Geophysical Research Letters

Modeling the plasmasphere with SAMI3

Authors


Corresponding author: J. Huba, Plasma Physics Division, Naval Research Laboratory, Washington, DC, USA. (huba@ppd.nrl.navy.mil)

Abstract

[1] The study of the plasmasphere is extremely important to understanding space weather phenomena; for example, it plays a critical role in the regulation of radiation belt dynamics. In this paper, the first 3D simulation of the plasmasphere based on the first-principles physics model SAMI3 is presented. We include the co-rotation potential, the neutral wind dynamo potential, and a time-dependent Volland-Stern-Maynard-Chen potential to model the response of the convection potential to an idealized magnetic storm. We find that prior to the storm the plasmasphere is largely toroidal and symmetric in magnetic local time with He+/H+ ~ 5–10%. After the storm, the plasmasphere substantially contracts because plasma is convected away from the outer plasmasphere by the enhanced convection velocity. Moreover, a plume-like structure forms in the mid-afternoon sector because of the modified convection pattern associated with the storm. Additionally good agreement is found between the simulation results and data for the L-shell dependence of the equatorial electron density as well as the electron density along the field line at a given L-shell under quiet geomagnetic conditions.

1 Introduction

[2] The Earth's plasmasphere [Lemaire and Gringuaz, 1998] has been the subject of renewed interest in the past decade primarily because of new and exciting data from the IMAGE mission [Sandel et al., 2000; Reinisch et al., 2000; Burch et al., 2001; Darrouzet et al., 2009]. Aside from a better characterization of electron and mass density of the plasmasphere during quiet times, the complex reconfiguration of the plasmasphere became more apparent during magnetic storms [Goldstein et al., 2002, 2005]. This latter finding is very important because erosion of the plasmasphere allows the radiation belts to move earthward and modify plasma waves that scatter radiation belt particles [Millan and Thorne, 2007; Bortnik and Thorne, 2007]. The European Space Agency is sponsoring the project PLASMON [Collier et al., 2011] to develop a data assimilation model of the plasmasphere density to support radiation belt models.

[3] To date, simulations of plasmasphere dynamics have generally been semi-empirical and often restricted to 2D motion. For example, Rasmussen et al. [1993] compute the plasmasphere density only in the equatorial plane, including the convective E × B drifts (an empirical model is used to get the density along each field line). The Global Plasma Ionosphere Density Model (GPID) [Webb and Essex, 2004] is similar in that the motion of individual flux tubes is followed in the equatorial plane. However, field-aligned ion dynamics are also computed within each flux tube, with the lower boundary being an empirical ionosphere. The kinetic model of Pierrard and Stegen [2008] is similar to GPID in that field-aligned ion dynamics are computed for numerous flux tubes, each with an empirical-ionosphere lower boundary. However, E × B drifts are computed for the purpose of determining the plasmapause rather than transporting the plasma. An exception to the above is the Sheffield University plasmasphere ionosphere model (SUPIM), which has been applied to the refilling problem [Sandel and Denton, 2007]. SUPIM is a 3D first-principles model but does not include convective transport (e.g., zonal E × B drift) or ion inertia parallel to the geomagnetic field.

[4] In this paper, we present the first 3D simulation of the plasmasphere based on the first-principles physics model SAMI3. We include the co-rotation potential, the neutral wind dynamo potential, and a time-dependent Volland-Stern-Maynard-Chen potential to model the response of the convection potential to an idealized magnetic storm. We show that a plume-like structure forms in the mid-afternoon sector because of the modified convection pattern associated with the storm. Additionally good agreement is found between the simulation results and data for the L-shell dependence of the equatorial electron density as well as the electron density along the field line at a given L-shell under quiet geomagnetic conditions.

2 Model

[5] The National Research Laboratory (NRL) 3D ionospheric code SAMI3 [Huba et al., 2008] is used in this study; it is based on the 2D ionospheric code SAMI2 [Huba et al., 2000]. Full 3D plasma transport is done on the entire grid for all ion species (H+, He+, O+, N+, inline image, NO+, and inline image). The complete ion temperature equation is solved for three ion species (H+, He+, and O+) as well as the electron temperature equation. Ion inertia is included in the ion momentum equation for motion along the geomagnetic field; this is important because it limits the ion velocity along the field line because of ion sound waves.

[6] The electrostatic potential comprises three parts: the neutral wind dynamo potential, the corotation potential, and the analytic Volland-Stern-Maynard-Chen potential (VSMC) [Reinisch et al., 2009]. We have added a time-dependence to the VSMC potential to simulate an idealized magnetic storm. The potential used in our model is given by

display math(1)

where

display math

and

display math

where Pi = 11.25, Pf = 45.00, ti = 52 h, tf = 60 h, and α = (PfPi)/(tf − ti). This is an idealized method to simulate a storm-time event, where the polar cap potential increases by a factor of 4 over an 8 h period from t = 52 h to t = 60 h.

[7] The geophysical parameters used in this study correspond to moderate solar activity: F10.7 = 120, F10.7A = 120, Ap = 4, Kp = 6, and the day-of-year is 80. The neutral composition and temperature are specified using NRLMSISE00 [Picone et al., 2002], and the neutral wind is specified using HWM93 [Hedin et al., 1991]. The plasma is modeled from hemisphere to hemisphere up to ±78° magnetic latitude; the minimum altitude is 90 km and the peak altitude is ~16 RE at the magnetic equator. A loss term ∝ ni/τd is added in the continuity equation for hydrogen and helium ions for r > 8 RE with a decay time τd = 6 s. Because the SAMI3 grid has closed field lines, this term is added to represent plasma loss on “open field lines,” i.e., field lines that are not connected interhemispherically. Additionally we include the centrifugal force on ions along the magnetic field. We assume a magnetic dipole field aligned with the spin axis of the Earth so geographic and geomagnetic coordinates are the same. This assumption allows us to easily incorporate a corotation potential into the model; however, it is an idealization and seasonal/longitudinal effects are not captured.

[8] The 3D model uses a grid (nz, nf, nl) = (204,124,96) where nz is the number grid points along each magnetic field line, nf the number of field lines, and nl the number in longitude. The grid spacing is nonuniform in nz and nf but uniform in nl. At t = 0 the ionosphere/plasmasphere is preloaded with plasma and we take He+ = H+/10. The only boundary condition on the plasma is at the foot of the field line where photochemical equilibrium is assumed.

3 Results

[9] In Figure 1, we show color contours of the hydrogen (Figures 1a and 1c) and helium (Figures 1b and 1d) ion densities in the magnetic equatorial plane looking down from the North Pole. The Sun is to the right. Overlain on the colored density contours are contours of the electrostatic potential mapped to the equatorial plane. The x and y axes are in units of Earth radii RE. Figures 1a and 1b are at time t = 52 h, just before the potential Φvsmc begins to increase (i.e., pre-storm conditions). Figures 1c and 1d are at time t = 96 h, which is 36 h after the potential has stopped increasing.

Figure 1.

The (a and c) H+ and (b and d) He+ densities in the magnetic equatorial plane at t = 52 h (Figures 1a and 1b) and t = 96 h (Figures 1c and 1d). Note the formation of a plume in the afternoon sector in Figure 1c.

[10] In Figures 1a and 1b, the boundary between the corotation potential (closed, circular-like contours) and convection potential (open contours) is r ~ 4 RE. The distortion of the electrostatic potential is caused by the inclusion of the neutral wind dynamo potential. Within this boundary, the plasma is approximately independent of magnetic local time. However, there is a slight decrease in the densities in the pre-dawn sector indicated by the indentation of the color contours. Moreover, the H+ and He+ track each other within this boundary as demonstrated by the similarity in the shapes of the color contours.

[11] In Figures 1c and 1d, the convection potential has increased by a factor of 4; the number of potential contours has increased and they are spaced closer together indicating a stronger convection electric field. The boundary between the corotation potential (closed, circular-like contours) and convection potential (open contours) has become smaller and is r ~ 3 RE. This is because plasma originally on closed equipotential lines is now on open equipotential lines and is convected away. Interestingly there is a pronounced asymmetry in magnetic local time with the development of a plume-like feature in the afternoon sector associated with the new convection pattern. This is clear in the H+ density in Figure 1c. It is less clear in the He+ density in Figure 1d; however, it does show up if a lower contour level (i.e., 10−1) is considered. This behavior is consistent with the theory of Grebowsky [1970].

[12] In Figure 2, we show color isosurfaces of the H+ and He+ densities at times t = 52 h (Figure 2a) and t = 96 h (Figure 2b). These figures correspond to Figure 1 and use a similar color scale and spatial scale. In this figure, the “arc” at the rear of each panel is midnight (the Sun is to the lower right, in the −x direction). At time t = 52 h, the isosurfaces of the H+ and He+ densities are largely toroidal and symmetric in magnetic local time for densities less than 103 cm−3. However, at time t = 96 h, the plasma has contracted substantially because of the enhanced convection potential. The gradients in the plasma density are clearly sharper in the dawn and midnight sectors as indicated in Figure 2. Moreover, a plume-like structure develops in the mid-afternoon sector. Again, this is most apparent in the H+ density but is exhibited in the He+ density as well.

Figure 2.

Isosurfaces of the H+ and He+ densities at times (a) t = 52 h and (b) t = 96 h. Note the axes are labeled differently from Figure 1.

[13] In Figure 3, we plot the H+ and He+ densities as a function of L-shell in the magnetic equatorial plane for noon, dusk, dawn, and midnight at times t = 51.5 h (black) and t = 96.7 h (dashed). At time t = 51.5 h, there is an exponential decay of the H+ and He+ densities for L ≳ 2 with He+/H+ ~ 5–10%. Although there is no clear transition of a plasmapause in the H+ profile, there is an indication in the He+ profile in the midnight and dawn sectors. Plots at time t = 96.7 h show a dramatic change in the radial behavior of the plasma associated with the enhanced convection field. There is a distinct departure from the t = 51.5 h profiles at L ~ 2.5, indicating the model plasmapause. This is most pronounced in the dawn and midnight sectors. We note that the modeled plasmapause boundary is not as steep as observed by satellite data [Chappell et al., 1970]. Observations indicate the boundary thickness can be ~RE/6. In our simulation model, the grid spacing is RE/4 above L = 3 which can account for some of the discrepancy. Additionally plasma may be on open field lines, which is not accounted for in the model within r = 8 RE.

Figure 3.

Plots of the H+ and He+ densities as a function of L-shell in the magnetic equatorial plane for noon, dusk, dawn, and midnight at times t = 51.5 h (black) and t = 96.7 h (dashed). The dotted in line in the noon plot shows the initial H+ density.

Figure 4.

Plots of the electron density as a function of L-shell in the magnetic equatorial plane for noon, dusk, dawn, and midnight at time t = 51.5 h (black). The dashed curve is the empirical relation from Berube et al. [2005] for quiet time conditions.

[14] In Figure 4, we plot the electron density as a function of L-shell in the magnetic equatorial plane for noon, dusk, dawn, and midnight at time t = 51.5 h (black). The different magnetic local times are not differentiated on the figure because of their overlap. The point is that they are very similar for 1.5 < L < 4 consistent with Figures 1a and 2a. The dashed curve is the empirical relation from Berube et al. [2005] for quiet time conditions (−9 < Dst < −3 nT) within 20° of the magnetic equator

display math(2)

We find the agreement between the quiet time empirical model and simulation results to be very good. The L-shell dependence is basically the same in the data and model results. The most significant difference is that the electron density in the simulation is a factor of 2–4 less than the empirical model for L > 2. However, our results are well within the observational data presented in Berube et al. [2005].

[15] Finally, in Figure 5, we plot the electron density as a function of magnetic latitude along field lines at L = 2.22 and 3.26 at t = 51.5 h and 0900 magnetic local time (MLT). The symbols X and O indicate observational values reported by Huang et al. [2004]. The functional agreement between the model results and data is good. But similar to Figure 4, the model results are less than the data by roughly a factor of 2. Again, we attribute this to the lower value of F10.7 used in the simulation study.

Figure 5.

Plots of the electron density as a function of magnetic latitude along field lines at L = 2.22 and 3.26 at t = 51.5 h and 0900 MLT. The symbols X and O indicate observational values reported by Huang et al. [2004].

4 Summary

[16] We have presented the first 3D simulation of the plasmasphere based on the first-principles physics model SAMI3. We have included the corotation potential, the neutral wind dynamo potential, and a time-dependent Volland-Stern-Maynard-Chen potential to model the response of the convection potential to an idealized magnetic storm. We find that prior to the storm the plasmasphere is largely toroidal and symmetric in magnetic local time with the helium to hydrogen ratio He+/H+ ~ 5–10%. After the storm, the plasmasphere substantially contracts because plasma is convected away from the outer plasmasphere by the enhanced convection potential. Moreover, a plume-like structure forms in the mid-afternoon sector because of the modified convection pattern associated with the storm [Grebowsky, 1970].

[17] Additionally we have compared the simulation results to quiet time data from the Radio Plasma Imager instrument on the IMAGE satellite. We find good agreement between the simulation results and data for the L-shell dependence of the equatorial electron density as well as the electron density along the field line at a given L-shell. However, the simulation results have a lower electron density by a factor of 2–4. The simulation results are still in the range of observed electron densities; however, possible reasons for the discrepancy are lack of a dipole tilt and an insufficient amount of time for refilling.

[18] Future studies using SAMI3 to study plasmaspheric dynamics will focus on incorporating more realistic conditions. For example, we will use high-latitude convection potentials from Lyon-Fedder-Mobarry model, Rice convection model, and/or the Weimer model, use a tilted dipole, and include a better model for the location of the “open/closed” field line boundary.

Acknowledgments

[19] We thank J. Fedder for a critical reading of the manuscript and the referees for constructive comments. This research has been supported by an LWS NASA grant and NRL Base Funds.