Transcript Document

Thayer School of Engineering
Dartmouth College
“Effects of the Active Auroral Ionosphere on
Magnetosphere - Ionosphere Coupling”
Dimitri Pokhotelov
Ph.D. Thesis Defense
Research Advisors:
William Lotko
Anatoly V. Streltsov
September 2002
Magnetosphere
Field-aligned currents and ionospheric convection
System of large-scale field-aligned
currents facilitates the ionospheric
convection flow.
Plasma flows anti-sunward over the polar
regions and streams back sunward at lower
latitudes forming two-cell convection pattern.
After Iijima and Potemra [1976]
Auroral ionosphere
The enhancement of collisions with neutrals at the
ionospheric E-layer enables transverse Pedersen and
Hall currents to flow in a thin (20-30 km) ionospheric
conducting layer at the altitude of about 100 km.
Narrow beams of accelerated electrons precipitate
into the ionosphere along magnetic field lines causing
discrete aurora.
System of magnetospheric field-aligned
currents projects into high-latitude region
of the ionosphere called auroral oval.
Image is a courtesy of APL
Johns Hopkins University
Introduction
The research is devoted to the effects of electromagnetic coupling between the Earth's
magnetosphere and the active auroral ionosphere focusing on the concept of ionospheric
feedback instability.
In the presence of ionospheric convection flow local conductivity irregularities lead to
the development of ionospheric feedback instability that radiates shear Alfvén waves
into the magnetosphere.
Strong parallel magnetospheric inhomogeneities facilitate simultaneous development
of local ionospheric resonator modes (fast feedback) and field line eigenmodes (slow
feedback).
Effects of plasma micro-instabilities excited in the large field-aligned currents of the
feedback-driven Alfvén waves generate fluxes of energetic electrons that precipitate into
the ionosphere producing discrete auroral arcs.
Satellite observations of seasonal and diurnal variations in the intensity of auroral
precipitation suggest that the feedback instability can be responsible for such asymmetry.
Studies of the heating effects imposed on the auroral ionosphere by powerful radio
waves suggest that the feedback instability can be excited artificially by HF radars.
Physical mechanism of the ionospheric feedback instability
In the presence of ionospheric
convection flow, an enhancement in
ionospheric conductivity generates
polarization electric field locally
reducing ionospheric Joule dissipation.
Energy released by this process
radiates into magnetosphere in the form
of shear Alfvén waves.
After reflection from the conjugate
ionosphere or a magnetospheric
inhomogeneity, generated Alfvén wave
returns to the ionosphere further
enhancing the initial conductivity
perturbation.
After Lysak [1990]
Historical review
A model for auroral arc formation involving active feedback between the magnetosphere and
ionosphere was first proposed by Atkinson [1970]. Using dispersion analysis Sato [1978]
demonstrated that the feedback instability growth rate is controlled by the ionospheric
parameters such as Pedersen and Hall conductances and convection electric field.
Miura and Sato [1980] and Watanabe et al. [1993] numerically modeled the auroral arc
formation due to the feedback instability in 2D geometry. However, the magnetospheric
response in their models was simulated in simplified way, in particular, they neglected the
effects of strong parallel plasma inhomogeneities in the magnetosphere.
The effects of parallel Alfvén speed inhomogeneities have been studied by Trakhtengertz
and Feldstein [1981] and Lysak [1991] who demonstrated that a feedback instability can also
develop at the local ionospheric resonant cavity.
Satellite observations of by Newell et al. [1996]; Shue et al. [2002] has demonstrated
connections between conductance of auroral ionosphere and the occurrence of auroral arcs
pointing to the role of ionospheric feedback in the formation of discrete aurora.
Using satellite measurements, Robinson et al. [2000] detected Alfvén waves and downward
fluxes of accelerated electrons above the region of the ionosphere heated by HF radar, which
they attributed to the development of ionospheric feedback instability.
Outline
Model of the active auroral ionosphere
Part 1: Simulations using lumped transmission line model of the magnetosphere
Dispersion analysis.
Numerical 2D simulations.
Part 2: Simulations using two-fluid MHD model of the magnetosphere
Numerical 2D simulations using the model with strong parallel plasma inhomogeneities.
Spectral analysis of the numerical solution.
Part 3: Applications
Effects of the seasonal asymmetry in ionospheric Pedersen conductance.
Artificial heating of the auroral ionosphere with HF radars.
Experimental diagnostics of feedback-driven field line resonances
Future developments
Model of the auroral ionosphere
Density Continuity Equation
j||
j|| hot
n1

 1   
 Si  n 2 ,
t
eh
eh
where n = n0 + n1 - plasma number density;
Si  n02 - ionization source maintaining equilibrium density n0
outside the region of auroral precipitations;
j|| - field-aligned current;  - recombination coefficient.
Current Continuity Equation


  S P E  S H E  bˆ   j|| ,
where SP and SH are height-integrated ionospheric Pedersen and
Hall conductances.
Part 1: Simulations using lumped transmission line
model of the magnetosphere
The model is based on the representation of the magnetosphere as a lumped
transmission line with explicitly specified impedance.
Similar to the approach used by Sato [1978] and Miura and Sato [1980].
Advantages of using transmission line model:
facilitate dispersion analysis of the feedback instability;
suggest an explanation for diurnal asymmetry in the occurrence of auroral
precipitation;
relatively easy to implement numerically.
Disadvantages:
does not include effects associated with the strong parallel plasma inhomogeneities
such as partial reflection of Alfvén waves;
does not allow to analyze effects that are responsible for generation of parallel electric
fields and auroral acceleration such as Alfvén wave dispersion or plasma anomalous
resistivity.
Lumped transmission line model of the magnetosphere
Linearized one-fluid MHD equations in cold collisionless plasma approximation
v1
mi n0
 j1  B 0  0; E1  v1  B0  0.
t
Assumptions:
1. Neglect curvature of the magnetic field lines
2. B0 and n0 are uniform along the field lines
Then the solution is given by
 l 
   E 1
.
 i 0 v A cot 
j||1
 vA 
Expansion around the fundamental eigenfrequency of the magnetic field line
 = vA /l gives equation of the magnetospheric response [Miura and Sato, 1980]
2


 l  2
2 0l j||1
2






1

1.
2
2



t
 v A  t

Dispersion analysis of the feedback instability
The linear dispersion analysis
has been performed to estimate
the stability criteria for the
coupled MI system.
Dispersion analysis
demonstrate that the feedback
instability becomes efficient
under conditions of:
low ionospheric conductivity;
strong ionospheric convection;
low plasma recombination.
Simulations using transmission line model
Background distributions of
ionospheric parameters calculated
using a lumped transmission line
model of the magnetospheric
response.
Simulations using transmission line model
Time evolution of fieldaligned current density
perturbation simulated using a
lumped transmission line model
of magnetospheric response.
An initial perturbation of
the ionospheric plasma
density has been chosen in
the form of a gaussian in
latitude with no variation
in longitude.
Due to the development of feedback
instability latitudinally-striated arcs are
developing in the pre-midnight sector
(similar to Miura and Sato [1980])
Part 2: Simulations using two-fluid MHD model
of the magnetosphere
The model is based on the two-fluid MHD equations that describe propagation of
shear Alfvén waves in an inhomogeneous, low-β magnetospheric plasma.
Similar to the approach used by Streltsov and Lotko [1997]; Streltsov et al. [1998].
The system of MHD equations is solved numerically in 2D dipolar geometry.
Strong parallel inhomogeneities in background magnetospheric plasma parameters
included in the model facilitate partial reflection of feedback-generated Alfvén waves
from the Alfvén speed maximum above the ionosphere.
The model allows to analyze a simultaneous development of ionospheric resonator
modes standing between the ionosphere and the Alfvén speed peak, and field line
eigenmodes standing along the entire magnetic field line between conjugate
ionospheres.
Inertial and kinetic dispersion of Alfvén waves and the effects of plasma anomalous
resistivity, included in the model, lead to the formation of parallel electric fields in the
magnetosphere.
Two-fluid MHD model of the magnetosphere
Electron parallel momentum equation
 v||e

me n0 
  AR   IC  v||e   en0 E||  bˆ  pe  0,
 t

where v||e - electron parallel speed; IC - electron collision frequency;
AR - effective collision frequency representing the effects of plasma anomalous resistivity.
Density continuity equation
n1
   n0 v||ebˆ  0,
t
Current continuity equation
2

 E 
c
2 2
2 2
ˆ
1  i     j||b   0  1  i    2 
 0,
v A  t



where ρi - ion Larmour radius.
Distribution of background parameters
System of equations describing MI
coupling has been solved numerically
in 2D dipolar geometry resembling
Earth’s magnetosphere
Computational Grid
L = 8.25
Distance, RE
L = 7.75
Equator
Magnetospheric plasma density decreases with altitude
faster then the magnetic field. It leads to the formation of
Alfvén speed maximum.
Distance, RE
The feedback instability simultaneously generates
ionospheric resonator modes (fast feedback) and field line
eigenmodes (slow feedback) standing along the entire
magnetic field line between two ionospheres.
Numerical simulations
t = 570s
S PN0  0.5 mho
SSP0  3 mho
Analysis of the numerical solution
A dynamic spectral analysis
demonstrates the relative contribution
of various modes of oscillation in the
numerical solution.
Instability saturation is controlled by
the nonlinear plasma recombination.
Instability saturation level is lower in
the high-conductivity southern
ionosphere.
The feedback instability may be
responsible for generation of higher
harmonics of field line resonances as
well as eigenmodes of the ionospheric
Alfvén resonator.
Part 3: Applications
Effects of seasonal asymmetry in ionospheric Pedersen conductance on the
energy deposition into auroral ionosphere.
Seasonal difference in the ionospheric conductance is modeled using empirical relation
between solar energy flux and ionospheric Pedersen conductance.
The effects of accelerated electron precipitation and resulting energy deposition is
analyzed using the Fridman-Lemaire model.
Artificial heating of the auroral ionosphere with HF radars.
Artificial heating can trigger the ionospheric feedback instability when the coupled MI
system is near a state of marginal stability.
The effects of artificial heating have been modeled by introducing variations in the
plasma recombination and the electron collision frequency.
Experimental diagnostics of feedback-driven field line resonances
Ionospheric Joule heating rate.
Time-averaged Poynting flux.
Differences in the phase properties of resonances.
Observed seasonal and diurnal variations in aurora occurrence
Images are courtesy of APL
Johns Hopkins University
DMSP satellite data [Newell et al., 1996] and Polar UVI imager observations
[Liou et al., 1997] demonstrated strong diurnal and seasonal asymmetry in the
energetic electron precipitation and occurrence of auroral arcs.
Analysis of Polar UV Imager data [Shue et al., 2002] established connection
between ionospheric Pedersen conductance and the occurrence of discrete aurora.
Plasma anomalous resistivity
When the electron parallel speed exceeds a critical value vc, the drifting electrons
excite plasma micro-instabilities which impose a drag force slowing parallel electron
motion.
The loss in electron parallel momentum is compensated by the formation of parallel
electric fields in the magnetosphere.
Simple model of anomalous resistivity has been suggested by Lysak and Dum [1983]:
 ci 1  vc / | v||e | if | v||e |  vc ,
 AR  
0
ot herwise,
where vc = vTe is a constant with a value equal to the critical velocity for
electrostatic ion-cyclotron instability at the altitude where v||e peaks.
This simplified model of plasma microturbulence effects appears to be a
reasonable way to incorporate plasma anomalous resistivity into the MHD model.
MHD simulations with this model of anomalous resistivity [Lysak and Dum, 1983;
Streltsov and Lotko, 1999] demonstrated good agreement with satellite
observations of auroral acceleration events.
Model for the auroral electron precipitation
Non-zero parallel potential drop Δ|| is due to the effects of
dispersion of Alfvén waves and
anomalous resistivity.
Field-aligned current provided by energetic electrons precipitating into the
ionosphere [Fridman and Lemaire, 1980]
j|| hot
1/ 2
 T 
B


en0E 
B
 2me 
I
0
E
0
E
e
Ionization rate due to the hot electron
precipitation [Banks et al., 1974]
 0
||3
  
3
||
3
|| cr
,
where 0 = 50 and ||cr = 1.5 kV

 exp  xe|| / TeE
1 
1 x




Numerical simulations with hot electron precipitation model
S PN0  0.5 mho
SSP0  3 mho
Seasonal variations in the auroral energy flux
Integral energy flux into the auroral ionosphere has
been calculated using Fridman-Lemaire model for the
hot electron precipitation as
W|| hot 
L2

1
2
j|| hot || hL dL,
L1
and the total energy deposition into the auroral ionosphere
t0
Phot   W|| hot dt.
0
The asymmetry in conductivity between the two
hemispheres leads to stronger energy flux into the
winter ionosphere.
Enhanced energy flux into the winter ionosphere
can increases the occurrence of discrete aurora in
the winter hemisphere as been reported by Newell,
Liou and their co-workers.
Heating of the ionosphere with HF radar
Heating of the ionosphere with HF radio
waves leads to the local enhancement of plasma
temperature.
The increase in electron temperature reduces
particle recombination coefficient in the
ionospheric E-layer and reduces electron
collision frequency in the F-layer [e.g.,
Gurevich, 1978; Robinson, 1989].
HF heating can be used to modulate auroral
electrojet at ULF frequencies thus generating
ULF magnetic pulsations [Stubbe et al., 1982;
1985].
Observations of Alfvén waves and electron
fluxes by FAST satellite during the ionospheric
heating experiment [Robinson et al., 2000] have
been interpreted as the effects of ionospheric
feedback.
After Robinson et al. [2000]
Heating effects
In the absence of
ionospheric heating the
MI system remains
stable (blue line).
After ionospheric
heating starts (t = 40 s)
the amplitude of initial
perturbation grows
exponentially (red line).
Heating effects are
modeled by 20 %
reduction in the particle
recombination
coefficient (green line)
and 20 % reduction in
the electron collision
frequency (red line).
Spatial structure of heater-induced Alfvén waves
t = 200 s
ΣP0 = 3 mho
E0 = 50 mV/m
Virtual satellite observations of heating effects
Flying at 2500 km
HF heater has been
centered at L = 8.
Heating of the ionosphere
leads to 20% reduction of
the particle recombination
coefficient in E-layer and
20% reduction of electron
collision frequency in Flayer.
Virtual satellite is flying
over the heated region of
ionosphere at 2500 km orbit
with speed of 5 km/s.
Diagnostics of feedback-driven resonances
Ionospheric Joule dissipation rate is locally reduced in
resonances driven by the feedback instability
Background Joule dissipation:
P0 
L2
2
S
E
p
0

0 hL dL

L1
Joule dissipation in a
feedback-driven resonance:
P
L2
 S
p 0  S p1  E 0  E 1  hL dL
2
L1
The ionospheric Joule heating rate can be inferred from ionospheric radar data
which can allow to distinguish feedback-driven resonances from those driven by
magnetospheric processes.
The field line resonances driven by magnetospheric ULF oscillations should
locally enhance the time-average field-aligned Poynting flux into the ionosphere,
whereas feedback-driven resonances locally reduce the field-aligned Poynting
flux. The Poynting flux can be inferred from sounding rocket measurements.
Future developments
Developments of the existing 2D magnetospheric model
Improved model for the energetic precipitation that would account for the finite
transit time of electrons.
Studies of the effects of seasonal asymmetry in the Alfvén speed profile.
Feedback effects on the magnetospheric generator
The interaction of feedback-driven Alfvén waves with equatorial plasma can locally
affect the magnetospheric generator on the time scales comparable to Alfvén wave
eigenperiods.
Full 3D magnetospheric model
2D model of the ionosphere includes the effects of Hall current closure.
Ionospheric Hall current closure can lead to the coupling between shear Alfvén and
compressional fast modes.
Convective nonlinearities introduced in 3D magnetospheric model can lead to the
development of shear instabilities.
Summary
Numerical studies of MI coupling have been performed using a model that includes active
ionospheric feedback and shear Alfvén wave dynamics of the magnetospheric response.
Under favorable conditions of low ionospheric conductivity and strong electric convection
the feedback instability leads to the formation of narrow, latitudinally-striated Alfvénic
structures.
Parallel magnetospheric inhomogeneities included in the numerical model permit
simultaneous development of local ionospheric resonator modes (fast feedback) and field
line eigenmodes (slow feedback).
Dispersion of Alfvén waves and the effects of plasma anomalous resistivity included in
the numerical model generate fluxes of energetic electrons that precipitate into the
ionosphere producing discrete auroral arcs
Numerical analysis of the effects of seasonal asymmetry in the ionospheric conductance
suggests that the feedback instability can be responsible for higher occurrence of auroral
arcs on the night side and in dark winter hemisphere as been confirmed by satellite
observations.
The results of numerical modeling demonstrate an agreement with satellite observations of
the Alfvén waves and electron fluxes registered during experiments of modulated heating
of the auroral electrojet.
Scientific achievements
Linear dispersion analysis of the ionospheric feedback instability has been performed
numerically for the wide range of ionospheric background parameters.
It is been demonstrated numerically that the parallel magnetospheric inhomogeneities
permit the simultaneous development of ionospheric resonator modes and field line
eigenmodes. Fourier analysis of the numerical solution has been used to study the
relative contribution of fast and slow feedback in the dynamics of MI coupling.
The effects of seasonal asymmetry in ionospheric conductivity on the development of
feedback instability have been analyzed numerically. It is been demonstrated that the
feedback-driven auroral precipitations are more intense in low-conductivity winter
hemisphere.
It is been shown that the artificial heating may trigger the ionospheric feedback
instability when the coupled MI system is near a state of marginal stability. The results
of numerical modeling demonstrate an agreement with satellite observations of the
Alfvén waves registered during experiments of modulated heating of the auroral
electrojet.
Observational criteria have been identified that can be used to distinguish feedbackdriven field line resonances from the resonances driven by other magnetospheric
processes.
Acknowledgements
To my advisors William Lotko and Anatoly V. Streltsov for their guidance and
kind support in the course of this research.
To many faculty members of Thayer School of Engineering and Department of
Physics and Astronomy.
To my colleagues who created friendly and productive atmosphere at Thayer
School space physics lab: Marc Lessard, Simon Shepherd, and Qiang Hu.
To all members of space plasma physics community, whose comments and
suggestions during AGU and GEM conferences were invaluable for this research
The research was funded by the NASA/Office of Space Science under grants
NAG 5-8441 and NAG 5-10216.