Transcript No Slide Title

Magnetosphere-Ionosphere Coupling
through Plasma Turbulence at HighLatitude E-Region Electrojet
Y. Dimant and M. Oppenheim
Center for Space Physics, Boston University
Dynamical Processes in Space Plasmas
Israel, 10-17 April 2010
Tuesday, April 13, 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
Inner Boundary for Solar-Terrestrial System
Solar Corona
Solar Wind
Magnetosphere
Ionosphere
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 MagnetosphereIonosphere 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
125 mV/m
Reproduced from Foster and Erickson, 2000
(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 dE.
• Heating by major turbulent-field components
dE^^ B is not sufficient.
• Small dE|| || k|| || B, |dE|||<<|dE^|, 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!
E0 direction
PIC simulations: electron density
E0 x B direction
3D simulations

4 Billion virtual
PIC particles 102
2D looks the
same!
Potential
(x-y cross-section)
E0 direction (m)

0
0
ExB direction (m)
102
Potential
(x-z cross-section)
410
B0 direction (m)
• 256x256x512 Grid
• Lower Altitude (more collisional)
• Driving Field: ~4x Threshold field (150
mV/m at high latitudes)
• Artificial e- mass: me:sim = 44me;
0
0
ExB direction (m)
102
Higher altitude 3D simulation
2-D Temps
3-D Temps
electrons: First Moment (RMS Of Ve)
Ions: First Moment (RMS Of Vi)
Anomalous heating
(comparison with Stauning and Olesen [1989])
3500
3000
radar
eff
T
2500
Ti
2000
1500
Te
1000
500
T0
100 105 110 115 120 125 130 135
h, km
E = 82 mV/m
[Milikh and Dimant, 2003]
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, dn.
• 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 B0 , k||  k^
• Low-frequency,    en
• E-region ionosphere (90-130km): dominant collisions with neutrals
- Magnetized electrons: e   en
- Demagnetized ions:
i   in
• Driven by strong DC electric field, E0 ^ B0
• Damped by collisional diffusion (ion Landau damping for FB)
Two-stream conditions

E0

B0



V0  E0  B0 / B02
ions
electrons
(magnetized electrons + unmagnetized ions)
Wave frame of reference

B0
Ions

dE
dn  0
_
+
_
_+

E0
Electrons
+
dn  0


Vn  VPh

dE
_
+
_
_+
+
dn  0
_
+
_
_ +
_
_
+
_+
+
dn  0



2
V0  E0  B0 B0

dE
Nonlinear Current

dE
e
-

E0


E 0  B0
e

J NL
-
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
        
E
E jj EE0E0 j0 j jE0 jNC
dE  d j
 
E0  jNC is total energy source for turbulence!
Nonlinear current:
 3-D heating?
 and NC can provide
How 2-D field
jNC   q dn dV
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 temperaturedependent 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.
Simulations 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 = 3ms (< cyclotron and plasma frequencies)
E2 (V/m)2
Fully Kinetic 2-D Simulations
E0 direction (m)
Time (s)
ExB direction (m)
ExB direction (m)
Threshold electric field
Equatorial ionosphere
High-latitude ionosphere
FB: Farley-Buneman instability
1: Ion magnetization boundary
IT: Ion thermal instability
2: Combined instability boundary
ET: Electron thermal instability
CI: Combined (FB + IT + ET) instability
[Dimant & Oppenheim, 2004]
3-D vs. 2-D, Temperatures
Ion Moments <Vx,y,z2>
2-D Temp
3-D Temp
Electron Moments <Vx,y,z2>
Time (s)
• 3-D Simulations get hotter!
Time (s)
‘5-moment’ transport equations
1. Continuity equation :
n
   nV  0, (quasineutrality: ne  ni )
t
2. Momentum equation (in neutral frame of reference) :


  n T 
dV
m
 q E  V  B0 
 m  nV
dt
n


3. Thermal balance equation :
Change of enthropy
Frictional heating
Collisional cooling
 T  2
d 
2
n

m

V

d

T

T
,
  V  
 2/3 
 n 
n n  
n
dt t
 n  3
where: m  m mn /  m  mn  , d  n is fraction of collisional energy loss
2/3
d
dt
Fluid-model equations for long-wavelength waves: they do not
include heat conductivity, Landau damping, etc., but contain all
essential factors.