Transcript Tutorial: 2009 Space Physics Seminar

Aurora, Alfvén Waves and Substorms:
Tutorial
A
Bob 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;
implication for substorms.
Outline of the Talk
Overview 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
Implications for Substorms
The Earth’s Magnetosphere
Field-Aligned Currents (FAC) and
the 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)
Production 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
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These lines are excited by electron and proton precipitation in 0.5-20
keV range. How do these particles get accelerated?
Bi-modal distribution of auroral arc
widths
(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.
Recent Observations From FAST
satellite
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)
Electric Field Structures in the
Auroral Zone
Perpendicular and parallel field observations indicate “U-shaped” or “Sshaped potential structures (Mozer et al., 1980)
Adiabatic 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 = mv2/2B
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.
Velocity space in the presence of
(upward) parallel electric fields
(Chiu and Schulz, 1978)
↑
v
v|| →
Key: M: magnetospheric; I: ionospheric; T: trapped; S: scattered
Note: Ion and electron plots reversed for downward electric fields
Evidence for E|| in Auroral Particles
“Monoenergetic Peak” in
Electrons (Evans, 1974)
Proton and Electron Velocity
Distributions from S3-3 satellite (Mozer
et al., 1980)
Knight (1973) Relation for Adiabatic
Response 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:
L
M
N
BI
e xe/ T
j|| n0 evth
1
B0
1 x
Relation is linear for moderate Φ
j||,lin  nevth
||
O
P
Q
T /T
x  || 
BI / B0 
1
vth  T|| / 2me
e
 K
T
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.
Knight Relation
(from Fridman and Lemaire, 1980)
See Boström (JGR, April 2003) for a good description of this type of model
Self-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.
Models 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”):
pe  pe||

2
nme ve    nme ve  neE||  nme  *ve||  || pe|| 
B

t
B


“Anomalous” resistivity: momentum transfer to ions due to waveparticle 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”!
So Why Does E|| form?
(Song and Lysak, 2001, 2006)
Magnetospheric processes twist magnetic field, Ampere’s Law gives:
0
E
t

1
  B   j
0
Note that if particles cannot carry required j||, parallel electric field
must increase, leading to enhancement of current:
j
ne2

E
t
m
Combining these equations, and assuming that B oscillates at a
frequency ω, we find
i
c2
E 
  B
2
2
2 
1  / p p
So even though the displacement current is numerically small for low
frequency, its presence is important for the development of parallel
electric fields
Use of displacement current formulation has numerical advantages:
explicit treatment of E|| (Lysak and Song, 2001)
Steady-state E||: Plasma Double Layers
Need to self-consistently maintain
field with particle distributions:
 E   / 0
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
distribution
Ions are accelerated to left, electrons
to the right.
Role of the Ionosphere: Electrostatic
Scale Size
(Lyons, 1980)
Ionosphere closes field-aligned currents:

j       E

For electrostatic conditions, uniform ionosphere, only Pedersen
conductivity matters:
j   2 
P

I
Assume the linear Knight relation is valid: j|| = K(ΦI – Φ0)
Combining these leads to equation for potential:
1  L   
2
Here L   P / K 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
2

I
 0
Some important details of ionospheric
interaction
Although Hall current doesn’t close current (in uniform
ionosphere), it produces magnetic signature seen on ground
Fields in atmosphere attenuated as e  k z 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.
MHD Wave Modes
Linearized MHD equations give 3 wave modes:

 Slow mode (ion acoustic wave):   k cs cs  p / 

Plasma and magnetic pressure balance along magnetic field
Electron pressure coupled to ion inertia by electric field

 Intermediate mode (Alfvén wave):   k VA VA  B / 0

Magnetic tension balanced by ion inertia
Carries field-aligned current
2 2
2 2
 Fast mode (magnetosonic wave):   k VA  k cs
Magnetic and plasma pressure balanced by ion inertia
Transmits total pressure variations across magnetic field
(Note dispersion relations given are in low β limit)
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, VA  B / 0

Transmission line is filled with a dielectric medium, the plasma, with
an inhomogeneous dielectric constant   1  c 2 / VA2 ( z )

Can define a characteristic admittance for the transmission line
 A  1/ 0VA (= 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.
Reflection of Alfvén Waves by the
Ionosphere
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:
R
(Mallinckrodt and Carlson, 1978)
Eup
Edown
 A  P

 A  P
Alfvén Wave Simulation
By
Ex
4 RE
r
Ionosphere
Fields from 100 km wide pulse, ramped up with 1 s rise time.
Simulation shown in “real time”
Field-Aligned Currents vs. Alfvén
Waves
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
Ex
1
800 km/s


By 0 P  P (mho)
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
Ex
B0
VA is usually much greater than 1000 km/s,
 VA 
can be up to speed of light
By
 0
Thus, large E/B ratios indicate Alfvén waves, smaller ratios static currents
Oversimplified picture! Wave reflections, parallel electric fields, kinetic
effects all affect this ratio.
Effects of E|| on Alfven Wave Reflection:
Alfvenic Scale Size
If assume linear Knight relation j = KΦ, Alfven wave reflection is
modified (Vogt and Haerendel, 1998)
Reflection coefficient same R  ( A   eff ) /( A   eff ) if replace
Pedersen conductivity with effective conductivity
P
 eff 
1  k2 L2
where L   P / K
This leads to a new scale where the Alfvén wave is absorbed
(providing energy to auroral particle acceleration) given by
LA   A / K ~ 10 km
Resonances of Alfvén Waves
Alfvén can bounce from one
ionosphere to the other: Field
Line Resonance (periods 1001000 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 lowdensity case.
Observational Evidence for 0.1-1.0 Hz
waves in the ionospheric Alfvén
resonator
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)
Simulations of Alfvén Wave Pulse along
auroral field line
By
Peak of Alfven
speed
Ex
r
Ionosphere
Spectral Structure of IAR
Spectrogram (left) and line plot (right) of the D-component of the magnetic field
from Sodankylä, Finland, showing multiple harmonics of the ionospheric Alfvén
resonator (Hebden et al., 2005) (Image courtesy of Darren Wright)
Models of IAR
B/E ratio and phase shift for IAR
model with ΣP/ΣAI = 1 (top) and
10 (bottom) (Lysak, 1991).
Model calculation of relative transmission to
the ground for a model with ΣP = ΣH = 10
mho and a magnetic zenith angle of 14° to
model Sodankylä data. (VAI=1000 km/s,
h=400 km)
Ionospheric Alfvén Resonator from FAST
FAST evidence for the IAR (Chaston et al., 2002). Left panel shows oscillations in E and B at
about 1 Hz with oscillating Poynting flux (after initial pulse). Right panel shows phase shifts
consistent with standing waves in IAR (Lysak, 1991). Similar results have been obtained
from Freja (Grzesiak, 2000) and Akebono (Hirano et al., 2005).
Phase mixing in Ionospheric Alfvén Resonator
Gradients in the Alfvén speed lead to phase
mixing, producing smaller perpendicular scales
(basic mechanism behind field line resonance.)
VA
Time scale for phase mixing given to a scale L
can be estimated by τ ~ (LA / L)T, where LA is perpendicular
scale length of Alfvén speed and T is wave period. For 1
second wave in IAR, 100 km scale reduced to <10 km in less
than a minute.
Suggests small-scale structure can be produced in presence of
large-scale density gradients.
Simulations of Phase Mixing
Simulations of linear wave propagation including
electron inertia effect were made in a overall
perpendicular density gradient.
Density
Alfvén speed
Simulation results
Ex
By
Simulation initiated with uniform pulse across system oscillating at 1 Hz.
Interference between up and downgoing waves leads to structuring of fields.
Series of harmonics seen due to change of IAR eigenfrequencies.
Waves phase mix to ~ 1 km scale waves.
Kinetic Alfvén 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):
2 2
1

k
 i
2  k 2VA2
1  k2  e2
 Warm plasma (vth >> VA):   k
2
2
VA2
1 
k2 (2s
E

 i2 )

E

E
E

k k  e2
1  k2  e2

k k2s
1  k2 i2
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”
s  cs / i  Te mi / eB
Kinetic Alfvén Wave: Local Theory
    n||2
 Kinetic Alfvén wave dispersion relation can be written as: det 
 n|| n
af
c 2 1 0 i

 1  2
VA
i
where
a fb afg
n||n 
0
||  n2 
0 e


1

1 
Z 
||
2 2
k|| De
 Dispersion relation is then solved to read:
2
  
k2 2s
1


  2 2
2 2
k
V
V
/
c

1



/



1


Z


k
 De










||
A
A
0
i
i
0
e
||


 In cold electron limit ( / k|| 
ae), dispersion relation becomes:
 k
2
For warm electrons (  / k
2
VA2
1  k2i2
1  k2  2
(for VA
c)
ae ), we find

2  k 2VA2 1  k2i2  k22s 1  i    / k ae  
assuming VA
c,  e
1, and k 2 2De
1.

Results 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/VA2 (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).
Field-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.
Sounding Rocket Observations
(Arnoldy et al., 1999)
Electron acceleration in Alfvén 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)
Observations of Poynting flux from
Polar Satellite at 4-6 RE (Wygant et
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.
Alfvén Waves on Polar Map to
Aurora 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)
Alfvénic Aurora as Transitional Phase
Observations show that Alfvénic aurora occur at polar cap boundary, and
during the onset of “auroral breakup” during magnetospheric substorms
Changes of field-aligned current require the passage of shear Alfvén waves
along field line.
Thus, Alfvénic nature of onset arc should not be surprising
Similarly, at polar cap boundary, plasma is convecting from open to closed
field lines, requiring transitional readjustment.
Alfvénic aurora can also occur within inverted-V’s: may indicate smaller
changes in current structure.
Speculation: Alfvénic interaction prepares system to allow for quasi-static
aurora, especially by excavating density cavity (e.g.., Chaston et al., 2006),
creating low densities that are conducive to static parallel electric fields (Song
and Lysak, 2006), and precipitating electrons into ionosphere to enhance
conductivity and produce secondary and backscattered electrons.
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).
Auroral Substorm as seen from space
(Note: movie duration is 5 hours)
Phenomenology of
Auroral Substorm
Akasofu picture of the aurora during
substorms:
(a) Quiet auroral arc before substorm
(b) Equatorward edge of aurora intensifies
(c) “Westward traveling surge” forms
(d) Poleward expansion of surge
(e) Aurora begins to fade; patchy
“pulsating aurora” forms on dawn
(f) Auroral oval retreats to pre-substorm
locations
Models for Substorm Initiation
“Near Earth Neutral Line” model
“Current Disruption” model
THEMIS mission includes 5 spacecraft plus ground-based
observatories to determine which model gives proper timing.
Results inconclusive!!
Propagation Speeds on 26 Feb 2008
Consider straight line distances to
find minimum velocities
required:
Reconnection (20.3 RE) to
Auroral Intensification: 96 s,
speed > 1284 km/s.
Reconnection to Expansion onset:
speed > 893 km/s.
Reconnection to electrojet
increase: > 520 km/s
Rec’n at P2 to flow at P3: > 375
km/s
Rec’n at P2 to dipolarization at
P3: > 278 km/s
Note: fast mode speed in plasma
sheet ~ 500 km/s, in lobe, 1500 km/s
(Angelopoulos et al., 2008)
Comments on 26 Feb event
Reconnection site cannot communicate with auroral
brightening by wave propagation through plasma sheet.
Propagation through lobe/boundary layer possible, but then,
how could aurora expand more poleward?
Reconnection, flow at P3, and electrojet formation could be
connected by flow or waves through plasma sheet: classic
NENL signature (but not connected to aurora!).
Auroral activity before electrojet formation: consistent with
Alfvénic nature of onset arc (e.g., Mende et al., 2003),
followed by development of large-scale current system.
Space-Time Diagram for Substorm
Events (N. Lin et al., 2009)
Events from a number of
THEMIS substorms were
placed on a space-time diagram
to get statistical picture of
substorm timing relative to
auroral expansion (t = 0).
Solid curve is model MHD
wave travel time; dotted lines
give variations of parameters
within limits of data.
Three 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)