#### Transcript Solar Wind-Magnetosphere-Ionosphere Coupling: Dynamics in

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

**Paul Song**

*Center for Atmospheric Research University of Massachusetts Lowell*

**Vytenis M. Vasyliūnas**

*Max-Planck Institut für Sonnensystemforschung, Katlenburg-Lindau, Germany*

**2006 AGU Fall Meeting San Francisco, 11-15 December Paper SA41A-1395**

# 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!

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

Faraday’s law Ampere’s law 0

**j**

**B**

*t*

1

*c*

2

**E**

*t*

Generalized Ohm’s law

*m e e*

**j**

*t*

0

*N e e*

( Plasma momentum equation 0 )

*N m e e*

(

*en*

*in*

)(

*n*

)

*m e e*

(

*m e m i*

*in*

*en*

*ei*

)

**j F**

*m i*

*N e*

*t*

**U**

0

*e i*

*in*

*m e*

*en*

)(

*n*

)

*m e e m e*

**F**

*i m i*

(

*en*

*in*

) Neutral momentum equation

*m n*

*N n*

**u**

*n*

*t*

*e i*

*in*

*m*

*e en*

)(

*n*

)

*m e e*

(

*en*

*in*

)

*n*

Energy equations 3 2

*P d dt*

[log

*P*

5 / 3 ]

**j E U**

*c*

**B**

] 1 2 [(

**u**

*n*

**U**

) 2 3 2

*P n d dt*

[log

*P n*

5 / 3

*n*

] 1 2

*in*

[(

**u**

*n*

**U**

) 2 (

*w n*

2

*n*

(

**u**

*n*

**U**

2 ) /[ ( 1 2

*n*

*w*

2 )

**j j**

*c w w*

2

*n*

] ~ 1

*q*

**U**

.

*w*

2 )] (

*w*

2

*n*

*w*

2 )]

**Time Evolution of a Quantity**

**Basic Equations: gyro-averaged, valid on most time and spatial scales**

**B**

*t*

**E**

**j**

*t*

*t*

*c*

2 (

**B**

*e m e*

[

**E**

**U**

*t*

(

**U**

) 0

**U**

0

**j**

)

*N e*

(

**E**

1

*e*

[

*t*

**u**

*t n*

1

*n*

**U**

[

*e i*

*in*

**B**

0 )

*m e*

*en*

)(

**U**

**j B**

0

*e*

**j**

**u**

*n*

)

*e*

**F**

*n i*

*e*

(

*en in*

...]

*in*

)(

**U**

**u**

*n*

) ...]

*m e*

*en*

)(

**U**

**u**

*n*

)

*q*

**E**

...] •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

**Plasma Flow and Electric Field: Primary vs. Derived**

• In MHD (Alfven, dynamic) time scales • 0

**B**

*t*

**B E**

0

**j**

0 0

*N e*

(

**E**

**U**

*t*

(

**U**

)

**U**

*t*

**U**

1

*e*

**B**

0 ) [

*e*

(

*en*

**j B**

0

*in*

)(

**U**

*e i*

*in*

**u**

*n*

)

*m e*

*en*

)(

**U**

**u**

*n*

)]

**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.

**Solar Wind-Magnetosphere Coupling: Conventional Steady State Convection**

• magnetosphere is coupled with interplanetary electric field via reconnection

*sw*

=

*msph*

• magnetospheric convection: electric drift

**M-I Coupling Models**

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

**Steady State Height-integrated M-I Coupling**

0

**E**

0 0 0

*sw*

=

*msph*

=

*isph*

= const 0

**j**

=>

*N e e*

(

**E**

0 )

**j**

= 0 => j = ||

*N m e e*

(

*en*

*in*

)(

**U**

( )

**u**

*n*

) 0 0

*t*

(

**U**

*e*

)

**U**

*i*

*in*

1

*m N i e m e*

*en*

[ )(

**U**

**U j B**

0

**u**

*n*

)

**F**

*n*

...

*e*

**E U B**

0

*i*

*in*

*m e*

*en*

)(

**U**

**u**

*n*

) ...] =

**Σ**

(

*n*

**B**

) •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

**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

*U*

*t x*

(

*U*

• Dayside force balance before the turning 2

*x B*

2 / 2 0 ) /

*x*

0 (

*p*

*B*

2 / 2 0 ) /

*x*

• Southward turning: reconnection creates outflow

*U MP*

at the magnetopause, which goes to the 3 rd dimension. • The outflow lowers the pressure at the magnetopause • Magnetospheric plasma is accelerated in the sunward direction

*U x*

*t*

2

*U MP x MP*

*U x*

2

*x*

• Nightside:

**j**

x

**B**

force

**Magnetosphere-Ionosphere Mapping: Collisionless**

• Static mapping: 0

**E**

*L v B MP n MP*

*L v PC isph B*

0

*sw*

=

*msph*

=

*isph*

=> =0 • Dynamic mapping: Poynting flux conservation 0,

*W v a*

*B B*

2

*B*

1/ 2 2

*const*

• Consider both incident and reflected perturbations

**B**

**B**

1

**B**

2

**U**

1

*V A B*

**B**

1

**U**

**U**

1

**U**

2

**U**

2

*V A*

**B**

2

*B*

• 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

*B*

*isph*

1/ 4

*isph*

*U*

*isph*

*isph*

1/ 4

*isph*

1/ 4

*isph*

**Ionospheric Parameters at Winter North Pole**

## 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.

**Dynamic M-I Coupling: Collisional**

0

**B**

*t*

**B E**

0

**j**

0 0

*N e*

(

**E**

**U**

*t*

(

**U**

)

**U**

1

*m N i e*

*t*

**u**

*t n*

1

**U**

*n*

[

*N e*

(

*m i*

*in*

**B**

0 ) [

*m e*

*en e*

**j**

**j B**

0 )(

**U**

**u**

*n*

)

*e*

(

*en N e*

**F**

*n*

*in*

)(

**U**

(

*m i*

*in*

...]

*m e*

**u**

*n*

)

*en*

...

)(

**U**

**u**

*n*

) ...] •Neutral wind velocity is a function of height and time •Neutral wind responds over a long time period => plasma and B

**Joule Heating**

•Magnetospheric energy input:

**j**

•

**E**

•Joule heating:

**j**

•

**E**

* frame dependent

**j E**

'

*n*

**B**

)

*n*

**B**

**σE**

' •Conventional interpretation:

**j**

**j**

**E u**

*n*

**j B**

) Heating Mechanical work

**Comments:**

• Ohm’s law is derived assuming cold gases, no energy equation is used.

• Ohm’s 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 3 2

*P d dt*

[log

*P*

5 / 3 ]

**j E U**

*c*

**B**

] 1 2 [(

**u**

*n*

**U**

) 2 (

*w*

2

*n*

*w*

2 )] 3 2

*P n d dt*

[log

*P n*

5 / 3

*n*

] 1 2

*pn*

[(

**u**

*n*

**U**

) 2 (

*w n*

2

*w*

2 )]

**Energy equations show:**

*n*

(

**u**

*n*

**U**

2 ) /[ ( 1 2

*n*

*w*

2 )

**j j**

*c w w*

2

*n*

] ~ 1

*q*

**U**

.

• Joule heating (electromagnetic dissipation) is near zero.

• Heating is through ion-neutral collisions: frictional • Thermal energy is nearly equally distributed between ions and neutrals

Evolutionary Equations (time derivative determined by present values):

**B**

*t*

**E**

*f t a*

4

**r v**

*t*

**j E B**

*f a*

**r**

•

*f*

**v**

*a*

*f t a*

*coll m a*

*q a*

(

**E v**

*c*

**B**

)

*m a*

**g**

Divergence equations: 0

**E**

4

*c*

**g**

4

Definition of current density:

**J**

*a q a*

**v**

*f a*

Generalized Ohm’s Law:

**J**

*t*

*a*

2

*q n a m a*

(

**E**

**V**

*a c*

Plasma momentum equation:

**B**

)

*q a m a*

(

**κ**

*a*

)

**V**

*t*

1

*c*

**J B**

Collision terms (ionosphere):

*t*

**V**

*coll a*

**g**

**J**

*t*

*coll*

**J**

*t*

*t*

**V**

*coll coll*

(

*ei*

(

*m i*

*in en*

*m e m i*

*in*

)

**J**

*m e*

*en*

)

*n e*

(

**V**

*en e*

(

*en*

**V**

*n*

)

*in*

)(

**V**

*m e*

(

*in*

**V**

*n*

)

*en*

)

**J**

*e*

**Simplified overview of key equations**

**E**

*t*

4

**j B J**

**B**

**J**

*t*

(

*p*

2

**E B**

/

*c*

**B**

/(

*n ec e*

)] ....

produces change of , on time scale ~ p -1 .

**B**

*t*

**E**

**V**

*t*

**J B**

/

*c*

*in*

(

**V**

**V**

*n*

) change of bulk flow produced only by stress imbalance.

•

**J**

# Implications

is determined by the motion of all the charged particles, and there is no

*a priori*

(

*c*

/4 )

**B**

.

reason why it should equal • The equality of the two is established as consequence of the

**E**

/ t (“displacement current”) term.

• In a large-scale plasma ( primarily by changing

**J**

p >>1, L p /

*c*

>> 1), this occurs 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/V A .

**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.

## 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

• Vasyli ū nas, V. M.: Electric field and plasma flow: What drives what?, Geophys. Res. Lett., 28, 2177 –2180, 2001.

• Vasyli ū nas, V. M.: Time evolution of electric fields and currents and the generalized Ohm’s law, Ann. Geophys., 23, 1347 –1354, 2005.

• Vasyli ū nas, 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 Ohm’s law, J. Geophys. Res., 106, 8149–8156, 2001.

• Vasyli ū nas, V. M., and Song, P.: Meaning of