Car

lso

n e

t al

. ‘0

1

Three Characteristic Acceleration Regions

Car

lso

n e

t al

. ‘0

1

Alfvén Wave Induced Outflow

OUTFLOW

Str

ang

ew

ay e

t al.

’02

Ponderomotive

Lifting

via Alfvén Waves

ap|| = ¼||(E/B0)2

> GME/r2

for E > 200 mV/m

at 1000 km altitude

Li and Temerin ‘93

Ponderomotive Force (in a cold magnetized plasma)

^

^^

= - »- w w

ww

wÑ Ñ

22

22

2i

2 2i

c

ci

i

02pi

me 1 1 EE

E4

E E 1

B4mF

• Electrodynamic Coupling: Energy Dissipation

/̶ Joule heating

/̶ Current-Voltage relation (Knight; ?)

/̶ Alfvén wave induced dissipation (?)

• Inertial Coupling: Mass Exchange

/̶ Bulk outflows – polar wind

/̶ Fractional outflows – energization (O+)

MIC

LFM

RCM

LFM

RCM RCM

LFM

LFM

RCM

TING MIC

MIC

TING

TING MIC

MICseconds

iterateminutes

minutes

1½-way LFM-RCM coupling w/ convergent, iterative, 2-way TING coupling

LFM

TING

Empirical Σ̶?

SWM

PrecipW|| , E0

j||

Φ,Σ?̶

nv

Φ

s

m

B

RCMs

TING

×ΦΣ?̶

||n Bv j

M-I Coupler

minutes

LFM

TING

SWM

B2> j||

s

m

B

RCMs

M-I Mass Coupler

ˆ ˆ/

+ +

+ + +

2n e 0O O

O n O O n

b g b2V V P P B

minutes

Gravity = Ponderomotive Force

at 1000-km altitude for

nO+ = 1010/m3 and B = 80 nT

ˆS E B b

j BMIC

LFM

RCM RCM

LFM

LFM

RCM

TING

TING

Keiling et al. ‘03

Visible FUV

Downward Poynting

Flux

UpwardPoynting Flux

Auroral Morphologyas seen in

Car

lso

n e

t al

. ‘0

1

Alfvénic Acceleration Regions

Intense, field-aligned Poynting fluxes flow earthward along the “lobe-plasma sheet” interface

Polar

FAST

MPAUVI

Lobe

Plasma Sheet

Polar Cap

AuroralZone

Wygant et al. ’00

CISM All Hands MeetingCISM All Hands Meeting 15 Sep 200315 Sep 2003

LFM Low-Altitude BoundaryLFM Low-Altitude Boundary

( , , )S L t E H

TING High-Altitude BoundaryTING High-Altitude Boundary

LFM Low-Altitude BoundaryLFM Low-Altitude Boundary

0( , , , )S L t E B

TING High-Altitude BoundaryTING High-Altitude Boundary

+ +

+ +O O

O O

20/

1 1ˆ 2e n

n

V P P VB

b g

, j B

+O,VE

TING High-Altitude BoundaryTING High-Altitude Boundary

,uE

ii

iS + L

uB

B

d

dt

ˆ ˆ1

2

0/2 b ri

in i n

i

e i

duP BP

dtg u u

252 ( ) (u u )

3 3

i i i in

i n i i n

i n

ni

dP

dt

uP B k T T

B m m

mQ

ˆ( )u b

E i

du

dt t

““Quasi-static” Alfvén Quasi-static” Alfvén waveswaves

3/2

01 0

3/2

02 0

( , ) ( , )

( , ) ( , )L L L L

rh B C L B B L

r

rh B C L B B L

r

2

0

v B v B

J B

2

i i Pol

Pol

en en

B

Alfvén-wave Alfvén-wave

Lorentz Lorentz ForceForce

Banks and Holzer ‘69

Questions

LFM

• BCs on , T?

• Inner boundary at r = constant where r b 0 r vE 0, i.e., vE has a component normal to the boundary.

TING

• Ion energy and momentum equations?

• Same ion composition in E and F layers?

Grid Specification

MM

RCM

TIM

MIC

CHART LEGEND

Source of Numerical Data

Magnetospheric Model

Ring-Current Model

Thermosphere-Ionosphere Model

M-I Coupler

“Variable A from MM on the MM grid and

variable A from RCM on the RCM grid

are interpolated onto the MIC grid” MIC

RCMMM

A

seconds

minutes

MIC

MM

RCM

MM

RCM RCM

MM

MM

RCM

MICMIC

1½-way LFM-RCM coupling

MM

Empirical Σ̶?

SWM

PrecipW|| , E0

j||

Φ

s

B

RCMs

ΦΣ?̶

||

jM-I Coupler

iterate

minutes

MM

RCM RCM

MM

MM

RCM

TIM MIC

MIC

TIM

TIM MIC

MIC

Convergent, iterative, 1-way TING coupling

MM

TIM

Empirical Σ̶?

SWM

PrecipW|| , E0

j||

Φ,Σ?̶

nv

s

m

B

RCMs

×ΦΣ?̶

||n Bv j

M-I Coupler

Auroral Electrodynamics

Opgenoorth et al. ‘02

Ionospheric Feedback

Atkinson ’70; Sato ‘78

Polarization Field-Aligned Current

Two-fluid MHD model of the magnetosphereTwo-fluid MHD model of the magnetosphere

Electron parallel momentum equationElectron parallel momentum equation

Density continuity equationDensity continuity equation

Current continuity equationCurrent continuity equation

,0ˆ ||0||||

0

eeICARe

e pEent

nm bvv

where v||e - electron parallel speed; IC - electron collision frequency;

AR - effective collision frequency representing the effects of plasma anomalous resistivity.

where ρi - ion Larmour radius.

,0ˆ||0

1

bent

nv

,01ˆ12

222

0||22

t

cj

Aii

Eb

v

Model of the auroral ionosphereModel of the auroral ionosphere

Density Continuity Equation

where n = n0 + n1 - plasma number density; - ionization source maintaining equilibrium density n0 outside the region of auroral precipitations; j|| - field-aligned current; - recombination coefficient.

Current Continuity Equation

where P and H are height-integrated ionospheric Pedersen and

Hall conductances.

,1 2||||1 nSeh

j

eh

j

t

ni

hot

20nSi

,ˆ||jHP bEE

“Feedback” Unstable Alfvén Waves

Growth rate vs

P, E and k

Two resonant cavities

Large-Scale Resonator

Small-Scale Resonator

Pokhotelov ‘02

Feedback Instability Ionospheric Alfvén Resonator

E Layer J J

Ne + –

Ne2 + –

P + –

E – +

Stable? yes no

Streltsov and Lotko ‘02

125 s

297 s

281 s

266 s

251 s

235 s

220 s

204 s

188 s

173 s

157 s

141 s

ENS

670 mV/m

equator

ionosphere

L = 7.25 8.25

Streltsov and Lotko ‘02

600

400

0

200

mV

/m

ENS

BEW

0 50 100 150 200

nT

distance, km

0

50

100

150

(mV

/m)2

km

0 0.05 0.250.200.150.10

k, km-1

(nT

)2 k

m

0

-50

-100

-150

-200

0

4

3

2

1

5

PE

PB

Time Step = 297 s

ENS

BEW

j

670 mV/m

270 nT

80 A/m2

ionosphere

equator

“Satellite” Measurements

ENS

(mV/m)

L = 8.25

7.25

IONOSPHERE

1 RE

44 RE

Animation sequence from0 < t < 300 s