Inner Magnetospheric Modeling with the Rice Convection Model

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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)

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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
  ring-current dynamics.
• We wont 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.

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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.

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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 pitch-angle
  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

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RCM Transport Equations

• Take a distribution function and slice it into
  invariant energy channels
• For each channel, transport is via an advection
  equation
• 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 Magnetosphere-Ionosphere coupling

• Current conservation equation at ionospheric
  hemispheric shell (assumes BisBin)
• Vasyliunas Equation (assumes BisBin)
• Combine two together
• High-latitude boundary condition Dirichlet
• Low-latitude boundary condition mixed
  with2nd-order spatial derivatives (simple model
  of equatorial. electrojet)
• Equatorial plane mapping changes in time, grid
  there is non-orthogonal.
• 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 l, h is
conserved along a drift path. Specific Entropy
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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 Inner-Magnetospheric 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
  cant give a good picture of the time response to
  a turning of the IMF.
• The potential distribution around the RCMs
  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
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Coupled Modeling Scheme
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Coupling Scheme
LFM
RCM
Coupling exchange time is 1 minute
LFM is nudged by the RCM
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AsideCoupling 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 310
  - 400)
• IMF turns southward at t 400 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 pVg Blob
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Example of shielding - RCM-LFM run
Low pVg Channels
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Example of undershielding - Standalone RCM
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Example of undershielding - LFM-RCM run
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Example of Overshielding- RCM-LFM run
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Example of Overshielding - Standalone RCM
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Electric fields and pVg

• 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 RCMs, this could be corrected by using a
  unified potential solver.
• However, the LFM is missing the corotation
  electric field
• Initially, the LFMs pVg is typically lower than
  empirical estimates, later it becomes higher as
  the x-line moves tailward.

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Comparisons of Log10(pVg)
LFM
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 BxBy5 nT, Bz -5nT, vsw 400 km/s, nsw5
/cc)
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Comparisons of Log10(pVg)
LFM
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 BxBy5 nT, Bz -5nT, vsw 400 km/s, nsw5
/cc)
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Comparisons of Log10(pVg)
LFM
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 BxBy5 nT, Bz -5nT, vsw 400 km/s, nsw5
/cc)
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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
  boundary-condition 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 pVg
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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.)

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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
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Effect on the LFM magnetic field
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Problems
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High speed flows do not seem to happen in the
standalone LFM
RCM LFM
Standalone LFM
Log of past runs http//rocco.rice.edu/toffo/lfm
/
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Adding a cold plasmasphere to the RCM did not
help
With plasmasphere
Without plasmasphere
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Density Fix helps some
With fix
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Resolution seems to help - but need longer runs
Low resolution
High resolution
(but with no density fix)
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Summary

• Coupled code runs
• From an RCM viewpoint, results dont look
  unreasonable
• Inner magnetospheric shielding
• Inner magnetospheric pressures
• Ring current injection
• Although LFM computed pVg 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
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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 ionospheric grid.

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RCM-MHD comparison