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MAGNETIC FIELD RECONNECTION FROM FIRST PRINCIPLES TO LATEST RESULTS by Forrest Mozer

MAGNETIC FIELD RECONNECTION FROM FIRST PRINCIPLES TO LATEST RESULTS by Forrest Mozer. RECONNECTION. Reconnection is the process that occurs when magnetized plasmas flow into each other. It produces a. Change of topology b. Particle acceleration

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MAGNETIC FIELD RECONNECTION FROM FIRST PRINCIPLES TO LATEST RESULTS by Forrest Mozer

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  1. MAGNETIC FIELD RECONNECTION FROM FIRST PRINCIPLES TO LATEST RESULTS by Forrest Mozer

  2. RECONNECTION • Reconnection is the process that occurs when magnetized plasmas flow • into each other. It produces • a. Change of topology • b. Particle acceleration • Reconnection occurs at the magnetopause, on the sun, on all scales in astrophysics (accretion disks, etc.) and in laboratory plasmas.

  3. QUESTIONS ABOUT MOVING FIELD LINES AND RECONNECTION • Why should one think about magnetic field lines that move? • What are the necessary conditions for field lines to move with ExB/B2? • Do magnetic field lines move with ExB/B2 in a vacuum, or is plasma needed to satisfy the frozen-in condition before field lines can move with ExB/B2? • If all field lines move with ExB/B2 everywhere, can there be reconnection? • Does the magnetic field line at point A move with the ExB/B2 velocity if the frozen-in condition is violated somewhere else along that field line? 6. What are the necessary conditions for being in the reconnection region? 7. The electron diffusion region is the place where reconnection occurs. Has any experiment seen the electron diffusion region?

  4. PLASMA AND FIELD LINE MOTION Consider Two magnetic field lines at time t1 They move with ExB/B2 velocity Ions and electrons move with ExB/B2 At later times B and plasma move to t2… At t5, magnetic field lines reconnect Plasma, B ejected vertically at later times

  5. PLASMA AND FIELD LINE MOTION Consider Two magnetic field lines at time t1 They move with ExB/B2 velocity Ions and electrons move with ExB/B2 At later times B and plasma move to t2… At t5, magnetic field lines reconnect Plasma, B ejected vertically at later times WHAT IS WRONG WITH THIS CARTOON? No perpendicular currents if ions and electrons move together jperp≠ 0 and jperp·Eperp > 0 on large scale No reconnection if B lines move with ExB/B2 everywhere

  6. GEOMETRY AT TIME t6 IF FIELD LINES MOVE WITH ExB/B2

  7. THE GENERALIZED OHMS LAW • In two fluid theory, the equations of motion for a unit volume of plasma are: • Ions nimi(Ui/t+Ui·Ui) = niZe(E+UixB)/c-·Pi+Pie (1) • Electrons neme(Ue/t+Ue·Ue) = -nee(E+UexB)/c-·Pe+Pei (2) • Pi, Pe= ion and electron pressure tensors • Pie= momentum transferred between ions and electrons • Subtract (2) from (1) assuming • neglect of quadratic terms • electrical neutrality • ignore me/mi terms • Gives THE GENERALIZED OHM’S LAW E+UixB = cjxB/en c·Pe/en + (mec2/ne2)j/t + j Equivalently, because j(c/ne) = UiUe E+UexB = c·Pe/en + (mec2/ne2)j/t + j

  8. FIELD LINE VELOCITY FROM FIRST PRINCIPLES The task is to show the conditions under which field line motion with velocity ExB/B2 causes the magnetic field MAGNITUDE and DIRECTION to evolve in time in a manner consistent with Maxwell’s equations. MAGNITUDE AT t+δt CONSISTENT WITH MAXWELL’S EQUATIONS Consider an infinitesmal surface in the x-y plane having B = BZ perpendicular to that surface. Because ·B = 0, the number of field lines is conserved, so δBZ/δt + ·(Bv) = 0 (equation of continuity) (1) Because v = ExB/B2, the components of Bv are (Bv)X = EY and (Bv)Y = -EX. So ·(Bv) = δEY/δx – δEx/δy which is the z-component of xE. Thus, the conservation equation is just Faraday’s law. So, without approximation and in the presence or absence of plasma, the magnitude of the magnetic field is always that expected from Maxwell’s equations if magnetic field lines move with the ExB/B2 velocity. It is noted that any velocity v' satisfying ·(Bv') = 0 may be added to ExB/B2 without modifying equation 1. Thus, there are an infinite number of magnetic field line velocities that preserve the magnitude of the field.

  9. FIELD LINE VELOCITY FROM FIRST PRINCIPLES DIRECTION AT t+δt CONSISTENT WITH MAXWELL’S EQUATIONS Consider two surfaces, S1 and S2, that are perpendicular to the magnetic field at times t and t + δt. At time, t, a magnetic field line intersects the two surfaces at points a and b. Thus, the vector (b – a) is parallel to B(t). At the later time, t + δt, the points a and b have moved at velocities ExB/B2(a) and ExB/B2(b) to points a’ and b’. What are the constraints on these motions that cause (b’ - a’) to be parallel to B(a, t+δt), i.e., that give (b’ - a’) xB(a, t+δt) = 0? (b’ − a’)/ε = B + B·(ExB/B2)δt Also B(a, t + δt) = B + (δB/δt) )δt + ((ExB/B2)·)Bδt After taking the cross product and simplifying, one gets B x (xE||)= 0 IF Ell = 0, ExB/B2 MOTION CAUSES THE FIELD TO EVOLVE IN A MANNER CONSISTENT WITH MAXWELL’S EQUATIONS

  10. CONCLUSIONS • A necessary condition is that Ell≠ 0 in the magnetic field reconnection region. • From E+UexB = cpe/en + (mec2/ne2)j/t + j, the left side of this equation is non-zero because Ell≠ 0, so · Electrons do not move with the ExB velocity. i.e., this is the “electron diffusion region.” “Electrons are demagnetized.” · A term on the right side of this Generalized Ohm’s Law must be non-zero to support the parallel electric field. WHICH TERM?

  11. SPATIAL SCALES OF RECONNECTION DIFFERENT PHYSICS OCCURS ON DIFFERENT SPATIAL SCALES • Ion scales c/ωpI ~ 100 km at the sub-solar magnetopause cjxB/en on right side of the Generalized Ohm’s Law becomes important to decouple ion motion and to allow perpendicular currents. Because this term is perpendicular to B, Ell = 0 so magnetic field lines and electrons move with ExB/B2 • Electron scales c/ωpe ~ 2 km at the sub-solar magnetopause The remaining terms on the right side of the Generalized Ohm’s Law can become important, so Ell can be non-zero and reconnection can occur. • Debye scales λDebye ~ 0.1 km Many large (~150 mV/m) fields seen on this scale. They are mostly perpendicular to B.

  12. COMPUTER SIMULATION OF RECONNECTION

  13. ION SCALES, ~ 100 -1000 KM • HALL MHD PHYSICS IS DUE TO ADDITION OF jXB term. IT ALLOWS FOR PERPENDICULAR CURRENTS AND POSITIVE jperp·EperpON LARGE SCALE, BUT IT DOES NOT ALLOW FOR MAGNETIC FIELD LINES TO RECONNECT. • THIS PHYSICS IS UNDERSTOOD FROM: • Computer simulations (the first prediction, eg., Shay, M.A., J.F. Drake, B.N. Rogers, and R.E. Denton J. Geophys. Res., 106, 3759, (2001)) • Wind measurements (Oieroset et al, Nature (London), 412, 414, (2001)) • Geotail measurements (Nagai, T. et al, J. Geophys. Res.,106, 25929, (2001)) • Polar measurements (F.S. Mozer, S.D. Bale, T.D. Phan, Phys. Rev. Lett., 89, 015002, (2002)) • Cluster measurements (Cluster separations allow exploring this scale with four spacecraft, as exemplified by recent publications by Vaivads, et al, Phys. Rev. Lett., 93(10), 105001 (2004), Runov et al, (2003), and Wygant, et al, in publication, (2004)) • Recently observed in the MRX lab reconnection experiment

  14. POLAR OBSERVATION OF THE ION SCALE

  15. Density (#/cc) Bz (nT): GSM Coords Bx (nT) Simulation Polar Data By (nT) COMPARISON OF COMPUTER SIMULATION AND MAGNETOPAUSE DATA

  16. 2. ELECTRON SCALES ~ 1-10 KM NECESSARY CONDITIONS FOR THE ELECTRON DIFFUSION REGION 1. Ell ≠ 0 2. jperp·Eperp >> 0 3. Scale size ~ c/ωpe OBSERVED ONLY BY ELECTRIC FIELD EXPERIMENTS ON THE POLAR AND CLUSTER SATELLITES Scudder, J.D., F.S. Mozer, N.C. Maynard, and C.T. Russell, J. Geophys. Res., 107, 1294 (2002) Mozer, F.S., S.D. Bale, T.D. Phan, J.A. Osborne, Phys. Rev. Lett., 91, 245002, (2003) Appear in satellite data as ~100 msec large perpendicular and parallel electric fields. No observations exist of magnetic fields and plasmas on this time scale and no multiple spacecraft data exists. The Polar electric field experiment has catalogued several hundred such events, so they are frequently observed.

  17. 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 ~ 1 MeV per particle per second • Major density change at this time.

  18. POLAR OBSERVATION OF THE ELECTRON DIFFUSION REGION

  19. POLAR OBSERVATION OF THE ELECTRON DIFFUSION REGION

  20. ELECTRON DIFFUSION REGION EVENTS NEAR THE SUB-SOLAR MAGNETOPAUSE, 2001-2003

  21. FOUR-SATELLITE OBSERVATIONS OF ELECTRON DIFFUSION REGIONS

  22. EXAMPLES OF ELECTRON DIFFUSION REGION CANDIDATES IN FOUR SATELLITE DATA

  23. ELECTRIC FIELDS IN GSE FROM THE FOUR CLUSTER SPACECRAFT

  24. THREE SECONDS OF EY, DENSITY, AND BY FROM FOUR SPACECRAFT NOTES: SINGLE POINT PEAKS OF EY ΔEY OF 40, 90, 30, 70 mV/m ΔE CORRELATES WITH Δn AND BY

  25. FOUR SPACECRAFT TIMING OF ELECTRIC FIELD PULSES AT 0745:38 ANALYSIS ASSUMES PLANAR, STATIC WAVEFRONT THAT PASSES OVER THE FOUR SPACECRAFT • nX, nY, nZ = (0.9260, -0.3526, 0.1352) • BOUNDARY SPEED = 179 km/sec • NORMAL DISTANCE BETWEEN TWO MEASUREMENT POINTS < 1.8 c/ωpe

  26. SPACECRAFT LOCATIONS IN THE PLANE ON 12/21/03 AT 0745:38 ELECTRON DIFFUSION REGIONS ARE STABLE IN SPACE OVER HUNDREDS OF KILOMETERS AND TIMES OVER MANY SECONDS

  27. PHYSICS OF PLASMAS VOLUME 11, NUMBER 10 OCTOBER 2004 Three-dimensional simulations of magnetic reconnection in slab geometry M. Onofri, L. Primavera, F. Malara, and P. Veltri CURRENT ISOSURFACES

  28. SUMMARY - ANSWERS TO QUESTIONS • Why should one think about magnetic field lines that move? To visualize the evolution of the magnetic field geometry with time. 2. What are the necessary conditions for field lines to move with ExB/B2? Ell = 0 3. Do magnetic field lines move with ExB/B2 in a vacuum, or is plasma needed to satisfy the frozen-in condition before field lines can move with ExB/B2? Magnetic field lines move with ExB/B2 in a vacuum if Ell = 0 4. If all field lines move with ExB/B2 everywhere, can there be reconnection? No 5. Does the magnetic field line at point A move with the ExB/B2 velocity if the frozen-in condition is violated somewhere else along that field line? Yes 6. What are the necessary conditions for being in the reconnection region? Ell≠ 0, jperp·Eperplarge, spatial scale ~ c/ωpe 7. The electron diffusion region is the place where reconnection occurs. Has any experiment seen the electron diffusion region? Yes, the Electric Field Instruments on Polar and Cluster have seen hundreds of them.

  29. DEBYE SCALE ~ 0.1-1 KM FIRST OBSERVATIONS RECENTLY REPORTED FROM ELECTRIC FIELD MEASUREMENTS ON POLAR (Mozer, F.S., S.D. Bale, and J.D. Scudder, 31, doi:10.1029/2004GL020062, (2004) 1-10 MILLISECOND DURATION, >100 mV/m AMPLITUDE, ELECTRIC FIELDS NO MAGNETIC FIELD OR PLASMA DATA ON THIS TIME SCALE VERIFIED IN SIMULATIONS (Ma, Z.W., J. Huang, J.D. Scudder, F.S. Mozer, Paper SM51D-02, Fall AGU meeting, San Francisco, (2004) POSSIBLE PRECURSER THAT ESTABLISHES CONDITIONS FOR RECONNECTION (Scudder, J.D., Z.W. MA, F.S. Mozer, Paper SM53B-0426, Fall AGU meeting, San Francisco, (2004) ~ HUNDREDS OF POLAR OBSERVATIONS MADE ALONG THE FIELD LINE CONNECTED TO THE RECONNECTION REGION.

  30. POLAR OBSERVATION OF DEBYE SCALE STRUCTURES

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