Thayer School of EngineeringDartmouth College

Ph.D. Thesis Defense

“Effects of the Active Auroral Ionosphere on Magnetosphere - Ionosphere Coupling”

Dimitri Pokhotelov

Research Advisors: William Lotko Anatoly V. Streltsov

September 2002

MagnetosphereMagnetosphere

Field-aligned currents and ionospheric convectionField-aligned currents and ionospheric convection

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]

System of large-scale field-aligned currents facilitates the ionospheric convection flow.

Auroral ionosphereAuroral ionosphere

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

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.

IntroductionIntroduction

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 instabilityPhysical 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 reviewHistorical 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.

OutlineOutline

Dispersion analysis.

Numerical 2D simulations.

Part 1: Simulations using lumped transmission line model of the magnetosphere

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 active auroral ionosphere

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 nSehj

ehj

tn

ihot

20nSi

,ˆ||jHP bEE

Part 1: Simulations using lumped transmission line model of the magnetosphere

Advantages of using transmission line model:

Disadvantages:

facilitate dispersion analysis of the feedback instability;

suggest an explanation for diurnal asymmetry in the occurrence of auroral precipitation;

relatively easy to implement numerically.

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].

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.

Linearized one-fluid MHD equations in cold collisionless plasma approximationLinearized one-fluid MHD equations in cold collisionless plasma approximation

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

Expansion around the fundamental eigenfrequency of the magnetic field line = vA /l gives equation of the magnetospheric response [Miura and Sato, 1980]

;0011

0 Bjv

tnmi .0011 BvE

. cot01||

1

AA

lij v

v E

.121

22

221||

20

tl

tjl

Av

Lumped transmission line model of the magnetosphereLumped transmission line model of the magnetosphere

Dispersion analysis of the feedback instabilityDispersion 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 magnetosphericresponse.

Simulations using transmission line model

An initial perturbation of the ionospheric plasma density has been chosen in the form of a gaussian in latitude with no variation in longitude.

Time evolution of field-aligned current density perturbation simulated using a lumped transmission line model of magnetospheric response.

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 modelof 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 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 ben

tn v

,01ˆ1 2

222

0||22

tcj

Aii

Ebv

Magnetospheric plasma density decreases with altitude faster then the magnetic field. It leads to the formation of Alfvén speed maximum.

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.

Distribution of background parametersDistribution of background parameters

System of equations describing MI coupling has been solved numerically in 2D dipolar geometry resembling Earth’s magnetosphere

Distance, RE

Computational Grid

Dis

tanc

e, R

E

L = 8.25

Equator

L = 7.75

Numerical simulations

t = 570s

mho 5.00 NP

mho 30 SP

Analysis of the numerical solutionAnalysis of the numerical solution

Instability saturation is controlled by the nonlinear plasma recombination.

Instability saturation level is lower in the high-conductivity southern ionosphere.

A dynamic spectral analysis demonstrates the relative contribution of various modes of oscillation in the numerical solution.

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

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.

Effects of seasonal asymmetry in ionospheric Pedersen conductance on the energy deposition into auroral ionosphere.

Artificial heating of the auroral ionosphere with HF radars.

Experimental diagnostics of feedback-driven field line resonances

Ionospheric Joule heating rate.

Time-averaged Poynting flux.

Differences in the phase properties of resonances.

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.

Observed seasonal and diurnal variations in aurora occurrenceObserved seasonal and diurnal variations in aurora occurrence

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.

Images are courtesy of APL Johns Hopkins University

Plasma anomalous resistivity

otherwise, 0

, || if ||/1 |||| ceecciAR

vvvv

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]:

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.

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]

Ionization rate due to the hot electron precipitation [Banks et al., 1974]

where 0 = 50 and ||cr = 1.5 kV

Model for the auroral electron precipitation

xTxe

mTen

BBj

Ee

e

EeE

E

I

hot 1/exp

12

||2/1

00

0||

,3||

3||

3||

0cr

Numerical simulations with hot electron precipitation model

mho 5.00 NP

mho 30 SP

Integral energy flux into the auroral ionosphere has been calculated using Fridman-Lemaire model for the hot electron precipitation as

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.

Seasonal variations in the auroral energy fluxSeasonal variations in the auroral energy flux

,2

1

||||21

|| L

LLhothot dLhjW

.0

0||

t

hothot dtWP

and the total energy deposition into the auroral ionosphere

Heating of the ionosphere with HF radarHeating of the ionosphere with HF radar

After Robinson et al. [2000]

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.

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

E0 = 50 mV/m

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 F-layer.

Virtual satellite is flying over the heated region of ionosphere at 2500 km orbit with speed of 5 km/s.

Virtual satellite observations of heating effects

Flying at 2500 km

Diagnostics of feedback-driven resonancesDiagnostics of feedback-driven resonances

Ionospheric Joule dissipation rate is locally reduced in resonances driven by the feedback instability

Background Joule dissipation:

Joule dissipation in a feedback-driven resonance:

dLhEP L

L

Lp

2

1

2000

dLhEEPL

LLpp

2

1

21010

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.

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 conductancesuggests 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 heatingof the auroral electrojet.

Summary

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 feedback-driven 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.