2.2 Initial conditions
Figure 2 shows the initial state of the system that is used for the main example presented in Section 3. Panels a and b show the initial field configuration. Panel b is simply a tracing of field lines that cross the equator. The density of field lines should not be taken as the field strength. The field consists of a two-dimensional dipole plus a tail field, based upon a model of Schindler [1972], with a scale thickness of 1RE. The dipole field strength at the Earth’s surface is 500 sec-1. This would be the gyrofrequency of a 5 AMU ion in a 0.25 G field, close to the geometric mean of the H+ and O+ masses. The asymptotic tail field strength is 3 sec-1. The code calculates the By component normal to the plane of the simulation, but this was initially set to zero. Panel c shows contours of the particle density. There are two populations. A cold population has a thermal velocity of 0.15 RE/sec. This fills the lobe regions of the magnetotail and the semicircular region surrounding the Earth at about 6 RE. The density in the lobe is a uniform 300/ RE2. The value of a = 0.02 to give a lobe Alfvén velocity of 1.2 RE/sec. A hot population occupies the plasma sheet with a thermal velocity of 0.45 RE/sec. The density of this population is adjusted to maintain initial stress balance with the tail field in the z-direction. No attempt is made to balance stresses in the x-direction. The simulation begins with about 2.2-million particles and rises to about 2.6-million particles. The region from 6 RE inward is filled with a cold fluid in the MHD approximation. The transition region between the kinetic and fluid populations has a scale thickness of 0.6 RE.
Panel d shows contours of constant flow speed, and panel e shows the flow directions. The plasma flow was initialized to an E´ B drift corresponding to a value of Ey = 0.45. The maximum flow speed indicated on the panels is 0.54 RE/sec. This value is considerably larger than observed flows in the magnetosphere. The reason is that in a two-dimensional simulation, where the dipole field falls off as r-2, rather than r-3, the magnetotail fields will be about a factor of 10 larger than in a full three-dimensional setting.
Finally, panel f shows the initial perpendicular pressure distribution. The initial velocity distribution was assumed to be isotropic, so the parallel pressure plot was almost identical.