Magnetosphere-Ionosphere Coupling through Plasma Turbulence at High-

Latitude E-Region Electrojet

Y. Dimant and M. Oppenheim

Tuesday, April 13, 2010

Center for Space Physics, Boston University

Dynamical Processes in Space Plasmas Israel, 10-17 April 2010

Outline

• Background and motivation• Anomalous electron heating• Nonlinear current; energy deposition• 3-D and 2-D fully kinetic modeling of E-region

instabilities• Anomalous conductivity• Conclusions; future work

Solar CoronaSolar Corona Solar WindSolar WindIonosphereIonosphereMagnetosphereMagnetosphere

Inner Boundary for Solar-Terrestrial System

Earth’s Ionosphere

What’s going on?

• Field-aligned (Birkeland) currents along equipotential magnetic field lines flow in and out.

• Mapped DC electric fields drive high-latitude electrojet (where Birkeland currents are closed).

• Strong fields also drive E-region instabilities: turbulent field coupled to density irregularities.– Turbulent fields give rise to anomalous heating.– Density irregularities create nonlinear currents.

• These processes can affect macroscopic ionospheric conductances important for Magnetosphere-Ionosphere current system.

Motivation

• How magnetospheric energy gets deposited in the lower ionosphere?

• Global magnetospheric MHD codes with normal conductances often overestimate the cross-polar cap potential (about a factor of two).

• Anomalous conductance due to E-region turbulence can account for discrepancy!

Strong electron heating

Reproduced from Foster and Erickson, 2000125 mV/m

(Reproduced from Stauning & Olesen, 1989)

Anomalous Electron Heating (AEH)

• Anomalous heating: Normal ohmic heating by E0 cannot account in full measure.

• Farley-Buneman, etc. instabilities generate E.

• Heating by major turbulent-field components E B is not sufficient.

• Small E|| || k|| || B, |E|||<<|E|, are crucial:

– Confirmed by recent 3-D PIC simulations.

Analyitical Model of AEH• Dimant & Milikh, 2003:

– Heuristic model of saturated FB turbulence (HMT),– Kinetic simulations of electron distribution function.

• Difficult to validate HMT by observations:– Radars:

• Pro: Can measure k|| (aspect angle ~ 1o),• Con: Only one given wavelength along radar LOS.

– Rockets: • Pro: Can measure full spectrum of density irregularities

and fields,• Con: Hard to measure E||; other diagnostic problems.

• Need advanced and trustworthy 3-D simulations!

PIC simulations: electron density

E0 x B direction

E0 d

irec

tion

3D simulations3D simulations• 256x256x512 Grid256x256x512 Grid

• Lower Altitude (more collisional)Lower Altitude (more collisional)

• Driving Field: ~4x Threshold field (150 Driving Field: ~4x Threshold field (150 mV/m at high latitudes)mV/m at high latitudes)

• Artificial eArtificial e-- mass: m mass: me:sime:sim = 44m = 44mee; ;

ExB direction (m)ExB direction (m)

E0

dir

ecti

on

(m

) B0

dir

ecti

on

(m

)

00

102

102

1020

0

410

Potential (x-y cross-section)

Potential (x-z cross-section)

4 Billion 4 Billion virtual PIC virtual PIC particlesparticles

2D looks the 2D looks the same!same!

Higher altitude 3D simulationHigher altitude 3D simulationIons: First Moment (RMS Of Vi)electrons: First Moment (RMS Of Ve)

3-D

Tem

ps

3-D

Tem

ps

2-D

Tem

ps

2-D

Tem

ps

100 105 110 115 120 125 130 135h,km

500

1000

1500

2000

2500

3000

3500radareffT

Anomalous heating

eT

iT

0T

[Milikh and Dimant, 2003] E = 82 mV/m

(comparison with Stauning and Olesen [1989])

Cross-polar cap potential

(Merkin et al. 2005)

Anomalous Electron Heating (AEH)

• Affects conductance indirectly:– Reduces recombination rate,– Increases density.

• All conductivities change in proportion.• Inertia due to slow recombination changes:

– Smoothes and reduces fast variations.

• Can account only for a fraction of discrepancy.• Need something else, but what?

Nonlinear current (NC)

• Direct effect of plasma turbulence:– Caused by density irregularities, n.

• Only needs developed plasma turbulence – no inertia and time delays.

• Increases Pedersen conductivity (|| E0)– Crucial for MI coupling!

• Responsible for the total energy input, including AEH.

Characteristics of E-region waves• Electrostatic waves nearly perpendicular to

• Low-frequency,

• E-region ionosphere (90-130km): dominant collisions with neutrals

- Magnetized electrons:

- Demagnetized ions:

• Driven by strong DC electric field,

• Damped by collisional diffusion (ion Landau damping for FB)

0 ||, k kB

ene

ini

0 0E B

en

0B

0E

20000 / BBEV

electronsions

Two-stream conditions

(magnetized electrons + unmagnetized ions)

Wave frame of reference

0E

_+_

+_ __

++ + +

_ _ _

+

+ + +

+

__ _ _

E E

0n

20000 BBEV

Ions

0n

0n

0n

Phn VV

Electrons

0B

00 BE

0E

E

E

-e

-eNLJ

Nonlinear Current

Mean Turbulent Energy Deposit

• Work by E0 on the total nonlinear current• Buchert et al. (2006):

– Essentially 2-D treatment,– Simplified plasma and turbulence model.

• Confirmed from first principles.• Calculated NC and partial heating sources:

– Full 3-D turbulence,– Arbitrary particle magnetization,– Quasi-linear approximation using HMT.

Anomalous energy deposition

jEjEjE jEjE

NC000 jEjEjE

Nonlinear current:

Vnqj

NC

jEjE

0

NC0 jE is total energy source for turbulence!

How 2-D field and NC can provide 3-D heating?

Density fluctuations in 3-D are larger than in 2-D!

3-D vs. 2-D, Densities

Nonlinear current (NC)

• Mainly, Pedersen current (in E0 direction).

• May exceed normal Pedersen current.

• May reduce the cross-polar cap potential.

• Along with the anomalous-heating effect, should be added to conductances used in global MHD codes for Space Weather modeling

E-region turbulence and Magnetosphere-Ionosphere Coupling

• Anomalous electron heating, via temperature-dependent recombination, increases electron density.

• Increased electron density increases E-region conductivities.

• Nonlinear current directly increases mainly Pedersen conductivity.

• Both effects increase conductance and should lower cross polar cap potentials during magnetic storms.

• Could be incorporated into global MIT models.

Conclusions

• Theory & PIC simulations: E-region turbulence affects magnetosphere-ionosphere coupling:– (1) Anomalous electron heating, via temperature-dependent

recombination, increases electron density.• Increased electron density increases E-region conductivities.

– (2) Nonlinear current directly increases electrojet Pedersen conductivity.

• Responsible for total energy input to turbulence.

– Both anomalous effects increase conductance and should lower cross-polar cap potentials during magnetic storms.

• Will be incorporated into a global MHD model.

Fully Kinetic 2-D SimulationsSimulations Parameters:• Altitude ~101km in Auroral region• Driving Field: ~1.5 Threshold field (50 mV/m at high

latitudes)• Artificial e- mass: me:sim = 44me; mi:sim=mi

• 2-D Grid: 4024 cells of 0.04m by 4024 cells of 0.04m• Perpendicular to geomagnetic field, B• 8 Billion virtual PIC particles• Timestep: dt = s (< cyclotron and plasma frequencies)

E2 (

V/m

)2

Time (s)

ExB direction (m) ExB direction (m)

E0 d

irec

tio

n (

m)

Threshold electric field

FB: Farley-Buneman instability

IT: Ion thermal instability

ET: Electron thermal instability

CI: Combined (FB + IT + ET) instability

1: Ion magnetization boundary

2: Combined instability boundary

High-latitude ionosphereEquatorial ionosphere

[Dimant & Oppenheim, 2004]

3-D vs. 2-D, Temperatures

• 3-D Simulations get hotter!3-D Simulations get hotter!

Electron Moments <Vx,y,z2> Ion Moments <Vx,y,z

2>

T$mp$ratur$s 0:

0.0 0.1 0.2 0.3tim$ (s)

400

600

800

1000

T (

K)

x0 y0 z0

FBI 128x128 psi=.3 M$=88m$ dx=0.08 E=140mV W$d May 17 15:43:21 2006

T$mp$ratur$s 1:

0.0 0.1 0.2 0.3tim$ (s)

300350

400

450

500

550

600

T (

K)

x1

y1

z1

FBI 128x128 psi=.3 M$=88m$ dx=0.08 E=140mV W$d May 17 15:43:21 2006

V$lociti$s 0:

0.0 0.1 0.2 0.3tim$ (s)

-1000

0

1000

2000

3000

V (

m/s

)

Vx0

Vy0 Vz0

V_hall0

V_p$d0

FBI 128x128 psi=.3 M$=88m$ dx=0.08 E=140mV W$d May 17 15:43:21 2006

V$lociti$s 1:

0.0 0.1 0.2 0.3tim$ (s)

0

50

100

150

200

V (

m/s

)

Vx1

Vy1

Vz1

V_hall1

V_p$d1

FBI 128x128 psi=.3 M$=88m$ dx=0.08 E=140mV W$d May 17 15:43:21 2006

3-D

Tem

p2-

D T

emp

Time (s) Time (s)

‘5-moment’ transport equations

0

Ch

2 / 32 / 3

1. Continuity equation :

0, (quasineutrality: )

2. Momentum equation (in neutral frame of reference) :

3. Thermal balance equation :

e i

n

nn n n

t

n Tdm q m

dt n

d Tn

dt n

V

VE V B V

ange of enthropy Frictional heatingCollisional cooling

22,

3

where: / , is fraction of collisional energy loss

n n n n

n n n

dV T T

dt t

m m m m

V

Fluid-model equations for long-wavelength waves: they do not include heat conductivity, Landau damping, etc., but contain all essential factors.