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Michigan MHD Model (BATS-R-US). The Michigan MHD Model
is the application of the BATS-R-US high performance multiscale MHD code
to space plasmas. The code has been successfully applied to the description
of several solar system plasmas, including the expansion of the solar
wind from the base of the solar corona to heliocentric distances well
beyond the orbit of Earth, and the global terrestrial magnetosphere. A
schematic representation of the physical domain described by the Michigan
MHD model is shown in the figure below: 
It is important to emphasize that BATS-R-US was written with portability and flexibility in mind. This means that the same code is used for the solar wind and magnetosphere simulations, and only the boundary conditions and input data files need to be changed when applying the code to various physical phenomena. In the solar wind simulation the source region of the solar wind (the base of the solar corona) is located at 1 Rs (solar radius). The boundary conditions describe a hot, rotating plasma reservoir with an embedded multipole field (up to octupole). The sum of the ion and electron temperatures is 3.1 million K, the magnetic field at the solar pole and equator are 8.4 G and 2 G, respectively, and the plasma density is 10 The BATS-R-US code was also used to simulate the formation and evolution of coronal mass ejections (CME) in the heliosphere. In this simulation a spatially and temporarily localized isothermal density pulse was introduced at the Sun (just above the solar equator). This density increase first "filled" the closed solar magnetic field line region with extra plasma. After a while the closed field magnetic configuration was unable to contain the increased plasma and the plasma "pierced" the closed field lines. The resulting CME rapidly moved through the near solar region and formed a structure which evolved and propagated outward passing the orbit of the Earth. The figure below shows a cut across the plane containing the CME about 6 hours after the initiation of the pressure pulse. One can see the adaptation of the computational blocks inside the CME as it has evolved. 
The next figure shows the results of a simulation describing the interaction of the magnetosphere with the solar wind. Earth is represented by its magnetic dipole field and with the height integrated ionospheric conductance tensor (describing field-aligned, Pedersen and Hall conductances at every point of the surface). The magnetosphere simulation is numerically very challenging, since the plasma ß varies several orders of magnitudes in the simulation domain. Near the surface of the Earth the terrestrial dipole field dominates and ß is very small, while in the free streaming solar wind ß is around unity. ß reaches values >100 in the inner plasma sheet. In addition, the Alfvén speed is very large in the vicinity of Earth making the equations very stiff. 
The simulation shown in the above figure was carried out for southward interplanetary magnetic field conditions. The above figure shows the pressure in the magnetosphere (grayscale) and the last closed magnetic field lines (magnetopause). The robustness of BATS-R-US makes it possible to handle such very challenging simulation with relative ease. Inner Magnetosphere Model (IMM) The Inner Magnetosphere Model portion of the KDI is being derived from the Rice Convection Model (RCM). The Rice Convection Model is a computer program that calculates the dynamic behavior of the particles and the electric fields and currents in the Earthsssssssss inner magnetosphere. The region is crucially important from a space-weather point of view, because it is home to most of the world's fleet of working spacecraft, including hundreds of communications spacecraft in geosynchronous orbit and the Global Positioning System (GPS), which occupies a beehive of orbits inside geosynchronous. The physics of the region is complicated, because it contains overlapping particle distributions with a wide range of energies and characteristics. These different coexisting particle populations cannot be treated as a single fluid, because they all move differently. The Rice Convection Model (RCM) is a heritage code developed over the last thirty years specifically to treat this unique and complicated region. In its present form, the RCM represents the particles in terms of about thirty separate fluids. Its equations and numerical methods have been specifically designed for accurate treatment of the inner magnetosphere [Jaggi and Wolf , 1973; Harel et al., 1981a; Wolf, 1983; Erickson et al., 1991], including the flow of electric currents along magnetic field lines to and from the conducting ionosphere. The RCM does its primary calculations on a 2D grid on a spherical shell in the ionosphere. Values in the magnetosphere are computed by mapping out along magnetic field lines. The ionospheric grid is fine, typically about 0.5 degrees latitude in the auroral zone. The RCM computes these currents and the associated electric fields self-consistently. Arguably the most sophisticated computational model of the inner magnetosphere, the RCM has been compared extensively with spacecraft and ground observations over a long period of years [e.g. Harel et al., 1981b; Chen et al., 1982; Wolf et al., 1982; Spiro et al., 1988]. The connections of the RCM to the outer magnetosphere above and to the ionosphere and thermosphere below are represented by complicated boundary conditions, which can be estimated only very imperfectly from available observations. Furthermore, the RCM traditionally uses for input, a semi-empirical magnetic field model that does not represent the full dynamics. In the KDI, the RCM will take dynamically computed magnetic field values from the MHD code. We are also merging the RCM with leading computational models of the adjacent regions to form a comprehensive computational representation of the entire natural system. The Upper Atmospheric General Circulation Model (UA-GCM) The atmospheric boundary of the KDI is the Upper Atmospheric General Circulation Model (UA-GCM), being derived from the thermospheric - ionospheric - electrodynamics - general circulation model (TIE-GCM). The TIE-GCM is a global model which calculates the dynamics of the upper atmosphere. This model determines the atmospheric composition, temperature, and flow pattern over the whole Earth from 95 km to 500 km altitude, a region of the atmosphere which is greatly affected by solar emissions and interactions with the magnetosphere. For example, auroral precipitation and joule heating at high latitudes cause atmospheric heating and expansion which affects the drag on low altitude satellites. As a result, the Skylab space station fell to Earth much earlier than expected because of a surprising number of large geomagnetic storms. Other processes produce irregularities in the ionospheric density structure which, in turn, affects radio signals from navigation and communication satellites. Developed at the National Center for Atmospheric Research, the TIE-GCM is another heritage code, with different "layers" being added over time as a series of evolving steps to a more comprehensive model. The initial model was the thermosphere general circulation model (the T-GCM). The development of the T-GCM was described in a series of papers by Dickinson et al. [1981], Dickinson et al. [1984], Roble et al.[1982], Roble et al.[1983], and Fesen et al. [1986]. In the next step, Roble et al.[1988] developed a new 3-D coupled thermosphere-ionosphere general circulation model (TI-GCM), and Richmond [1992] extended the TI-GCM to include self-consistent electrodynamic interactions between the ionosphere and thermosphere (TIE-GCM). Roble and Ridley [1994] extended the model to include the mesosphere and upper stratosphere (the TIME-GCM). For our immediate goal of developing the KDI, using the TIE-GCM provides a sufficient specification of the atmospheric boundary of the system. The additional difficulty of including the mesosphere dynamics by using the TIME-GCM during the initial development of the KDI would provide little additional benefit in the resulting space weather information. The TIE-GCM solves the pressure coordinate primitive equations for horizontal momentum, continuity, hydrostatics, and thermodynamics to predict neutral winds, ion drifts, neutral, ion, and electron temperatures, and the neutral and ion densities. The number densities of the major constituents N2 ,O2 , O, and of the minor neutral constituents NO, O3 , He, Ar, N(4S), N(2D) are calculated. The model also solves for the ionospheric structure giving global distributions of O+ ,O+2, N+ ,N+2, and NO+. Both the neutral and ion equations are solved on a spherical grid in latitude, longitude, and altitude. The horizontal resolution is 5° by 5°; the vertical resolution varies from a fine grid (several kilometers) in the lower thermosphere to a coarser spacing (40-60 kilometers) at high altitudes with 25 levels overall. The dynamo portion of the code uses the neutral winds and conductivities to compute the electric potential at each time step.
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