatrix • 10% exhibited turbulence in the current layer • 6% exhibited turbulence in the magnetosheath • Turbulence amplitude was greatest at the magnetospheric separatrix. • Two frequency bands of electrostatic waves with similar occurrence frequencies were observed: lower hybrid drift waves, and electrostatic whistler mode waves • One crossing passed through the X-line and waves were unimportant.

  5. LOWER HYBRID WAVE NOISE Data in minimum variance of B coordinate system, X perpendicular to current and points sunward, Z is direction of reconnecting B Spacecraft passed from the magnetosphere to the sheath and observed turbulence at the magnetospheric separatrix (~ 150 mV/m) 9.9 RE, 13:48 MLT, 3o MLAT Electrostatic lower hybrid drift waves because: Spectra peaked below νLH (the red line) Ewave at 89.5o to B At density gradient No correlation of δE and δB δEY/δBZ >0.1c

  6. LOWER HYBRID DRAG Data is <0.25 seconds> Drag correlates with EY and is <10% of EY near the magnetospheric separatrix Drag is <1% of EY in the current layer CONCLUSION Waves and anomalous drag are unimportant to reconnection (or the data is far from the reconnection region where drag could be important)

  7. OBSERVATION AT THE X-LINE Random chance of passing within an electron skin depth of the X-line is ~1/1000 Have examined ~thousands of crossings and found one that did • CRITERIA FOR PASSING THROUGH THE X-LINE DURING A CROSSING • Bnormal ≠ 0 (so it is a reconnection event) AND • BZ = 0 AND • Low energy field-aligned electrons AND • Perpendicular outflowing super-Alfvenic electron jet at the same time as the field aligned electrons AND • UI<< VALFVEN AND • E ≠ -UIxB 7

  8. OVERVIEW OF THE CROSSING 9.4 RE, 12:38 MLT, -10o MLAT Data in minimum variance of B coordinate system. Electrostatic lower hybrid drift waves at magnetospheric separatrix. Betae < 0.02 Tperp/Tpar =1±.15 for e and I TI = 800 eV, Te = 100 eV Bguide ~ 0.6 We will discuss the 0.7 second interval between the dashed lines during which there is little turbulence and BZ = 0

  9. PLASMA AND FIELD DATA SHOW THAT THE SPACECRAFT CROSSED THROUGH THE RECONNECTION REGION NEAR THE X-LINE • EXPECTATIONS • BZ = 0, BX ≠ 0 • Field aligned electrons of 20-150 eV (panel a) • 0.3-3 keV super-Alfvenic electrons perpendicular to B (panel a) • See field aligned magnetosheath electrons and super-Alfvenic jet almost simultaneously. • UiZ << VALFVEN (panel b) • –UixB ≠ E (panel c) • Occasional spiky Eǀǀ (panel d)

  10. THEMIS D ELECTRONS ON AUGUST 30, 2009 Columns represent 3 successive 3 second spin periods Rows represent 109 eV and 2220 eV electrons B is at the center of each plot and anti-B is around the periphery Observe ~100 eV field-aligned electrons and ~2 keV perpendicular electrons with velocity ~6 VA

  11. Region of interest is at 44 seconds in this plot Ion outflow speed is <0.1VA Electric fields at 3 second spin period resolution EX≠ -(UixB)X EY ≠ -(UixB)Y EZ ≠ -(UixB)Z

  12. WAVE TURBULENCE AND Eǀǀ AT THE X-LINE 0.7 seconds of data in field-aligned coordinates Spiky parallel E Similarity of waves in n and EX (correlation = -0.94) Similarity of waves in EY and BZ (correlation = 0.72 after phase shift) HAVE ELECTROSTATIC AND ELECTROMAGNETIC WAVE COMPONENTS DURING THE SAME 0.2 SECONDS If relative speed = 10-50 km/sec, 0.1 second wave covers 1-5 km, which is 0.7-3.5 c/ωpe

  13. ELECTROSTATIC WAVE IN EX AND DENSITY For waves of 10-200 Hz DRAG < .01EX CONCLUSION: Anomalous drag due to the electrostatic wave is not sufficient to support EX, even at the X-line k in X(min var) direction

  14. ELECTROMAGNETIC WAVE IN EY AND BZ PROPERTIES - fLH = 34-40 Hz - Fields filtered 30-60 Hz - δBZ parallel to Bo - Waves ~90o out of phase - δEY/δBZ = 24 mV/m-nT - k in X(min var) direction - Poynting flux small ~0.05 eV/particle 14

  15. LOWER HYBRID PLATEAU FROM NUMERICAL VLASOV-MAXWELL CALCULATION PROPERTIES OF MODE ν ≈ νLH δB ǀǀ B0 δEY and δBZ 90o out of phase Weakly damped, |γ/fcp| ~ 10-3 δEY/δBZ → λ = 9 km ~ 5c/ωpe Phase speed = νλ = 360 km/sec THESE WAVES ARE NOT THE SAME AS THOSE SEEN IN MRX OR SIMULATIONS

  16. WHAT ACCELERATES THE ELECTRONS IN THE SUPER-ALFVENIC JET? Their speed was an order-of-magnitude greater than (ExB)/B2 Their speed was a few times greater than the electron Alfven speed They were not accelerated by the observed Epar Potential due to single spike < 10s of volts They were not accelerated by the observed Eperp Potential across c/ωpe < 100 volts Density gradient might have pressure gradient of many 10s of mV/m. Off diagonal terms not measured.

  17. SUMMARY AN X-LINE CROSSING HAS BEEN FOUND. ANOMALOUS DRAG OF THE WAVES IS INSUFFICIENT TO SUPPORT THE ELECTRIC FIELD AT THE X-LINE THE WAVE POYNTING FLUX IS SMALL AT THIS CROSSING THE ELECTRIC FIELDS ARE NOT LARGE ENOUGH TO EXPLAIN THE ACCELERATION CONCLUSION OBSERVATIONALLY, THE FIELDS AT THE X-LINE AND RECONNECTION SITE ARE INSUFFICIENT (AT LEAST FOR ONE EVENT) This same conclusion has been reached from simulations P. L. Pritchett and F. S. Mozer, Phys. Plasmas, 16, 080702, 2009

  18. SPARE SLIDES

  19. SCALING OF EY AND THE ENERGY CONVERSION RATE WITH B AND DENSITY EY = out-of-plane electric field, i.e., the reconnection electric field M ≡Reconnection Rate ≡ EY/(BZVA) Experiments and simulations give M ~ 0.05-0.20 which means that the plasma inflow, normalized by the Alfven speed is constant to within a factor of 2 or so. If this is correct EY = MxBZxVAα B2/n0.5 and Poynting vector EYBZ/μ0α B3/n0.5

  20. SCALING OF EX Consider the terms in the Generalized Ohm’s Law in the ion diffusion region E+UixB = jxB/en pe/en + (mec2/ne2)∂j/∂t The last three terms are zero. UixB is zero So EX = jYBZ/en = jY(B1/2)/en Because jY = (B1+B2)/d(c/ωpi) where d = thickness of the current layer in units of the ion skin depth Putting E in units of mV/m, B in units of nT, n in units of cm-3 EX = B1(B1+B2)/80.38dn0.5 which scales like B2/n0.5

  21. TESTING THE SCALING ON A SUB-SOLAR RECONNECTION EVENT IN THE EARTH’S MAGNETOSPHERE On May 4, 1998, a magnetopause crossing occurred at 5.3 RE The magnetic field at a typical crossing at 9 RE is ~50 nT. So a crossing at 5.3 RE should have B1 ~ (9/5.3)3 x 50 = 250 nT Measured <B1> = 238 nT

  22. For n = 7 and 16 cm-3 M = 0.1 d = 2 skin depths <B1> = 238 nT <B2> = -161 nT Scaling equations give EX = 189 mV/m EY = 17 mV/m Measurements give <EX> = 162 mV/m <EY> = 24 mV/m Typical values at a 9 RE crossing are EX ~ 10 mV/m EY ~ 1 mV/m

  23. TESTING THE SCALING LAW WITH 48 SUB-SOLAR MAGNETOPAUSE CROSSINGS • Can’t test the EY scaling law because EY is not well-enough measured because: • Temporal fluctuations are the same order as the average value. • Because EY ~0.1EX, the uncertainty in EY associated with rotation into the minimum variance frame is too large. • The transformation of the data into the frame of the magnetopause changes EY by an amount comparable to its average value, which is not done for the data of interest because the speed of the magnetopause over the spacecraft is not known. For EX, problems 2 and 3 do not apply. However, fluctuations in the measured EX cause a typical uncertainty of about 25% of its value

  24. XIII WAVES AND ANOMALOUS DRAG IN RECONNECTION IN THIS DISCUSSION WE WILL FOCUS ON EY AND ASK WHAT SUPPORTS IT Assume there is an out-of-plane EY This causes ExB/B2 drift of plasma and magnetic field lines toward the center from the right and left. Field lines meet at the X and reconnect This causes ExB/B2 flow of field lines and accelerated plasma vertically THE KEY TO UNDERSTANDING MAGNETIC FIELD RECONNECTION IS UNDERSTANDING WHAT SUPPORTS EY

  25. ELECTROSTATIC WHISTLER WAVE NOISE Sub-solar crossing from sheath to magnetosphere at 9.3 RE, local time 09:30, and latitude 4o Data in minimum variance of B coordinate system. Waves observed at magnetospheric separator with amplitudes ~80 mV/m These are electrostatic whistler waves because: Spectra peaked below 0.5νegyro (the red line) Electron temperature gradient provided free energy No correlation of δE and δB δEY/δBZ >3c Same spectrum as observed in the lab

  26. ELECTROSTATIC WHISTLER DRAG Drag is <1% of EY near the magnetospheric separatrix Drag is <0.01% of EY in the current layer CONCLUSION Waves and anomalous drag are unimportant to reconnection (or the data is far from the reconnection region where drag could be important)

  27. DY DOES NOT ACCOUNT FOR THE RECONNECTION ELECRIC FIELD, EY TO TEST IF THIS IS BECAUSE THE OBSERVATIONS WERE MADE FAR FROM THE RECONNECTION REGION, A SATELLITE PASSAGE THROUGH THE RECONNECTION SITE WAS SEARCHED FOR AND FOUND.

  28. DRAG AT MAGNETOSPHERIC SEPARATRIX NEAR THE X-LINE At the magnetospheric separatrix, DY < 0.1EY At the current layer and especially where BZ = 0, DY < 0.01EY ANOMALOUS DRAG DUE TO WAVES IS UNIMPORTANT

  29. ANOMALOUS DRAG DUE TO ELECTROMAGNETIC WAVES For electrostatic waves we had <EY> =<nm(∂Ue/∂t+Ue·Ue)Y>/e<n><(nUexB)Y>/<n><(·Pe)Y >/e<n>+DY DY = Anomalous drag due to electrostatic waves ≡ – <δnδEY>/<n> One may also include the drag due to electromagnetic waves by averaging the second term on the right of the above equation in the same way that the left side was averaged. i.e., by setting nUeZ = <nUeZ> + δ(nUeZ), etc. In this way the second term becomes [<nUeZ><BX> + <nUeX><BZ>  <δ(nUeZ)δBX> + <δ(nUeX)δBZ>]/<n> For electromagnetic drag to be important the terms involving the fluctuations must be comparable to the terms involving the averages Experimentally δ(n)/<n> <0.1 and δBX/<BX> <0.1 so, even with perfect correlations of the fluctuating density and magnetic field, the fluctuation terms must be small compared to the average terms unless δUeZ/<UeZ> 100, which is unreasonable. ANOMALOUS DRAG DUE TO THE ELECTROMAGNETIC WAVE IS SMALL

  30. TIMING OF EVENTS in seconds after 14:41:08 E ≠ UxB TURBULENCE AT MAGNETOSPHERIC SEPARATRIX CURRENT LAYER BZ ~0 REGION ELECTROSTATIC AND ELECTROMAGNETIC WAVES PARALLEL ELECTRIC FIELD PULSE FIELD ALIGNED ELECTRONS AND ACCELERATED ELECTRON OUTFLOW 5-35 8-9.5 9.5-14 11.1-11.8 11.2-11.4 11.55 13-14 31

  31. R2 FOR DIFFERENT FUNCTIONS OF B AND n SHOW THAT THE BEST SCALING FIT TO THE DATA IS B2/n0.5 The correlation coefficient, R2, is the fraction of the total squared error explained by the equation

  32. SUMMARY - PROPERTIES OF THESE WAVES Signatures of the reconnection X-line Low beta (βe < 0.1) and large BG ~ 0.6 ES and EM waves that are coupled δB parallel to Bo ν = LH and above λ = 9 km ~ 5 electron skin depths k for both waves is perpendicular to the current sheet Unimportant electrostatic and electromagnetic drag associated with them δE and δB are ~90 degrees out of phase so waves carry little Poynting flux Not the mode observed in MRX because, in MRX δB is not parallel to Bo, it is right circular polarized Lab waves are below LH frequency Lab example had BG ~ 0 Waves propagate obliquely to Bo δB/Bo ~5%, (In the magnetosphere δB/Bo ~2%)

  33. PROPERTIES OF THE RECONNECTION SITE • E ≠ -UxB • Significant parallel electric field not found (Consistent with simulations) • Parallel electric field spike observed. (Often seen in other data and simulations) • Electrostatic wave present, but anomalous drag is ineffective in supporting the quasi-DC electric field. • Electromagnetic wave present, but with little Poynting flux and drag. • No ion outflow • Field aligned 20-150 eV electrons are present. • Perpendicular beams of ~0.3-3 keV electrons are present with speeds ~6VA 34

  34. PARALLEL ELECTRIC FIELD AT THE X-LINE At the X-line, do not expect to see a DC E|| May see short duration, spiky E||

  35. FOUR MILLISECOND PARALLEL ELECTRIC FIELD PULSE Observed within 0.2 seconds of the wave Pulse lasts 4 milliseconds with amplitude of 15 mV/m. If speed = 100 km/sec, pulse potential = 6 V

  36. I SCALING RECONNECTION TO OTHER BODIES (Phys. Plasmas, 17, 102906, 2010) If the process that occurs at the sub-solar magnetopause is transported to the sun, it is too weak to explain the energy conversion by a factor of about 1015 The magnetic field and other parameters are different than they are at the earth so one should scale the magnetopause data to the sun, not transport it to the sun OUTLINE Conjecture that the E-field scales as B2/n0.5 and energy conversion scales as B3/n0.5 ValfvenB α B2/n0.5 Hall term = jxB/n α B2/n0.5 Confirm scaling laws with Polar Satellite sub-solar reconnection data Apply scaling laws to Mercury, Jupiter, Saturn and the Sun Apply scaling laws to astrophysical objects

  37. From the slope of the least squares fit, the thickness of the current layer is about two ion skin depths

  38. APPLICATION OF SCALING TO THE PLANETS EARTH At the sub-solar point B α r-3. Because energy conversion α B3, the energy conversion rate at the sub-solar magnetopause varies like r-9!! MERCURY On the Messenger satellite, the magnetic energy content of the tail increased at a rate greater than 5 times that at similar events in the terrestrial magnetotail and the magnetotail field was ≥5 times larger than that at Earth. This may be explained by enhanced dayside reconnection due to scaling. JUPITER Controversial whether reconnection is important but it probably isn’t. (Fast rotation, large internal B and IO emission, may dominate) For B~1-2 nT and n ~1 cm-3, the energy conversion rate is smaller at Jupiter than at Earth by more than a factor of 10,000. SATURN Saturn’s auroral emissions depend on solar wind pressure and internal processes, so reconnection is probably unimportant. This may be explained by the energy conversion rate being at least 15,000 times smaller for Saturn than for the Earth.

  39. APPLICATION OF SCALING TO THE SUN Solar flares release as much as 1022 W Helmet streamers release ~1020 W If B = 100 G and n = 108 cm-3 in the solar corona Energy release per unit area = 107 W/m2 (1010 greater than without scaling) If this power is dissipated over an area of 20,000x20,000 km2 (the size of a flare) Power dissipated by one reconnection event = 4*1021 W Another solution is to have reconnection occur at multiple sites with island coalescence that releases further energy. So there might be several reconnection events over the area of a solar flare

  40. APPLICATION TO ASTROPHYSICAL OBJECTS Including displacement current VA(relativistic) = sqrt[VA2/(1 + VA2/c2)] Leroy, B., Astron.Astrophys., 125, (1983) Assume that E scales as cB, so energy conversion scales as cB2 Energy of ultrahigh energy cosmic rays > 1020 eV. Power >1039 Watts. Reconnection might support these values, even over the very small dimensions of ion skin depths (c/ωpI ~ centimeters)

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