The Rice Convection model (RCM) is a bounce averaged-drift kinetic model of the ring current and inner plasma sheet and their coupling to the ionosphere. It assumes an isotropic distribution function for all magnetospheric particles and calculates the temporal and spatial variation of the phase space density in the inner-plasma-sheet and ring current. The model considers particle drift in an inputted, time varying magnetic field, and a self consistent potential electric field that is computed taking into account current closure in the ionosphere.
The particle population in the inner magnetosphere is represented by three species (H+, O+, and electrons); in addition, a model plasmasphere is included. RCM solves a special form of the collisionless Vlasov equation for the distribution function of the three species that includes transport due to ExB and gradient/curvature drifts. The source terms include inflow through the outer boundary, the losses are due to boundary outflows and charge-exchange (for H+ and O+) with neutral hydrogen of geocorona. For the plasmasphere, parameterized refilling is included as a source term. The potential electric field used in the transport equations is obtained self-consistently by solving the current-conservation equation. Divergent drift currents are allowed to close through the ionosphere via field-aligned (Birkeland) currents and horizontal Pedersen and Hall ionospheric currents. Both potential and induction electric fields are included in the transport equations.
The transport equations and the current-conservation equation are solved on a high-resolution ionospheric polar orthogonal grid. The standard grid offered through runs on request has grid spacing that is uniform in local time (0.25 hrs MLT resolution). Latitudinal grid spacing varies from about 0.1 degrees in the auroral zone to about 2 degrees close to the equator. The modeling region is set to be an ellipse in the equatorial plane that extends near the magnetopause on the dayside and about twice the standoff distance in the tail. The location of the boundary is mapped to the ionosphere (where it is not aligned with the grid) and varies throughout simulations as the magnetic field is time-dependent. The equatorward/earthward boundary is at L=1.05 (~10 degrees latitude).
In solving the potential equation, the conductance tensor has two contributions. The solar EUV-produced "background" ionosphere is represented by the empirical IRI-90 model. Auroral enhancements due to energetic particle precipitation are evaluated from the computed magnetospheric distribution function assuming loss rates that are a fraction of the strong pitch-angle scattering limit rate, and conductance values are estimated using the expressions of Robinson et al. (1987).
The basic theory of the equations that RCM solves is described in detail in [Wolf, 1983; Toffoletto et al., 2003]. Some of the physics studied with the RCM can be found in [Sazykin et al., 2002; Wolf et al., 2007].
Many input models feed boundary conditions and other necessary information into the RCM, which provides opportunity for a great deal of computer experimentation, but at the cost of complexity. For runs on request, sensible default models and options are used to provide most of the input parameters, so that the model can be run with only a few input parameters. In the future, developers and CCMC plan to implement additional user options that will become available for runs on request.
Specifying time history of the solar wind speed and density, interplanetary magnetic field, and Dst, Kp, and ABI indices will be sufficient to obtain plasma boundary conditions and polar cap potential and drive the magnetic field model. These will all be automatically supplied by CCMC when the desired event interval is specified.
In the CCMC implementation, the magnetospheric particle distribution is represented by 85 invariant-energy channels for H+, 85 channels for O+, and 29 for electrons. (Invariant energy is particle energy times (flux tube volume)^2/3.) One channel is set aside for cold plasmaspheric particles. The invariant energy channels cover energies from about 0.05*kT to 10*kT in the inner plasma sheet.
- Magnetic field models: The user has the choice of two magnetic field models: Hilmer and Voigt  and T-89 [Tsyganenko, 1989]. The first of these is a more flexible and dynamic global magnetic field model that varies with the magnetopause standoff distance, Dst, and the auroral boundary index ABI, and is appropriate for most situations.
- Plasma parameters at outer boundary of the RCM: The total ion number density and temperature are set as N [cm-3]=(0.4*(Kp-1)+0.5*(5-Kp))/4, T=(0.385*(Kp-1)+0.2083*(5-Kp)) keV following linear regression fits to the results of Huang and Frank [1986, 1989]. The phase space density for each species is assumed to be a kappa=6 function. Ion composition is estimated from Kp and results from Young et al. .
- Plasma initial condition: default is an initially empty magnetosphere. A preexisting plasma sheet population is built by starting the model a few hours prior to the time of interest. Potential on the poleward boundary. Total potential drop defaults to a Boyle et al. value with saturation effect from Siscoe et al. . The potential is a sine wave in local time, antisymmetric about 23-11 LT.
RCM raw output consists of time history of the full distribution function of all three species, as well as electric and magnetic fields, currents, and auroral particle precipitation. For runs on request, typical output available to the user will be:
- Various moments of the phase space density of magnetospheric species H+, O+, and electrons, such as plasma pressure P, number density N, temperature (average energy), flux-tube entropy parameter PV^gamma, etc
- Electrodynamics quantities such as ionospheric electrostatic potential, field-aligned (Birkeland currents), magnetic field flux-tube volume, and ionospheric ExB drift velocities.
- Auroral precipitation quantities such as precipitating electron energy flux, average electron energy, Pedersen and Hall elements of the conductance tensor (field-line integrated from the bottom of the ionosphere to 1000 km altitude), etc.
- Differential particle fluxes of magnetospheric species (to become available soon).
- Flux-tube content or number density of the plasmaspheric population.
Limitations and Caveats
- The RCM uses empirical magnetic field models, which are not self-consistent with the RCM-computed pressure. <li?isotropic particle="" distributions="" are="" assumed,="" so="" that="" drift-shell="" splitting="" effects="" not="" considered.="" <li="">The Earth's internal magnetic field is assumed to be a dipole aligned with the rotation axis. There is assumed to be symmetry about the equatorial plane. For comparison with observations, RCM ionospheric latitude is best interpreted as invariant latitude.</li?isotropic>
- Field-aligned potential drops are neglected.
- Boyle, C. B., P. H. Reiff, and M. R. Hairston (1997), Empirical polar cap potentials, J. Geophys. Res., 102(A1), 111-125.
- Hilmer, R. V., and G. H. Voigt (1995), A magnetospheric magnetic field model with flexible current systems driven by independent physical parameters, J. Geophys. Res., 100(A4), 5613-5626.
- Robinson, R. M., R. R. Vondrak, K. Miller, T. Dabbs, and D. Hardy. (1987), On calculating ionospheric conductances from the flux and energy of precipitating electrons, J. Geophys. Res., 92, 2565-2569.
Sazykin, S., R. A. Wolf, R. W. Spiro, T. I. Gombosi, D. L. De Zeeuw, and M. F. Thomsen (2002), Interchange instability in the inner magnetosphere associated with geosynchronous particle flux decreases, Geophys. Res. Lett., 29(10), 1448, doi:10.1029/2001GL014416.
- Siscoe, G. L., N. U. Crooker, and K. D. Siebert (2002), Transpolar potential saturation: Roles of region 1 current system and solar wind ram pressure, J. Geophys. Res., 107(A10), doi:10.1029/2001ja009176.
- Toffoletto, F., S. Sazykin, R. Spiro, and R. Wolf (2003), Inner magnetospheric modeling with the Rice Convection Model, Space Sci. Rev., 107, 175-196.
- Tsyganenko, N. A. (1989), A magnetospheric magnetic field model with a warped tail current sheet, Planetary and Space Science, 37, 5-20.
- Wolf, R. A. (1983), The quasi-static (slow-flow) region of the magnetosphere, in Solar Terrestrial Physics, edited by R. L. Carovillano and J. M. Forbes, pp. 303-368, D. Reidel, Hingham, MA.
- Wolf, R. A., R. W. Spiro, S. Sazykin, and F. R. Toffoletto (2007), How the Earth's inner magnetosphere works: An evolving picture, J. Atmos. Sol.-Terr. Phys., 69(3), 288-302, doi:10.1016/j.jastp.2006.07.026.
- Young, D. T., H. Balsiger, and J. Geiss (1982), Correlations of magnetospheric ion composition with geomagnetic and solar activity, J. Geophys. Res., 87, 9077.