R. L. Lysak GEM 2003 Tutorial Electrodynamic Coupling of the Ionosphere and Magnetosphere Bob Lysak,...
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Transcript of R. L. Lysak GEM 2003 Tutorial Electrodynamic Coupling of the Ionosphere and Magnetosphere Bob Lysak,...
R. L. Lysak GEM 2003 Tutorial
Electrodynamic Coupling of the Ionosphere and Electrodynamic Coupling of the Ionosphere and MagnetosphereMagnetosphere
Bob Lysak, University of MinnesotaBob Lysak, University of Minnesota
Auroral particle acceleration is the result of the transmission of electromagnetic energy along auroral field lines and its dissipation in the auroral acceleration region.
Electrostatic models have been widely used to understand parallel electric fields, but do not address dynamics.
Time-dependent transmission of electromagnetic energy is accomplished by shear Alfvén waves.
Strong Alfvénic Poynting flux observed at plasma sheet boundary: leads to field-aligned acceleration of electrons.
R. L. Lysak GEM 2003 Tutorial
Outline of the TalkOutline of the TalkOverview of the Auroral Zone
Single Particle Motions: the Knight relation
Parallel Electric Fields
The Ionosphere and Current Closure
Alfvén Waves
Particle Acceleration in Alfvén Waves
Sources of Alfvén Waves
Focus on:
Auroral zone: But low and mid-latitude coupling important
Electrodynamics: But mass coupling also important
R. L. Lysak GEM 2003 Tutorial
The Earth’s MagnetosphereThe Earth’s Magnetosphere
R. L. Lysak GEM 2003 Tutorial
Field-Aligned Currents (FAC) and Field-Aligned Currents (FAC) and the Aurorathe Aurora
Currents can flow easily along magnetic field lines, but not perpendicular to the magnetic field
Pattern of FAC is similar to auroral oval
Field-aligned current pattern (Iijima and Potemra, 1976) UV Image from DE-1 satellite (Courtesy, L. Frank)
R. L. Lysak GEM 2003 Tutorial
Production of Auroral LightProduction of Auroral Light
• Auroral Spectrum consists of various emission lines: 557.7 nm (“Green line”), 1S → 1D
forbidden transition of atomic Oxygen ( = 0.8 s)
630.0 nm (“Red line”), 1D→ 3P forbidden transition of Oxygen ( = 110 s)
391.4 nm, 427.8 nm transitions in molecular Nitrogen ion N2
+ Hα (656.3 nm) and Hβ (486.1 nm) lines
due to proton precipitation
These lines are excited by electron and proton precipitation in 0.5-20 keV range. How do these particles get accelerated?
R. L. Lysak GEM 2003 Tutorial
Bi-modal distribution of auroral arc Bi-modal distribution of auroral arc widthswidths
(Knudsen et al., Geophys. Res. Lett., 28, 705, 2001)
Auroral arcs show a bi-modal distribution, with a peak at very small scales of < 1 km and a second peak at about 10 km. Larger-scale structures are consistent with linear calculations; however, narrow-scale arcs are still not understood.
R. L. Lysak GEM 2003 Tutorial
Recent Observations From FAST Recent Observations From FAST satellitesatellite
30 seconds of data from the Fast Auroral SnapshoT (FAST) satellite are shown.
Top 4 panels give energy and pitch angle of electrons and ions (red is most intense; 180 degrees is upward).
Next is perpendicular electric field. Strong perpendicular fields always are seen in auroral zone. Perpendicular fields separate different plasma regions.
(McFadden et al., 1998)
R. L. Lysak GEM 2003 Tutorial
Electric Field Structures in the Electric Field Structures in the Auroral ZoneAuroral Zone
Perpendicular and parallel field observations indicate “U-shaped” or “S-shaped potential structures (Mozer et al., 1980)
R. L. Lysak GEM 2003 Tutorial
Adiabatic Motion of Charged ParticlesAdiabatic Motion of Charged Particles
Motion of charged particles in a dipole magnetic field is governed by conservation of energy E = (1/2)mv2 + qΦ and magnetic moment μ = mv2/2B where is pitch angle of particle.
Conservation of E and μ leads to magnetic mirror, creating “loss cone” in velocity space: particles with sin2 < B/BI, where BI is ionospheric field, are lost. Since on auroral field, LC = 1.8. Thus, very few particles lost.
For electrons, if > 0 (upward parallel electric field), loss cone becomes hyperboloid; therefore more particles lost. For ions, upward E|| leads to fewer particles in loss cone.
R. L. Lysak GEM 2003 Tutorial
Velocity space in the presence of Velocity space in the presence of (upward) parallel electric fields (upward) parallel electric fields
(Chiu and Schulz, 1978)(Chiu and Schulz, 1978)
Key: M: magnetospheric; I: ionospheric; T: trapped; S: scattered
Note: Ion and electron plots reversed for downward electric fields
v|| →
↑
v
R. L. Lysak GEM 2003 Tutorial
Evidence for EEvidence for E|| || in Auroral Particlesin Auroral Particles
“Monoenergetic Peak” in Electrons (Evans, 1974)
Proton and Electron Velocity Distributions from S3-3 satellite (Mozer et al., 1980)
R. L. Lysak GEM 2003 Tutorial
Knight (1973) Relation for Adiabatic Knight (1973) Relation for Adiabatic Response to Parallel Potential DropResponse to Parallel Potential Drop
Consider bi-Maxwellian electron population at source region (density n0, temperatures T|| and T, magnetic field B0) in dipole field with upward parallel potential drop Φ. Total current corresponds to those particles that avoid mirroring before reaching the ionosphere. This gives:
Relation is linear for moderate Φ
For large potential drops, a saturation current is reached: j||,sat = nevthBI /B0
Important point: Knight relation only gives the field-aligned current resulting from an assumed potential drop. It does NOT explain the existence of parallel electric fields.
j n eB
B
e
xthI
xe T
||
/ ||
LNM
OQP
00
11
v
xT T
B BI
|| /
/ 0 1
vth eT m || / 2
||, vlin th
ej ne K
T
R. L. Lysak GEM 2003 Tutorial
Knight Relation Knight Relation (from Fridman and Lemaire, 1980)(from Fridman and Lemaire, 1980)
See Boström (JGR, April 2003) for a good description of this type of model
R. L. Lysak GEM 2003 Tutorial
Self-consistent E parallelsSelf-consistent E parallels
To find E||, must combine adiabatic trajectories with Poisson’s equation to find self-consistent model.
For example, Ergun et al. (2000) used 7 populations to model FAST data.
Two “transition regions” found with large parallel electric fields.
R. L. Lysak GEM 2003 Tutorial
Models for Parallel Electric FieldsModels for Parallel Electric Fields
High electron mobility would suggest electrons can short out parallel electric fields. Creating a significant E|| requires some inhibition of the electron motion, so consider electron momentum equation (“generalized Ohm’s Law”):
“Anomalous” resistivity: momentum transfer to ions due to wave-particle interactions.
Magnetic mirror effect: requires anisotropic pitch angle distributions
Electric “double layers”: self-consistent E|| on Debye length scales
Electron inertia: finite electron mass in time-dependent fields (linear) or spatially varying case (nonlinear): BUT this is “ma” not “F”!
||2|| || || ||* e e
e e e e e e e
p pnm v nm v neE nm v p B
t B
R. L. Lysak GEM 2003 Tutorial
So Why Does ESo Why Does E|||| form? form?(Song and Lysak, 2001)(Song and Lysak, 2001)
Magnetospheric processes twist magnetic field, Ampere’s Law gives:
00
1Ej
t
B
Note that if particles cannot carry required j||, parallel electric field must increase, leading to enhancement of current:
2j neE
t m
Combining these equations, and assuming that oscillates at a frequency ω, we find
B
2
2 2 21 / p p
i cE
B
So even though the displacement current is numerically small for low frequency, its presence is important for the development of parallel electric fieldsUse of displacement current formulation has numerical advantages: explicit treatment of E|| (Lysak and Song, 2001)
R. L. Lysak GEM 2003 Tutorial
Steady-state ESteady-state E||||: Plasma Double Layers: Plasma Double Layers
Need to self-consistently maintain field with particle distributions:
0/ E
A simple such structure is the plasma “double layer” Note when particles are reflected, their density increases. Thus, ion density is highest just to right of axis, and electron density to the left, making a “double layer” of charge.This is consistent with potential distributionIons are accelerated to left, electrons to the right.
R. L. Lysak GEM 2003 Tutorial
Role of the Ionosphere: Electrostatic Role of the Ionosphere: Electrostatic Scale SizeScale Size(Lyons, 1980)(Lyons, 1980)
Ionosphere closes field-aligned currents:
For electrostatic conditions, uniform ionosphere, only Pedersen conductivity matters:
Assume the linear Knight relation is valid: j|| = K(ΦI – Φ0)
Combining these leads to equation for potential:
Here is electrostatic auroral scale length.
For ΣP = 10 mho and K = 10-9 mho/m2, L = 100 km
Parallel potential drops only exist on scales shorter than L
j E
�
2P Ij
2 201 IL
/PL K
R. L. Lysak GEM 2003 Tutorial
Some important details of ionospheric Some important details of ionospheric interactioninteraction
Although Hall current doesn’t close current (in uniform ionosphere), it produces magnetic signature seen on ground
Fields in atmosphere attenuated as so structures small compared with ionospheric height (~ 100 km) are shielded from ground: so scales that produce potential drops are not seen at ground!
On very narrow scales (~ 1 km), collisional parallel conductivity becomes important (Forget et al., 1991)
At higher frequencies (~ 1 Hz), two effects:Hall currents lead to coupling to fast mode, signal can propagate
across field lines in “Pc1 waveguide”Effective height of ionosphere can be decreased by collisional skin
depth effect.
k ze
R. L. Lysak GEM 2003 Tutorial
MHD Wave ModesMHD Wave Modes
Linearized MHD equations give 3 wave modes:Slow mode (ion acoustic wave):
Plasma and magnetic pressure balance along magnetic field
Electron pressure coupled to ion inertia by electric field
Intermediate mode (Alfvén wave):
Magnetic tension balanced by ion inertia
Carries field-aligned current
Fast mode (magnetosonic wave):
Magnetic and plasma pressure balanced by ion inertia
Transmits total pressure variations across magnetic field
/s sk c c p
0/A Ak V V B
2 2 2 2A sk V k c
(Note dispersion relations given are in low β limit)
R. L. Lysak GEM 2003 Tutorial
The “Auroral Transmission Line”
The propagation of Alfvén waves along auroral field lines may be considered to be an electromagnetic transmission line. Energy is propagated in the “TEM” mode, the shear Alfvén wave at the Alfvén speed, 0/ AV B
Transmission line is filled with a dielectric medium, the plasma, with an inhomogeneous dielectric constant 2 21 / ( ) Ac V z
Can define a characteristic admittance for the transmission line
01/ A AV (= 0.8 mho for 1000 km/s)
Transmission line is “terminated” by the conducting ionosphere. In general, Alfvén waves will reflect from this ionosphere, or from strong gradients in the Alfvén speed.
R. L. Lysak GEM 2003 Tutorial
Reflection of AlfvReflection of Alfvén Waves by the én Waves by the IonosphereIonosphere
Ionosphere acts as terminator for Alfvén transmission line.
But, impedances don’t match: wave is reflected
Usually P >> A, so electric
field of reflected wave is reversed (“short-circuit”)
Reflection coefficient:
(Mallinckrodt and Carlson, 1978)
up A P
down A P
ER
E
R. L. Lysak GEM 2003 Tutorial
AlfvAlfvén Wave Simulationén Wave SimulationEx
By
Ionosphere
r
4 RE
Fields from 100 km wide pulse, ramped up with 1 s rise time. Simulation shown in “real time”
R. L. Lysak GEM 2003 Tutorial
Field-Aligned Currents vs. AlfvField-Aligned Currents vs. Alfvén én WavesWaves
Field-aligned current is often quoted as energy source for aurora.
But, the kinetic energy of electrons is negligible: Poynting flux associated with FAC is responsible.
FAC closed by conductivity in ionosphere; electric and magnetic fields related by
0
1 800km/s
(mho)x
y P P
E
B
ΣP is usually > 1 mho, so ratio is less than 800 km/s
Alfvén waves have a similar electric and magnetic field signature, but for these waves
0
0
xA
y
E BV
B
VA is usually much greater than 1000 km/s, can be up to speed of light
Thus, large E/B ratios indicate Alfvén waves, smaller ratios static currentsOversimplified picture! Wave reflections, parallel electric fields, kinetic effects all affect this ratio.
R. L. Lysak GEM 2003 Tutorial
Effects of EEffects of E|| || on Alfven Wave Reflection: on Alfven Wave Reflection:
Alfvenic Scale SizeAlfvenic Scale Size
If assume linear Knight relation j = KΦ, Alfven wave reflection is modified (Vogt and Haerendel, 1998)
Reflection coefficient same if replace Pedersen conductivity with effective conductivity
where
This leads to a new scale where the Alfvén wave is absorbed (providing energy to auroral particle acceleration) given by
2 21P
eff k L
/PL K
/ ~ 10 kmA AL K
( ) /( )A eff A effR
R. L. Lysak GEM 2003 Tutorial
Resonances of AlfvResonances of Alfvén Wavesén WavesAlfvén can bounce from one ionosphere to the other: Field Line Resonance (periods 100-1000 s)
However, Alfvén speed has sharp gradient above ionosphere: wave can bounce between ionosphere and peak in speed: Ionospheric Alfvén Resonator (Periods 1-10 s)
Fluctuations in the aurora are seen in both period ranges. Feedback can structure ionosphere at these frequencies.
Profiles of Alfvén speed for high density case (solid line) and low-density case (dashed line). Ionosphere is at r/RE = 1. Sharp rise in speed can trap waves (like quantum mechanical well). Note speed can approach c in low-density case.
R. L. Lysak GEM 2003 Tutorial
Observational Evidence for 0.1-1.0 Hz Observational Evidence for 0.1-1.0 Hz waves in the ionospheric Alfvwaves in the ionospheric Alfvén én
resonatorresonator
Above: Spectrogram from ground magnetic observations from Finland, showing waves at about 0.5 Hz (Koskinen et al., 1993)
Right: Electric field data and spectrum from Viking satellite, showing harmonics of resonator (Block and Fälthammar, 1990)
R. L. Lysak GEM 2003 Tutorial
Simulations of AlfvSimulations of Alfvén Wave Pulse along én Wave Pulse along auroral field lineauroral field line
ExBy
r
Pe
ak o
f Alfv
en
spe
ed
Ionosphere
R. L. Lysak GEM 2003 Tutorial
Ionospheric FeedbackIonospheric FeedbackIonospheric feedback instability (Atkinson, 1970; Miura and Sato, 1980; Lysak, 1991) can produce structuring of auroral arcs through ionospheric modification.
Upward current carried by energetic downward electrons can lead to localized enhanced conductivity.
Secondary field-aligned currents develop at conductivity gradients. The Alfvén waves carrying these currents can be reflected at conjugate ionosphere or ionospheric Alfvén resonator. If returning wave reinforces conductivity change, instability develops.
Growth rate proportional to wave travel time: few minutes for conjugate ionosphere (FLR), few seconds for ionospheric resonator.
Instability damped by recombination, so strong damping for large background conductivity. Recombination time ~ 50 s for 1 mho, 5 s for 10 mho.
j
j
→
(Lysak, 1990)
R. L. Lysak GEM 2003 Tutorial
What sets lower limit on scale size?What sets lower limit on scale size?
Feedback instability favors short wavelength waves. What can limit how small the waves are?
Some basic scale sizes: Electron inertial length e = 5 km/n1/2. For n = 104-106 cm–3, this gives 50-5 m.
Electron/ion gyroradius: for e–, e = 5 cm T(eV)1/2; for ions, H = 2 m T1/2
and O = 8 mT1/2. All < 100 m for temperatures < 100 eV in ionosphere (B = 0.5 G).
Electron parallel resistivity (not anomalous!) becomes important in ionosphere. Gives diffusion in current on scale where e is electron collision frequency (103-104 s–1 in ionosphere). This gives 150 m-5 km for ionospheric resonator ( ~ 1 s–1) and 1.5-50 km for FLR’s ( ~ 0.01 s–1).
Shear in EB flow can give instabilities when dv/dx ~ 0.1 i (e.g., Ganguli et al., 1988). For E = 1 V/m (upper limit!), this gives 40 m for H+ and 640 m for O+.
These suggest that parallel resistivity is most likely limiting mechanism.
/res e eL
R. L. Lysak GEM 2003 Tutorial
Kinetic AlfvKinetic Alfvén Wavesén Waves
Alfvén waves develop a parallel electric field on short perpendicular scales
Two-fluid theory gives modification to dispersion relation in two limits:
Cold plasma (vth << VA):
Warm plasma (vth >> VA):
The first is sometimes called “inertial Alfvén wave” and second “kinetic Alfvén wave,” but they are both limits of the full kinetic dispersion relation
Common misconception “ion gyroradius effect causes E||” but really it is electron inertia or pressure, through “acoustic gyroradius”
22 22 2 2
2 2 2 2
1
1 1ei
Ae e
E k kkk V
Ek k
2
2 2 2 2 2 22 2
1 ( )1
sA s i
i
E k kk V k
E k
/ /s s i e ic T m eB
R. L. Lysak GEM 2003 Tutorial
Kinetic AlfvKinetic Alfvén Wave: Local Theoryén Wave: Local Theory
Kinetic Alfvén wave dispersion relation can be written as: 2|| ||
2|| ||
det 0
n n n
n n n
where
112
20c
VA
i
i
af
||||
1 102 2
e
DekZ
af afb g Dispersion relation is then solved to read:
22 2
2 2 2 2|| 0 0 ||
1
/ 1 / 1
s
A A i i e De
k
k V V c Z k
In cold electron limit ( / ||k ae ), dispersion relation becomes:
2 2
2 2 22 2
1
1(for )
A Aik
k Vk
cV
For warm electrons ( / ek a ), we find
2 2 2 2 2 2 21 1 / A i s ek V k k i k a
assuming 2 2, 1, and 1A e DeV c k .
R. L. Lysak GEM 2003 Tutorial
Results from Local TheoryResults from Local Theory
Solutions for the local dispersion relation for equal ion and electron temperatures as a
function of perpendicular wavelength, kxc/pe (horizontal axis) and the ratio of
electron thermal speed to Alfvén speed, ve2/VA
2 (vertical axis). Left panel gives real
part of the phase velocity normalized to Alfvén speed; right panel gives damping rate
normalized to wave frequency (Lysak and Lotko, 1996).
R. L. Lysak GEM 2003 Tutorial
Field-aligned acceleration on FASTField-aligned acceleration on FAST
Figure shows data from FAST satellite (Chaston et al., 1999). Note strong low energy electron fluxes (red regions at bottom of panel 4) which are field-aligned (0 degree pitch angle in panel 5).
These particle fluxes are associated with strong Alfvén waves (top 3 panels: electric field, magnetic field, and Poynting flux), suggesting wave acceleration.
R. L. Lysak GEM 2003 Tutorial
Sounding Rocket ObservationsSounding Rocket Observations
(Arnoldy et al., 1999)
R. L. Lysak GEM 2003 Tutorial
Electron acceleration in AlfvElectron acceleration in Alfvén Wavesén Waves
Parallel electric fields can develop in narrow-scale Alfvén waves due to finite electron inertia.
Test particle models have been used to determine distributions from this effect.
Results from a test-particle simulation of electron acceleration in Alfvén resonator, showing bursts at ~ 0.5 s (Thompson and Lysak, 1996)
Results from a similar simulation with more particles in pitch angle vs. energy format compared with FAST data (Chaston et al., 1999)
R. L. Lysak GEM 2003 Tutorial
Non-local theory of Alfvén waves on auroral field lines (e.g., Rankin et al., 1999; Tikhonchuk and Rankin, 2000)
Idea is to integrate Vlasov equation over past history of a particle. Trajectory is defined by considering constants of motion: magnetic moment 2 / 2mv B and total energy
212
W mv B z q z
Linearized Vlasov equation can then be integrated to get perturbation in the distribution function; calculation of first velocity moment gives field-aligned current.
Since distribution function is linear in the parallel electric field, this integral can be given in terms of a non-local conductivity relation:
,j z dz z z E z
R. L. Lysak GEM 2003 Tutorial
Phase Space Trajectories: Ionospheric Phase Space Trajectories: Ionospheric ParticlesParticles
R. L. Lysak GEM 2003 Tutorial
Phase Space Trajectories: Magnetospheric Phase Space Trajectories: Magnetospheric ParticlesParticles
R. L. Lysak GEM 2003 Tutorial
Observations of Poynting flux from Observations of Poynting flux from Polar Satellite at 4-6 RPolar Satellite at 4-6 REE (Wygant et (Wygant et
al., 2000)al., 2000)
Left Panel: From Top to Bottom: Electric Field, Magnetic Field, Poynting Flux, Particle Energy Flux, Density
Right Panel: Particle Data. Top 3 panels are electrons, bottom 3 are ions. Panels give particles going down the field line, perpendicular to the field, and up the field line.
R. L. Lysak GEM 2003 Tutorial
AlfvAlfvén Waves on Polar Map to én Waves on Polar Map to Aurora and Accelerate ElectronsAurora and Accelerate Electrons
Left: Ultra-violet image of aurora taken from Polar satellite. Cross indicates footpoint of field line of Polar (Wygant et al., 2000)
Right: Electron distribution function measured on Polar. Horizontal direction is direction of magnetic field. Scale is ±40,000 km/s is both directions (Wygant et al., 2002)
R. L. Lysak GEM 2003 Tutorial
How are these waves produced?How are these waves produced?
Linear mode conversion: Mode conversion can take place from a surface Alfvén wave (Hasegawa, 1976), from compressional plasma sheet waveguide modes (Allan and Wright, 1998), or from compressional waves in plasma sheet (Lee et al., 2001).
Reconnection at distant neutral line: Presence of finite By component in tail lobe gives rise to field-aligned currents on boundary layer (Song and Lysak, 1989). Bursty reconnection at this point will launch Alfvén waves along boundary layer.
Bursty Bulk Flows: Localized flow regions can generate Alfvén waves due to the twisting and compression of magnetic field lines (Song and Lysak, 2000), perhaps associated with localized reconnection. BBF association with Alfvénic Poynting flux observed by Geotail (Angelopoulos et al., 2001).
R. L. Lysak GEM 2003 Tutorial
Simulations of Linear Mode ConversionSimulations of Linear Mode Conversion
Left: compression of magnetic field: Blue area is plasma sheet; red is lobe. Yellow region is compression pulse on boundary layer.
Right: Field-aligned currents: Blue is parallel to magnetic field; red is anti-parallel. Pre-existing currents are on bottom; currents in upper part are generated at the boundary layer.
Acknowledgements: T. W. Jones, D. Ryu for code; D. Porter for visualization software
R. L. Lysak GEM 2003 Tutorial
Three Regions of Auroral AccelerationThree Regions of Auroral Acceleration
Illustration of three regions of auroral acceleration: downward current regions, upward current regions, and the region near the polar cap boundary of Alfvénic acceleration (from Auroral Plasma Physics, International Space Science Institute, Kluwer, 2003, adapted from Carlson et al., 1998)
R. L. Lysak GEM 2003 Tutorial