Relation Between Electric Fields and Ionosphericmagnetospheric Plasma Flows at Very Low Latitudes

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Relation Between Electric Fields and
Ionospheric/magnetospheric Plasma Flows at Very
Low Latitudes

• Paul SongCenter for Atmospheric Research
• University of Massachusetts Lowell
• Vytenis M. VasyliunasMax-Planck-Institut für
  Sonnensystemforschung,
• Katlenburg-Lindau, Germany
• 2006 AGU Fall Meeting
• San Francisco, 11-15 December
• Paper SA41A-1395

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Conventional Model
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Can Electric Field Drive Magnetosphere/Ionosphere?

• Imposing an E-field (without flow) charge
  separation at boundaries in plasma oscillation
  period, nearly no E-field inside. Most E-field is
  concentrated in the sheath near the boundary
• Imposing a flow at the top boundary perturbation
  propagates along the field (Alfven wave),
  E-field is created accordingly.
• Finite collisions result in leakage current and
  small E-field inside
• Flow is driven by forces and not by E-field!

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Equations for SW-M-I-T Coupling(neglecting
photo-ionization, horizontally uniform)

• Faradays law
• Amperes law
• Generalized Ohms law
• Plasma momentum equation
• Neutral momentum equation
• Energy equations

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Time Evolution of a QuantityBasic Equations
gyro-averaged, valid on most time and spatial
scales

• For given values on the right at one time, the
  system evolves continuously. (No time derivatives
  on the right.)
• Right-hand-side terms are the drivers of
  left-hand-side variable

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Plasma Flow and Electric FieldPrimary vs.
Derived

• In MHD (Alfven, dynamic) time scales
• B and U are determined (primary), E and j then
  can be derived (secondary).
• Time variations of E and j cannot cause changes
  in B and U because they are results of B and U
  changes.
• In quasi-equilibrium, E and U appear to be
  mutually determined.

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Solar Wind-Magnetosphere Coupling Conventional
Steady State Convection

• magnetosphere is coupled with interplanetary
  electric field via reconnection
• magnetospheric convection electric drift

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M-I Coupling Models

• coupled via field-aligned current, closed with
  Pedersen current
• Ohms law gives the electric field and Hall
  current
• electric drift gives the ion motion

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Steady State Height-integratedM-I Coupling

• Time variations are introduced as boundary
  conditions in the solar wind. All quantities
  respond instantaneously, except density.
• E and U cannot be distinguished as to which is
  the cause.
• Neutral wind velocity is independent of height
  and time
• Some models introduce time dependence by ?(t)
  through all heights not self-consistent

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Sunward Convection on Closed Field Lines (after
an IMF southward turning)

• Convection of a flux tube can be cause by a force
  imbalance either in equator or ionosphere
• Simplified momentum equation is, x-component,
  equatorial plane
• Dayside force balance before the turning
• Southward turning reconnection creates outflow
  UMP
• at the magnetopause, which goes to the 3rd
  dimension.
• The outflow lowers the pressure at the
  magnetopause
• Magnetospheric plasma is accelerated
• in the sunward direction
• Nightside jxB force

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Magnetosphere-Ionosphere MappingCollisionless

• Static mapping
• Dynamic mapping Poynting flux conservation
• Consider both incident and reflected
  perturbations
• If the phase difference between the two is not
  important (120 km 3 Re)
• Perturbation velocity is related to local
  density
• Potential change is a function of height

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Ionospheric Parameters at Winter North Pole
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Proposed Model

• Distortion of the field lines result in current
• Continuity requirement produces convection cells
  through fast mode waves in the ionosphere and
  motion in closed field regions.
• Poleward motion of the feet of the flux tube
  propagates to equator and produces upward motion
  in the equator.

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Dynamic M-I Coupling Collisional

• Neutral wind velocity is a function of height and
  time
• Neutral wind responds over a long time period gt
  plasma and B

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Joule Heating

• Magnetospheric energy input j? E?
• Joule heating j? E? frame dependent
• Conventional interpretation
• Comments
• Ohms law is derived assuming cold gases, no
  energy equation is used.
• Ohms law is defined in a given frame
• In multi-fluid, there are multiple frames
  plasma and neutral wind.
• The behavior at lowest frequencies indicates a
  drag process, not Joule heating
• Energy equations show
• Joule heating (electromagnetic dissipation) is
  near zero.
• Heating is through ion-neutral collisions
  frictional
• Thermal energy is nearly equally distributed
  between ions and neutrals

• Heating Mechanical work

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Evolutionary Equations (time derivative
determined by present values) Divergence
equations


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Definition of current density Generalized Ohms
Law Plasma momentum equation Collision terms
(ionosphere)
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Simplified overview of key equations
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Implications

• J is determined by the motion of all the charged
  particles, and there is no a priori reason why it
  should equal (c/4?)??B.
• The equality of the two is established as
  consequence of the ?E/?t (displacement current)
  term.
• In a large-scale plasma (?p ? gtgt1, L?p/c gtgt 1),
  this occurs primarily by changing J to match the
  existing (c/4?)??B, while E takes the value
  implied by the generalized Ohms law (LH side
  0), both on time scale of order ?p-1.
• V is changed by stress imbalance, while ?? B
  changes as consequence of changing B to achieve
  stress balance, both on time scale typically of
  order L/VA .

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Summary

• When dynamic processes are considered, B and U
  are primary/causes and E and j are
  derived/results.
• Sunward magnetospheric convection is driven by
  pressure forces and not by E-field. It produces
  an E-field.
• Dynamic mapping indicates that the amplitude of
  the ionospheric velocity/E-potential) varies with
  height/density.
• Neutral wind velocity should be treated as a
  function of height and time in M-I coupling.
• Energy equations are derived for the thermal
  energy. The term Joule heating has been misused
  in M-I coupling.

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Conclusions

• Throughout the magnetosphere and the ionosphere,
  large-scale plasma flows and magnetic field
  deformations are determined by stress
  considerations. Tangential stress from the solar
  wind is transmitted predominantly by Alfven
  (shear) waves along open magnetic field lines and
  by fast-mode (compressional/rarefactional) waves
  across closed magnetic field lines. Large-scale
  electric fields and currents are determined as
  consequences of the above.
• Within the poorly conducting atmosphere below the
  ionosphere, electromagnetic propagation at nearly
  the speed of light can occur, but the resulting
  fields have only a minor effect on the
  ionosphere.
• Magnetospheric convection propagates from the
  polar cap to low latitudes on a time scale set by
  the fast-mode speed ( Alfven speed) just above
  the ionosphere.

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References

• Vasyliunas, V. M. Electric field and plasma
  flow What
• drives what?, Geophys. Res. Lett., 28,
  21772180, 2001.
• Vasyliunas, V. M. Time evolution of electric
  fields and
• currents and the generalized Ohms law, Ann.
  Geophys.,
• 23, 13471354, 2005.
• Vasyliunas, V. M. Relation between magnetic
  fields and
• electric currents in plasmas, Ann. Geophys., 23,
  2589
• 2597, 2005.
• Song, P., Gombosi, T. I., and Ridley, A. J.
  Three-fluid
• Ohms law, J. Geophys. Res., 106, 81498156,
  2001.
• Vasyliunas, V. M., and Song, P. Meaning of
  ionospheric
• Joule heating, J. Geophys. Res., 110, A02301,
• doi10.1029/2004JA010615, 2005.