Next Generation of Magnetosphere-Ionosphere-Thermosphere Coupling Models

1
Next Generation of Magnetosphere-Ionosphere-Thermo
sphere Coupling Models

• P. Song
• University of Massachusetts Lowell
• Acknowledgments V. M. Vasyliunas, and J. Tu
• Conventional Models Steady-state coupling
  between magnetosphere and ionosphere
• (Steady state) Ohms law with constant
  conductivities
• Electrostatic potential
• Constant magnetic field self-consistency breaks
  when there are currents and spatially varying
  electric field
• Dynamics in the magnetosphere does not couple
  dynamically to the ionosphere
• Ionospheric horizontal motion is not derived
  with dynamic effects
• Observationally, difficult to explain the
  overshoot of an onset (lt 30 min)
• New generation 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

2
M-I Coupling

• Explain the observed ionospheric responses to
  solar wind condition/changes, substorms and
  auroras etc. and feedback to the magnetosphere
  (not to simply couple codes)
• Conventional Ohms law in the neutral framegt
  the key to coupling
• Derived from steady state equations (no
  ionospheric acceleration)
• Conductivities are time constant
• J and E are one-to-one related no dynamics
• Magnetospheric Approach
• Height-integrated ionosphere
• Neutral wind velocity is not a function of height
  and time
• Ionospheric Approach
• Structured ionosphere
• Magnetosphere is a prescribed boundary
• Not self-consistent steady state equations to
  describe time dependent processes (In steady
  state, imposed E-field penetrates into all
  heights)
• Do not solve Maxwell equations

3
Field-aligned Current Coupling Models
Full dynamics
Electrostatic
Steady state (density and neutrals time varying)

• coupled via field-aligned current, closed with
  Pedersen current
• Ohms law gives the electric field and Hall
  current
• electric drift gives the ion motion

4
M-I Coupling (Conventional)

• Ohms law in the neutral frame the key to
  coupling
• Magnetospheric Approach
• Height-integrated ionosphere
• Current conservation
• Neutral wind velocity is not a function of height
  and time
• No self-consistent field-aligned flow
• No ionospheric acceleration
• Ionospheric Approach
• Structured ionosphere
• Magnetosphere is a prescribed boundary
• Not self-consistent steady state equations to
  describe time dependent processes (In steady
  state, imposed E-field penetrates into all
  heights)
• Do not solve Maxwell equations

5
M-I coupling model Driven by imposed E-field in
the polar cap
6
Conventional Model Results Penetration E-field
7
M-I Coupling (Conventional)

• Ohms law in the neutral frame the key to
  coupling
• Magnetospheric Approach
• Height-integrated ionosphere
• Neutral wind velocity is not a function of height
  and time
• Ionospheric Approach
• Structured ionosphere
• Magnetosphere is a prescribed boundary
• When upper boundary varies with time, the
  ionosphere varies with time (misinterpreted as
  dynamic coupling)
• Not self-consistent steady state equations to
  describe time dependent processes (In steady
  state, imposed E-field penetrates into all
  heights)
• Do not solve Maxwells equations
• No wave reflection
• No fast and slow modes in ionosphere (force
  imbalance cannot propagate horizontally)
• No ionospheric acceleration

8
Theoretical Basis for Conventional Coupling Models

• B0 gtgtdB and B0 is treated as time independent
  in the approach, and dB is produced to compare
  with observations
• not a bad
  approximation
• 
  questionable for short time scales dynamics
• 
  questionable for short time scales
• Time scale to reach quasi-steady state
  dtdLdB/dE
• given dL, from the magnetopause to ionosphere,
  20 Re
• dB, in the ionosphere, 1000 nT
• dE, in the ionosphere, for V1 km/s, 6x10-2 V/m
• dt 2000 sec, 30 min, substorm time scale!
• Conventional theory is not applicable to
  substorms, auroral brightening!

9
Ionospheric Dynamic Processes
Epoch analysis showing on average an overshoot in
ionospheric velocity for 30 min.
An overshoot lasting 40 min was seen on ground
but not in geosynchronous orbits indicating the
overshoot is related to the ionospheric processes
Huang et al, 2009
10
North Pole, Winter Solstice
11
Ion-neutral Interaction

• Magnetic field is frozen-in with electrons
• Plasma (red dots) is driven with the magnetic
  field (solid line) perturbation from above
• Neutrals do not directly feel the perturbation
  while plasma moves
• Ion-neutral collisions accelerate neutrals (open
  circles), strong friction/heating
• Longer than the neutral-ion collision time, the
  plasma and neutrals move nearly together with a
  small slippage. Weak friction/heating
• On very long time scales, the plasma and neutrals
  move together no collision/no heating

12
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)

13
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

14
Expected Heating Distribution
sun

• For uniform conductivity, velocity pattern
  coincides with the magnetic perturbation.
• FAC forms at the center of the convection cells
• Poynting flux is proportional to V2, weakest at
  the center of convection cells
• Neglecting the heating from precipitation
  particles,
• Conventional model (EJ paradigm) predicts
  heating, J2/?p, is highest at the FAC
• New model (BV paradigm) predicts heating,
  ?in?iV2, is highest at compression region of
  dayside and nightside cusps and strong along the
  noon-midnight meridian

15
Consequence of Heating

• Energy equation
• Neglecting radiative loss, R, and heat conduction
• Enhanced temperature and upward motion are
  expected

16
Basic Equations

• Continuity equations
• Momentum equations
• Temperature equations
• Faradays Law and Ampere's Law

s e, i or n, and es -e, e or 0
Field-aligned flow allowed
17
Simplifying Assumptions (dt gt 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.

18
Momentum equations without electric field E
19
Numeric Consideration
Large collision frequencies make equations
strongly stiff
is very large at low altitude, e.g., at 80 km
s-1
Extremely small time step (lt 10-6 s) is required
for explicit algorithms to be numerically stable.
Implicit algorithms are necessary
20
1-D Stratified Ionosphere/thermosphere

• Equation set is solved in 1-D (vertical), assume
  ?BltltB0.
• 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 Maxwells
  equations using explicit method
• test 2 use implicit method (increasing time
  step by 105 times)
• test 3 include continuity and energy equations
  with
• field-aligned flow

2000 km
500 km
21
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
22
30 Alfvén Travel Time

• The quasi-steady state is reached in 20 Alfvén
  time.
• During the transition, antisunward flow in the
  F-layer can be large
• During the transition, E-layer 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
23
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
24
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
25
After 1 hour, a flow reversal at top boundary
Pedersen current more than doubled just after
the reversal
Song et al., 2009
26
Electric field variationsNot Constant!
Electric field in the neutral wind frame E E
unxB Not Constant!
Song et al., 2009
27
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 defined as 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
28
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(EunxB) 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
29
Summary

• A new scheme of solar wind-magnetosphere-ionosphe
  re-thermosphere coupling is proposed
• Including continuity, momentum equation, and
  energy equation for each species of multi fluids
• Including Maxwells equations
• Including photochemistry
• No imposed E-field is necessary, and no imposed
  field-aligned current is necessary
• 1-D studies steady state, wave dispersion
  relation and attenuation, time dependence,
  ionospheric heating, coronal heating
• An implicit numerical scheme has been developed
  to make the time step large (5 orders) enough for
  global simulations
• In 1-D simulations, there are 4 major differences
  between the dynamic (and inductive) coupling and
  the steady-state coupling
• Transient time for M-I equilibrium not Alfvén
  travel time, but 10-20 ? tA 20-30 min.
• Reflection effect enhanced Poynting flux and
  heating rate during the dynamic transient period
  can be a factor of 1.5 greater than that given in
  of steady-state coupling
• Plasma inertia effect velocity, magnetic field,
  and electric field perturbations depend on
  density profile during the transition period
• Field-aligned upflow allowed
• In 2-D and 3-D ionosphere can be an active
  player in determining magnetospheric convection.
  It can be the driver in some regions.
• Using Ohms law in the neutral wind frame in
  conventional M-I coupling will miss
• the dynamics during the transition lt 30 min
• neutral wind acceleration gt 1 hr.

30
Comparison of Steady-state Coupling with Dynamic
Coupling

• Coupling speed Vphase
• Steady-state Coupling
• Original model (Vasyliunas, 1970, Wolf, 1970)
  not specific, presumed to be VA
• Implemented in simulations ? (instantaneously)
• Dynamic Coupling Vphase a1/2 VA (? is
  neutral inertia loading factor)
• Coupling time dt
• Steady-state Coupling
• Original model not specified,
• Implemented in simulations 0
• Dynamic Coupling

12 min (Alfvén transient) 30 min (M-I
equilibrium) 13 hours (neutral acceleration)
31
Comparison of Steady-state Coupling with Dynamic
Coupling, cont.

• Reflection
• Steady-state Coupling
• Original model Multiple reflections assumed,
  V,B
  final result, (depends on ionospheric
  conductivity)
• Implemented in simulations No reflection,
• EEinc, V and dB are derived
• Dynamic Coupling TotalIR for both dB and V
• Reflection coefficient ? depends on gradient
  (height) and frequency (time lapse)
• Reflection may be produced continuously over
  height
• Incident perturbation may consist of a spectrum
  dispersion effect
• A phase delay f due to propagation to and from
  the reflection point

32
Comparison of Steady-state Coupling with Dynamic
Coupling, cont.

• Velocity perturbation V
• Steady-state Coupling
• Original model Include final result of multiple
  reflections
• Implemented in simulations
• Dynamic Coupling For single A-wave, parallel
  propagation, weakly damped (there are reflected
  waves)

33
Comparison of Steady-state Coupling with Dynamic
Coupling, cont.

• Magnetic perturbation dB
• Steady-state Coupling not included as part of
  model evolution,
• calculated from J
• Dynamic Coupling For single A-wave parallel
  propagation weakly damped (there are reflected
  waves)
• Local along B, from
• B0, V0, dB0, ?i0,
• Electric field perturbation E
• Steady-state Coupling
• Dynamic Coupling For single A-wave parallel
  propagation weakly damped (there are reflected
  waves)
• Dynamic with reflection

34
Comparison of Steady-state Coupling and Dynamic
Coupling, cont.

• Current J
• Steady-state Coupling
• Dynamic Coupling (derived from dB, current
  continuity satisfied)
• Poynting vector S
• Steady-state Coupling Not considered
  explicitly,
• DC part included implicitly in dissipation
• Dynamic Coupling For single A-wave parallel
  propagation weakly damped
• Dynamic with reflection

35
Comparison of Steady-state Coupling with Dynamic
Coupling, cont.

• Heating Rate q
• Steady-state Coupling
• Dynamic Coupling For single A-wave parallel
  propagation weakly damped
• The perturbations include incident and
  reflected waves
•  

36
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Digisonde DPS
Transmit antenna
40
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41
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42
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43
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