Transcript Inner Magnetospheric Modeling with the Rice Convection Model Frank Toffoletto, Rice University (with thanks to: Stan Sazykin, Dick Wolf, Bob Spiro, Tom Hill, John.

Inner Magnetospheric Modeling
with the Rice Convection Model
Frank Toffoletto, Rice University
(with thanks to: Stan Sazykin, Dick Wolf, Bob Spiro, Tom Hill,
John Lyon, Mike Wiltberger and Slava Merkin)
Outline
• Motivation
– Importance of the inner magnetosphere
• The tool of choice is the Rice Convection Model (RCM)
• Code Descriptions
– RCM
– Coupled LFM RCM
• Physics Examples
• Issues
• Discussion and Conclusion
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Why is the Inner Magnetosphere
so important?
•
Basic Physical understanding of plasmaspheric and ringcurrent dynamics.
–
•
We won’t understand ring current injection until we understand the
associated electric and magnetic fields self consistently.
Space Weather:
–
–
Many Earth orbiting spacecraft are inner magnetosphere.
Radiation belts: Many space weather effects are related to to
understanding and predicting highly energetic particles.
•
–
For that we need a model of the electric and magnetic fields.
The low- and mid-latitude ionosphere: Disruptions of the mid- and
low-latitude ionosphere seem to be the most important aspects of
space weather at present, particularly for the military.
•
Inner magnetospheric electric fields appear to be the most unknown
element in ionospheric modeling of the subauroral ionosphere.
3
What can an Inner magnetospheric model
(such as the RCM) provide?
• Missing physics: Global MHD does not include
energy dependent particle drifts, which become
important in the Inner Magnetosphere.
• An accurate and reasonable representation of the
Inner Magnetosphere should be able to compute both
Electric and Magnetic fields.
• Inputs to ionosphere/thermosphere models, such as
electric fields and particle information.
4
RCM Modeling Region
• In the ionosphere, the modeling region includes the diffuse auroral oval (the
boundary lies in the middle of the auroral oval, shifted somewhat equatorward
from the open-closed field line boundary).
• The modeling region includes the inner/central plasma sheet, the ring current,
and the plasmasphere.
•Region-2 Field-Aligned currents (FAC) connect magnetosphere and ionosphere.
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RCM Physics Model
• Three pieces:
– Drift physics: Inner magnetospheric hot plasma population
on closed magnetic field with flow speeds much slower than
thermal and sonic speeds while maintaining isotropic pitchangle distribution function.
– Ionospheric coupling: perpendicular electrical currents and
electric fields in the current-conservation approximation.
• Field-aligned currents connecting the magnetosphere and
ionosphere assuming charge neutrality.
– Plasma population and magnetic fields are in quasi-static
equilibrium
6
RCM Transport Equations
• Take a distribution function and “slice” it into “invariant energy”
channels:
2/3
k  WkV (x)
• For each “channel”, transport is via an advection equation:
 

 (x, t)

V
(

,x,
t)



(x,t)


  t
D
2 
 (x,t)
V (,x, t) 
D
E(x, t)  B(x, t) B(x, t)  W (,x, t)

2
B(x)
qB(x, t)2
where the equations are in non-conservative form, and in the (,)
parameter space these “fluids” are incompressible
• Ionospheric grid, where B-field is assumed dipolar, Euler
potentials can be easily defined that are (essentially) colatitude
and local-time angle.
• (Equations are solved using the CLAWPAK package)
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Equation of MagnetosphereIonosphere coupling
•
Current conservation equation at ionospheric hemispheric shell
(assumes Bis=Bin):
   ˆ    J  J  J sin I
h
•
•
w
 
||in
||is

Vasyliunas Equation (assumes Bis=Bin):
J||in J||is J||in  J||is bˆ


  V  p
Bin Bis
Bi
B
Combine two together:
 bˆ

ˆ
 h       J w  Bi sin I   V  p 
B

High-latitude boundary condition: Dirichlet
Low-latitude boundary condition: mixed with
2nd-order spatial derivatives (simple model of equatorial. electrojet)

•
•


•
Equatorial plane mapping changes in time, grid there is nonorthogonal.
•
Equatorial boundary is a circle of constant MLT. Polar boundary does
not coincide with a grid line and moves in time.
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Basic RCM Physics
Electrons
Ions
For each species and invariant energy ,  is
conserved along a drift path.
Specific Entropy
2
pV    s s
3 s
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Basic RCM Physics- Electric Fields
Inner magnetospheric
electric field shielding
Formation of region-2
field-aligned currents
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Limitations to the Conventional RCM
Approach to Calculating InnerMagnetospheric Electric Field
• The change in magnetic field configuration due to a northward
or southward turning has a large effect on the inner
magnetospheric electric field.
– Hilmer-Voigt or Tsyganenko magnetic field models can’t give a
good picture of the time response to a turning of the IMF.
• The potential distribution around the RCM’s high-L boundary
must evolve in a complicated way just after a northward or
southward turning hits the dayside magnetopause.
• The time changes in the polar-cap potential distribution occur
simultaneously with the changes in magnetic configuration.
• Magnetic field model is input and not in MHD force balance with
the RCM computed pressures.
• A fully coupled MHD/RCM code is an obvious choice to address
these limitations.
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Coupled Modeling Scheme
Solar Corona
SAIC
Solar Wind
ENLIL
Magnetosphere
LFM
SEP
Active Regions
Ionosphere
T*GCM
MI Coupling
Ring Current RCM
Radiation Belts
Plasmasphere
Geocorona and
Exosphere
Inner
Magnetosphere
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Coupled Modeling Scheme
Magnetosphere
LFM
Ring Current RCM
Plasmasphere
Ionosphere
T*GCM
Geocorona and
Exosphere
Inner
Magnetosphere
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Coupling Scheme
LFM
ur
P  B
sr
bc 
time t
Cs
ur
P  B
sr
bc 
 time t
Cs
ur
P  B
sr
bc 
 time t
Cs

RCM
Coupling exchange time is 1 minute
LFM is nudged by the RCM
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Aside:Coupling approach
• In order to minimize code changes, we plan to use the
InterComm library coupling software developed by Alan
Sussman at the University of Maryland
– InterComm allows codes to exchange data using ‘MPI-like’ calls
• It can also handle data exchanges between parallel codes
– For now, the data exchange is done with data and lock files
• The plan is to replace the read/write statements with InterComm calls
• Data is exchanged via a rectilinear intermediate grid - this allows
for relatively fast and simple field line tracing
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Inner Magnetospheric Shielding
• The inner edge of the plasma sheet
tends to shield the inner
magnetosphere from the main Electric
convection field.
• This is accomplished by the inner edge
of the plasma sheet coming closer to
Earth on the night side than on the day
side.
– Causes region-2 currents, which
generate a dusk-to-dawn E field in the
inner magnetosphere.
• When convection changes suddenly,
there is a temporary imbalance.
– For a southward turning, part of the
convection field penetrates to the inner
magnetosphere, until the nightside
inner edge moves earthward enough to
re-establish shielding.
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Example of shielding Standalone RCM
(RCM Runs courtesy of Stan Sazykin)
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RCM LFM: Run Setup
• Steady solar wind speed of 400 m/s, particle
density of 5 /cc
• Uniform Pederson conductance of 5 Siemens
(0 Hall conductance)
• LFM run for 50 minutes without an IMF (from
3:10 - 4:00)
• IMF turns southward at t = 4:00 hours and
coupling is started
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IMF and Cross polar cap
potential for RCM LFM run
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Example of shielding RCM-LFM run
Region 2 currents
High pV ‘Blob’
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Example of shielding RCM-LFM run
Low pV Channels
23
Example of undershielding Standalone RCM
24
Example of undershielding LFM-RCM run
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Example of OvershieldingRCM-LFM run
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Example of Overshielding Standalone RCM
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Electric fields and pV
• RCM -LFM exhibits many of the same characteristics
as the standalone RCM, albeit much noisier
– Caveat: In order achieve reasonable shielding, the density
coming from the LFM was floored. Otherwise the LFM
plasma temperature in the run becomes very high as the run
progresses, which effectively destroys shielding.
• LFM ionospheric electric field is not the same as the
RCM’s, this could be corrected by using a unified
potential solver.
– However, the LFM is missing the corotation electric field
• Initially, the LFM’s pV is typically lower than empirical
estimates, later it becomes higher as the x-line
moves tailward.
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Comparisons of Log10(pV)
Empirical
Figure courtesy of Xiaoyan Xing and Dick
Wolf, based on Tsyganenko 1996 magnetic
field model and Tsyganenko and Mukai
2003 plasma sheet model. (IMF Bx=By=5
nT, Bz = -5nT, vsw = 400 km/s, nsw=5 /cc)
LFM
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Comparisons of Log10(pV)
Empirical
Figure courtesy of Xiaoyan Xing and Dick
Wolf, based on Tsyganenko 1996 magnetic
field model and Tsyganenko and Mukai
2003 plasma sheet model. (IMF Bx=By=5
nT, Bz = -5nT, vsw = 400 km/s, nsw=5 /cc)
LFM
30
Comparisons of Log10(pV)
Empirical
Figure courtesy of Xiaoyan Xing and Dick
Wolf, based on Tsyganenko 1996 magnetic
field model and Tsyganenko and Mukai
2003 plasma sheet model. (IMF Bx=By=5
nT, Bz = -5nT, vsw = 400 km/s, nsw=5 /cc)
LFM
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Ring Current Injection:
The effect of the magnetic field
• Lemon et al (2004 GRL) used a coupled RCM equilibrium code
(RCM-E) to model a ring current injection.
• A long period of adiabatic convection causes a flow-choking, in
which the inner plasma sheet contains high-pV, highly stretched
flux tubes.
– Nothing like an expansion phase or ring-current injection occurs.
• In order to study the inner-magnetospheric consequences of a
non-adiabatic process, Lemon did an RCM-E run which started
from a stretched configuration, but then moved the nightside
RCM model boundary in to 10 RE and reduced the boundarycondition value of pV5/3 along this boundary within ±2 hr of local
midnight.
– The result was rapid injection of a very strong ring current. Low
content flux tubes filled a large part of the inner magnetosphere,
forming a new ring current.
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Do we see similar behavior in the
coupled RCM LFM?
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Channels of Low pV
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What about the LFM?
• Should produce a more reasonable representation of
the inner magnetospheric pressures, densities and
(hopefully) the magnetic field.
– Trapped Ring Current
• The presence of a ring current should encourage the
formation of Region-2 currents
– Ideal MHD should produce region-2 currents.
– It is not clear why the global MHD models do not.
– (Actually, higher resolution LFM runs show the beginnings of
region-2 currents.)
37
Pressure comparisons at ~midnight
(RCM values computed along a constant LT in the ionosphere and
then mapped to the equatorial plane.)
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Weak Region-2 currents form in the LFM
39
Effect on the LFM magnetic field
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Problems
41
High speed flows do not seem to happen
in the standalone LFM
RCM LFM
Standalone LFM
42
Log of past runs: http://rocco.rice.edu/~toffo/lfm/
Adding a cold plasmasphere
to the RCM did not help
Without plasmasphere
With plasmasphere
43
Density ‘Fix’ helps some
With ‘fix’
44
Resolution seems to help but need longer runs
Low resolution
High resolution
(but with no density ‘fix’)
45
Summary
• Coupled code ‘runs’
• From an RCM viewpoint, results don’t look
unreasonable
– Inner magnetospheric shielding
– Inner magnetospheric pressures
– Ring current injection
• Although LFM computed pV are low compared to empirically
computed values
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Summary - 2
• From an LFM viewpoint
– Magnetic field responds, to first order, as one would expect
– Get weak region-2 currents
– But get spectacular outflows from the inner magnetosphere
• Decoupled from the ionosphere
• May be a resolution issue, for a given resolution, perhaps the
code is unable to find equilibrium solutions that match
computed pressures
– Turning off the coupling results in disappearance of the ring
current in ~15 minutes
• High speed flows seem to be associated with high plasma
betas
– It seems we are pushing the MHD in a way that it was not
designed for
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Outlook
• Ultimately we hope to couple to
TING/TIEGCM in a 3-way mode
• Ionospheric outflow could also be
incorporated
• A version of the RCM that includes a non-spin
aligned non-dipolar field is in testing phase
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Extra Slides
RCM: Inputs and Assumptions
• Inputs
– Magnetic field model
• Usually an empirical model
– Initial condition and boundary particle fluxes
• Usually an empirical model
– Loss rates and ionospheric conductivities
• Parameterized empirically-based models
– Electric field model is computed self-consistently
• Ionosphere is a “thin” conducting (anisotropic) shell
• Electric field in the ionosphere is potential
• Assumptions
–
–
–
–
Plasma flows are adiabatic and slow compared to thermal speeds.
Inertial currents are neglected
Magnetic field lines are equipotentials
Pitch-angle distribution of magnetospheric particles is isotropic
• The formalism allows the main calculations to be done on an 2D
50
ionospheric grid.
RCM-MHD comparison
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