ULF OSCILLATIONS Simulation of Radiation Belt INTRODUCTION

Simulation

The January 1997 magnetic cloud event has provided an opportunity to combine a very complete satellite and groundbased data set with modelling tools developed in support of the ISTP program. The model described here employs field output from a global MHD simulation code as input to a guiding center test particle code used to advance radiation belt particle trajectories [Hudson et al., 1996; 1997]. These results in turn were an outgrowth of a simpler analytic model for the effect of a CME-produced storm sudden commencement (SSC) which generates a magnetosonic wave compression of the dayside magnetosphere. This model, applied to the March 24, 1991 great storm (Dst = -300), was very effective at reproducing the observed transport and acceleration of outer zone electrons into L=2.5 on the time scale of the electron drift period [Li et al., 1993]. The rise in relativistic electron flux occurred several hours after the SSC in January 1997, and was precipitated by a much slower interplanetary shock moving at a nominal solar wind speed of 400 km/s [Burlaga et al., 1998], vs. the 1000-1400 km/s estimates for the March 1991 event. Another significant difference from the diagnostic point of view was the absence of an upstream solar wind monitor for the March 1991 event, in contrast to the current era of WIND and other L1 spacecraft measurements.

A magnetic and electric field time series has been obtained from a 3D global MHD simulation of the January 1997 magnetic cloud event. The evolving solar wind parameters measured by WIND are used as input to the Lyon-Fedder-Mobarry code [Fedder and Lyon, 1987]. The solar wind conditions were taken from WIND key parameter data interpolated to a constant one minute time resolution. Only the transverse components - B_x and B_y - of the IMF were used. The data were input in GSM coordinates with the Earth's dipole at a fixed tilt of 23 degrees away from the sun in the Northern hemisphere (corresponding roughly to 0 UT). The inner boundary of the simulation was at 2 R_E to allow for low-latitude convection during the magnetic cloud passage and to allow for the extreme compression inside geosynchronous orbit observed later in the event. The simulation covered the entire time period from 0 UT on January 10 to 13:00 UT on January 11, with field results recorded approximately every 75 seconds. Other details of the MHD simulation are described elsewhere [Goodrich et al., 1998].

A guiding center test particle code was implemented to follow electron trajectories in the equatorial plane with interpolation of output from the MHD field time series [Hudson et al., 1996; 1997]. A first adiabatic invariant conservation criterion is well satisfied for > 99.9$\%$ of simulation electrons [Hudson et al., 1997]. The specific criterion imposed here is to remove from the simulation domain electrons whose gyroradius equals the magnetic gradient scale length (field variation on the gyrofrequency time scale is not an issue in these MHD-driven simulations). An initial AE8MIN energy - flux profile is used as input [Vette, 1991], and relative flux in selected energy ranges at fixed L and varying longitude $\phi$ can be plotted, with $\phi$ variation corresponding to an equatorial satellite period at the specified L value. The entire (L - $\phi$) flux time series is available, and can be extrapolated to other latitudes assuming that flux dynamics is dominated by behavior in the equatorial plane.
  

PLate 1 : (a)Total $\bf B$ (nT) and two components of $\bf E$ (mV/m), azimuthal $E_{\phi }$ and radial E_r, at L=4.2 in the equatorial plane at LT of GPS satellite NS39, from 03:00 UT Jan 10 to 09:00 UT Jan 11. Initial GPS NS39 local time was LT₀=12.79, moving roughly two hours eastward in LT for each hour UT. (b)-(e)Relative flux in four energy channels measured by GPS, 0.2 - 0.4, 0.4 - 0.8, 0.8 - 1.6 and 1.6 - 3.2 MeV, with same trajectory format as (a).

Plate 1a shows two components of the electric field time series, azimuthal $E_{\phi }$ and radial E_r, along with total magnetic field strength B for a virtual satellite flown through the MHD simulation data in an equatorial orbit at L = 4.2. The particle simulations are begun at 02:02 UT on January 10 when GPS satellite NS39 was at 12.8 hours LT, with little change occurring during the first hour (not shown). Since GPS data has been used to infer time evolution of equatorial plane fluxes [Li et al., 1998; Reeves et al., 1998a], and since the present particle simulation is restricted to the equatorial plane, we do not attempt here to reconstruct fluxes at the GPS orbit inclination. Relative electron flux in four energy channels measured by GPS NS39 is shown in Plates 1b -1e for the same trajectory and time period, encompassing a rapid rise in flux around 09:00 UT by half an order of magnitude in the simulation output from a value initially depressed by buildup of the ring current (Dst effect discussed below). Field signatures characteristic of substorm dipolarization (compression in B and large negative, westward E_phi) are seen before and after this flux increase, while it continues to rise gradually and flatten out by the time the IMF turns northward $\sim$ 17:30 UT.
  

PLate 2 : (a)Flux vs. energy and L for the initial, AE8MIN model electron population, whose drift trajectories are then advanced in time with MHD code field output. (b)Same as (a) after advancing electron trajectories to 09:46 UT on 10 Jan 98. (c)Same at 12:40 UT. (d) Same at 17:27 UT. (e)Same at 12:02 UT on 11 Jan 98.

Plates 2a - e, in the same format, show simulation data at the location of geosynchronous satellite 1994-084. Here, ULF oscillations are evident in the field data, beginning at the time of substorm field signatures in Plate 1a, $\sim$ 007:00 UT. The dropout in flux associated with the passage of the satellite into the magnetosheath during the period following a high density solar wind pressure pulse [Burlaga et al., 1998] is in good agreement with the geosynchronous measurements [Reeves et al., 1998b].
  

PLate 3 : Same as Plate 1 at location of geosynchronous satellite 1994-084.

Plate 3a shows a plot of flux vs. energy and L for the initial AE8MIN model, peaked between L = 5 - 6 at low energies. By 09:46 UT, Plate 3b shows that enhanced convection during several hours of southward IMF B_z has transported the outer boundary of the AE8MIN profile radially inward in the simulations, along with the flux peak at low energies, which by this time lies between L = 4 - 5. The flux stays peaked around L = 4, as the outer boundary expands outward during the ensuing period of northward IMF, with the end simulation result shown in Plate 3e at 12:02 UT on January 11, eleven hours after arrival of the high density solar wind impulse which caused the magnetopause to move inside geosynchronous orbit.