MAGNETIC FIELD RECONNECTION FROM FIRST PRINCIPLES TO LATEST RESULTS

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

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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.
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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?

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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

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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 jperpEperp gt
0 on large scale No reconnection if B lines
move with ExB/B2 everywhere
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GEOMETRY AT TIME t6 IF FIELD LINES MOVE WITH
ExB/B2
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THE GENERALIZED OHMS LAW

• In two fluid theory, the equations of motion for
  a unit volume of plasma are
• Ions nimi(?Ui/?tUi?Ui)
  niZe(EUixB)/c-?PiPie (1)
• Electrons neme(?Ue/?tUe?Ue)
  -nee(EUexB)/c-?PePei (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 OHMS LAW

EUixB cjxB/en ?c?Pe/en (mec2/ne2)?j/?t ?j

Equivalently, because j(c/ne) Ui ? Ue
EUexB ?c?Pe/en (mec2/ne2)?j/?t ?j
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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 Maxwells equations.
• MAGNITUDE AT tdt CONSISTENT WITH MAXWELLS
  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
• dBZ/dt ?(Bv) 0 (equation
  of continuity)
  (1)
• Because v ExB/B2, the components of Bv are
  (Bv)X EY and (Bv)Y -EX. So
• ?(Bv) dEY/dx dEx/dy
• which is the z-component of ?xE. Thus, the
  conservation equation is just Faradays law. So,
  without approximation and in the presence or
  absence of plasma, the magnitude of the magnetic
  field is always that expected from Maxwells
  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.

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FIELD LINE VELOCITY FROM FIRST PRINCIPLES

• DIRECTION AT tdt CONSISTENT WITH MAXWELLS
  EQUATIONS

Consider two surfaces, S1 and S2, that are
perpendicular to the magnetic field at times t
and t dt. 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 dt, 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, tdt), i.e., that give (b - a) x B(a,
tdt) 0?
(b - a)/e B
B?(ExB/B2)dt Also B(a, t dt) B (dB/dt)
)dt ((ExB/B2)?)Bdt 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 MAXWELLS
EQUATIONS
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• CONCLUSIONS
• A necessary condition is that Ell ? 0 in the
  magnetic field reconnection region.
• From EUexB ?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 Ohms Law
• must be non-zero to support the
  parallel electric field.
• WHICH TERM?

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SPATIAL SCALES OF RECONNECTION

• DIFFERENT PHYSICS OCCURS ON DIFFERENT SPATIAL
  SCALES
• Ion scales
• c/?pI 100 km at the sub-solar
  magnetopause
• cjxB/en on right side of the Generalized
  Ohms 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/?pe 2 km at the sub-solar
  magnetopause
• The remaining terms on the right side of
  the Generalized Ohms Law can become important,
  so Ell can be non-zero and reconnection can
  occur.
• Debye scales
• ?Debye 0.1 km
• Many large (150 mV/m) fields seen
  on this scale. They are mostly perpendicular to
  B.

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COMPUTER SIMULATION OF RECONNECTION
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ION SCALES, 100 -1000 KM

• HALL MHD PHYSICS IS DUE TO ADDITION OF jXB term.
  IT ALLOWS FOR PERPENDICULAR CURRENTS AND POSITIVE
  jperpEperp ON 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

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POLAR OBSERVATION OF THE ION SCALE
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COMPARISON OF COMPUTER SIMULATION AND
MAGNETOPAUSE DATA
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ELECTRON SCALES 1-10 KM
2.
NECESSARY CONDITIONS FOR THE ELECTRON DIFFUSION
REGION 1. Ell ? 0 2.
jperpEperp gtgt 0 3. Scale size c/?pe

• 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.

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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/?pe).
• Ell 8 mV/m
• jperpEperp/n 1 MeV per particle per second
• Major density change at this time.

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POLAR OBSERVATION OF THE ELECTRON DIFFUSION REGION
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POLAR OBSERVATION OF THE ELECTRON DIFFUSION REGION
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ELECTRON DIFFUSION REGION EVENTS NEAR THE
SUB-SOLAR MAGNETOPAUSE, 2001-2003
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FOUR-SATELLITE OBSERVATIONS OF ELECTRON DIFFUSION
REGIONS
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EXAMPLES OF ELECTRON DIFFUSION REGION CANDIDATES
IN FOUR SATELLITE DATA
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ELECTRIC FIELDS IN GSE FROM THE FOUR CLUSTER
SPACECRAFT
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THREE SECONDS OF EY, DENSITY, AND BY FROM FOUR
SPACECRAFT
NOTES SINGLE POINT PEAKS OF EY ?EY OF 40, 90,
30, 70 mV/m ?E CORRELATES WITH ?n AND BY
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FOUR SPACECRAFT TIMING OF ELECTRIC FIELD PULSES
AT 074538

• 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 lt
  1.8 c/?pe

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SPACECRAFT LOCATIONS IN THE PLANE ON 12/21/03 AT
074538
ELECTRON DIFFUSION REGIONS ARE STABLE IN SPACE
OVER HUNDREDS OF KILOMETERS AND TIMES OVER MANY
SECONDS
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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
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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, jperpEperp large, spatial
  scale c/?pe
• 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.

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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,
  doi10.1029/2004GL020062, (2004)
• 1-10 MILLISECOND DURATION, gt100 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.

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POLAR OBSERVATION OF DEBYE SCALE STRUCTURES
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