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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 Code Descriptions Physics Examples Issues**

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 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.

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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 Bis=Bin): Vasyliunas Equation (assumes Bis=Bin): Combine two together: 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 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 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 Ionosphere T*GCM Solar Wind ENLIL Magnetosphere LFM SEP MI Coupling Active Regions Ring Current RCM Geocorona and Exosphere Radiation Belts Inner Magnetosphere Plasmasphere

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**Coupled Modeling Scheme**

Magnetosphere LFM Ionosphere T*GCM Ring Current RCM Geocorona and Exosphere Inner Magnetosphere Plasmasphere

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**Coupling Scheme LFM 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 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 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 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 Bx=By=5 nT, Bz = -5nT, vsw = 400 km/s, nsw=5 /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 Bx=By=5 nT, Bz = -5nT, vsw = 400 km/s, nsw=5 /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 Bx=By=5 nT, Bz = -5nT, vsw = 400 km/s, nsw=5 /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:

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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 don’t 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**

Magnetic field model Usually an empirical model Initial condition and boundary particle fluxes 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

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