1. Quasi-Static Alfvén Wave Dynamics
and Scale-Dependent Energy Deposition
in Magnetosphere-Ionosphere Coupling
W. Lotko, A. Streltsov
Dartmouth College
R. Lysak
University of Minnesota
What is a quasi-static Alfvén wave?
Consequences for m-i coupling
Low-altitude energy deposition
Observational features
SM 71B-05
Theory Program

2.  < 1 / 0P (low altitude)
Quasi-static Alfvén Wave: Conditions
0PvA() >> 1
 < 1 / 0P (low altitude)
 f < 14 mHz (Freja)
e.g., P = 5 S  f < 6 mHz (FAST)
f < 1 mHz (Polar, Cluster)
, f wave frequency
 field-aligned distance above E region
P Pedersen conductance
vA() local Alfvén speed

3. Shear Alfvén Wavefunction
0.6
0.7
0.8
0.9
1.0
/i
0.5
1.5 1 2 50
100
150
200
B , nT
hB , nT– m
equator
P = 10 S
Rankin et al. ‘00
ionosphere

4. Chiu-Cornwall-Lyons ‘80
Quasi-static Alfvén Wave: Fields
E>
E<
J|| = K ||
J = PE  i d
B0ê
Vogt & Haerendel ‘98
Knudsen et al. ‘92
Transverse Length Scale for 
Chiu-Cornwall-Lyons ‘80
Weimer et al. ‘85

5. Reflection and Absorption
J|| = K ||
J = PE 
inc
ref
vAm
2 RE
0.1 1 10
100
1000
Wavelength, km -1
Reflection Coefficient
Absorption, %
Insulator
Conductor
~ d
vAi
Lysak and Carlson ‘81
Vogt and Haerendel ‘98

6. Energy Deposition: Length-Scale Dependence
Dissipation
Layer
P = 10 S
constant current
constant voltage
Streltsov and Lotko ‘02

7. E> d E< i Collisionless absorption J|| = K ||
Inferred Quantity i
Poynting Fluxes
J = PE 

8. Feedback Instability Ionospheric Alfvén Resonator
ENS
670 mV/m
equator
ionosphere
L = 7.25
8.25
Feedback Instability Ionospheric Alfvén Resonator
E Layer J  J 
Ne + –
Ne2 + –
P + –
E – +
Stable? yes no
Streltsov and Lotko ‘02

9. “Satellite” Measurements
Time Step = 297 s
ENS
BEW
j
670 mV/m
270 nT
80 A/m2
ionosphere
equator
600
400
200
mV/m
ENS
BEW 50
100
150 nT
distance, km
(mV/m)2 km
0.05
0.25
0.20
0.15
0.10
k, km-1
(nT)2 km
-50
-100
-150
-200 4 3 2 1 5 PE PB
Streltsov and Lotko ‘02

10. SUMMARY Alfvén waves  quasi-static at low altitude ( < 10 mHz )
MI Coupling
Lower magnetosphere: vA() >>   High “rigidity”
Jump in E at   (Haerendel - “fracture”)
Observational Features
Impedance:
S  electron energy flux
Feedback  low-altitude structure