Prompt Penetration of Magnetospheric Convection to Low Latitudes: What is the Physical Mechanism?

Vytenis M. VasyliūnasMax-Planck-Institut für Sonnensystemforschung,

Katlenburg-Lindau, Germany

Paul SongCenter for Atmospheric Research

University of Massachusetts Lowell

2006 AGU Fall Meeting

San Francisco, 11-15 December

Paper SA44A-05

Conventional Model

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!

Evolutionary Equations (time derivative determined by present values):

Divergence equations:

4

( , , )

( )

a a a a

coll

a a a

ct

ctf t f f f

t t

m q mc

BE

Ej B

r vv v

r v

vv E B g

•

•

0 4 4 c G B E g

Definition of current density:

Generalized Ohm’s Law:

Plasma momentum equation:

Collision terms (ionosphere):

3

2

( )

( ) ( )

1

( ) ( )( )

( ) ( )

a aa

a a a aa a a

a colla a

coll

eei en in e en in n

coll i

i in e en e ncoll

q f d v

q n qq n

t m c m t

t c t

men

t m

m m nt

J v v

VJ JE B κ g

V Vκ J B

JJ V V

VV V ( )e in enm

e

J

Simplified overview of key equations

2

4

difference between & ( /4 ) produces change of .

( / 4 )[ / /( )] ....

deviation of from value given by generalized Ohm's law

produces change of , on time scale

p e

ct

c

c n ect

Ej B

J B E

JE V B J B

E

J -1p~ .

change of produced only if there is spatial variation.

... / ( )

change of bulk flow produced only by stress imbalance.

in n

ct

ct

BE

B

VJ B V V

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 >>1, Lp/c >> 1), this occurs primarily by changing J to match the existing (c/4)B, while E takes the value implied by the generalized Ohm’s 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 .

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.

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.

References• Vasyliūnas, V. M.: Electric field and plasma flow: What

drives what?, Geophys. Res. Lett., 28, 2177–2180, 2001.• Vasyliūnas, V. M.: Time evolution of electric fields and

currents and the generalized Ohm’s law, Ann. Geophys.,23, 1347–1354, 2005.

• Vasyliūnas, V. M.: Relation between magnetic fields andelectric currents in plasmas, Ann. Geophys., 23, 2589–2597, 2005.

• Song, P., Gombosi, T. I., and Ridley, A. J.: Three-fluidOhm’s law, J. Geophys. Res., 106, 8149–8156, 2001.

• Vasyliūnas, V. M., and Song, P.: Meaning of ionosphericJoule heating, J. Geophys. Res., 110, A02301,doi:10.1029/2004JA010615, 2005.