Transcript Alaska-SubstormChap

Substorms: Ionospheric Manifestation of
Magnetospheric Disturbances
P. Song, V. M. Vasyliūnas, and J. Tu
University of Massachusetts Lowell
• Substorms:
• Defined by ground observations: AE index
• Originated in the magnetosphere
• There is an ionosphere between the magnetosphere and ground
• Conventional (global) ionospheric models
• Electrostatic: B=constant
• Ionosphere does not “generate” waves
• Oscillations in the ionosphere are controlled by the magnetospheric driver
• Processes at the interface between magnetosphere and ionosphere
• Magnetospheric wave reflection
• Wave mode conversion: transmitted waves in the ionosphere are fast modes
• New M-IT models:
• Inductive: B changes with time
• Dynamic: in particular ionospheric motion perpendicular to B
• Multi fluid: allowing upflows and outflows of different species
• Wave propagation/reflection: overshoots
• Summary
M-I Coupling via Waves (Perturbations)
• The interface between magnetosphere and ionosphere is idealized as a contact
discontinuity with possible small deformation as the wave oscillates
• Magnetospheric (Alfvenic) perturbation incident onto the ionospheric interface
• For a field-aligned Alfvenic incidence (for example on cusp ionosphere)
B  k, B0 : B in a plane normal to k (2 possible components)
• Polarizations (reflected and transmitted)
(noon-midnight meridian)
• Alfven mode
(toroidal mode)
B,u  k-B0 plane
Magnetosphere
• Fast/slow modes
Ionosphere
(poloidal mode)
B,u in k-B0 plane
• Antisunward ionospheric motion
=>fast/slow modes (poloidal)
=> NOT Alfven mode (toroidal)
Global Consequence of A Poleward Motion
•
Antisunward motion of open field line in the open-closed boundary creates
– a high pressure region in the open field region (compressional wave), and
– a low pressure region in the closed field region (rarefaction wave)
•
•
•
Continuity requirement produces convection cells through fast mode waves in the
ionosphere and motion in closed field regions.
Poleward motion of the feet of the flux tube propagates to equator and produces upward
motion in the equator.
Ionospheric convection will drive/modify magnetospheric convection
Ionosphere Reaction to Magnetospheric Motion
• Slow down wave propagation (neutral inertia loading)
• Partial reflection
• Drive ionosphere convection
– Large distance at the magnetopause corresponds to small distance in
the ionosphere
– In the ionosphere, horizontal perturbations propagate in fast mode
speed
– Ionospheric convection
modifies magnetospheric
convection
(true 2-way coupling)
•
Amplification of Magnetic Perturbation at
the Ionosphere
At the magnetosphereionosphere boundary, the
boundary conditions are
maintained by the incident,
reflected and transmitted
perturbations.
   u  nu
i , f ,a , s
 B |
interface
•
The reflected
perturbations have a phase
reversal between dB and
dV from the incident.
The inertia of the
ionospheric plasma
minimizes the velocity
change across the
boundary

 B ' |
interface
f ,a , s
 p|
   p ' |interface
i, f ,s
 u f ,s
 |interface    u ' nucontact  |interface
f ,a , s
i , f ,a , s
interface
•
contact
f ,s
ˆ  B
B
 B f ,s
C A2
C A2 ˆ
0
f ,s
ˆ
ˆ
 2
V f ,sk f ,s 
k f ,s  B0
,
V f , s  Cs2
B0
V f ,s
B0
 ua  CA

 Ba
B0

.
V  Vinc  Vref ,
 B   Binc   B ref  2 Binc
• The magnetic perturbation nearly doubles across the boundary =>
forming a strong current
Basic Equations
• Continuity equations
ns
   (ns v s )   Pss '  ns L s
t
s'
• Momentum equations
 (ns v s )
nk T
ne
   (ns v s v s  s B s I)  s s (Es  v s  B)
t
ms
ms
s = e, i or n, and es = -e, e or 0
Field-aligned flow
allowed
 ns (G r  2Ωr  v s  Ωr  (Ωr  r ))   ns st ( vt  v s )   v s Pss '  ns vs L s
t
s'
• Temperature equations
Ts
m
2
2 1
2 mt
 v s  Ts  Ts (  v s ) 
  q   s st [2(Tt  Ts ) 
( vt  v s )2 ]
t
3
3 ns k B
3 kB
t ms  mt
 Q s  CL s
• Faraday’s Law and Ampere's Law
B
   E
t
1
0
  B  0
E
 J   ni ev i  ne ev e
t
i
Simplifying Assumptions (dt > 1sec)
• Charge quasi-neutrality
– Replace electron continuity with
• Neglecting the electron inertial term in the
electron momentum equation
– Electric field, E, can be eliminated in other equations;
– electron velocity will be calculated from current
definitions.
Momentum equations without electric
field E
 (ns v s )
ns k BTs
ns k BTene  ne(k BTe )
   (ns v s v s 
I) 
t
ms
ne
ms
ns es

( v e  B  v s  B)  ns (G r  2Ω r  v s  Ω r  (Ω r  r ))
ms

m , n ,e
m,n
ts
t
 ns st ( vt  v s )   ns
me
 et ( v t  v e )   v s ' Pss '  ns v s L s
ms
s'
1-D Stratified Ionosphere/thermosphere
• Equation set is solved in 1-D (vertical), assume B<<B0.
• Neutral wind velocity is a function of height and time
• The system is driven by a change in the motion at the top boundary
• No local field-aligned current; horizontal currents are derived
• No imposed E-field; E-field is derived.
• test 1: solve momentum equations and Maxwell’s equations using explicit method
• test 2: use implicit method (increasing time step by 105 times)
• test 3: include continuity and energy equations with
2000 km
field-aligned flow
500 km
Dynamics in 2-Alfvén Travel Time
x: antisunward; y: dawnward, z: upward, B0: downward
On-set time: 1 sec
Several runs were made: the processes are characterized in
Alfvén time
Building up of the Pedersen current
Song et al., 2009
30 Alfvén Travel
Time
• The quasi-steady state is
reached in ~ 20 Alfvén time.
• During the transition,
antisunward flow in the Flayer can be large
• During the transition, Elayer and F-layer have
opposite dawn-dusk flows
• There is a current
enhancement for ~10 A-time,
more in “Pedersen” current
Song et al., 2009
Neutral wind velocity
•The neutral wind driven by M-I coupling is strongest in F-layer
•Antisunward wind continues to increase
Song et al., 2009
After 1 hour, a flow
reversal at top boundary
•Antisunward flow reverses and
enhances before settled
•Dawn-dusk velocity enhances
before reversing (flow rotates)
•The reversal transition takes
slightly longer than initial
transition
•Larger field fluctuations
Song et al., 2009
After 1 hour, a flow reversal at top boundary
“Pedersen” current more than doubled just after the reversal
Song et al., 2009
Electric field
variations
Not Constant!
Electric field in the neutral
wind frame E’ = E + unxB
Not Constant!
Song et al., 2009
Heating rate q as function of
Alfvén travel time and height.
The heating rate at each height
becomes a constant after about
30 Alfvén travel times. The
Alfvén time is the time
normalized by tA, which is
ztop
defined as
tA  
dz / VA
zbottom
If the driver is at the
magnetopause, the Alfvén time
is about 1 min.
Height variations of frictional
heating rate and true Joule
heating rate at a selected time.
The Joule heating rate is
negligibly small. The heating is
essentially frictional in nature.
Tu et al., 2011
Heating rate divided by total
mass density (neutral mass
density plus plasma mass
density) as function of Alfvén
travel time and height. The
heating rate per unit mass is
peaked in the F layer of the
ionosphere, around about 300
km in this case.
Time variation of height integrated
heating rate. After about 30 Alfvén
travel times, the heating rate reaches a
constant. This steady-state heating rate
is equivalent to the steady-state heating
rate calculated using conventional
Joule heating rate J∙(E+unxB) defined
in the frame moving with the neutral
wind. In the transition period, the
heating rate can be two times larger
than the steady-state heating rate.
Tu et al., 2011
Summary
• When the ionosphere is treated self-consistently and dynamically, it
– reflects magnetospheric perturbations
– oscillates at magnetospheric eigen-mode frequencies (not simply responds to
magnetospheric disturbances)
– forms an envelop over the eigen-mode oscillations due to constructive or destructive
interference until steady state is reached.
– has a transient time of 10-20 Alfven times, or 20-40 min
– sets convection pattern with the fast mode speed
• The above distinct processes predict/explain
– Substorm time geomagnetic measurements have intrinsic oscillations, the frequency of
which is less correlated with the oscillations in the solar wind
– Substorm time geomagnetic perturbations are less correlated with specific time scales of
reconnection
– Substorm time is about 30 min
– The whole ionosphere responds to the magnetospheric changes in 1 min
– During substorms, more energy is dissipated within the polar cap proper where frictional
heating is the strongest, not in the auroral oval or field-aligned current sheets where
convection velocity is the smallest.
– The requirement for a substorm is a substantial change in the magnetospheric convection
which has to be maintained, with its variations, for at least 30 min.