The velocities of the protons and electrons are initialized with values consistent with a velocity distribution function described by a displaced Maxwellian. The electric field is initialized with E1=B1 x V0, where V0 is the initial bulk velocity of the two populations. The electromagnetic field depends on only one spatial coordinate, x, normal to the discontinuity. The particles are injected from sources distributed along the x-axis. Their orbits are integrated numerically. In a steady state situation the orbits in the physical space correspond to the characteristics of the Vlasov equation (Delcroix and Bers, 1994). The velocity distribution function is reconstructed using the Liouville theorem. It is assumed that each particle 'carries' a 'part' of the VDF that corresponds to its initial position in the velocity space and do not change along the orbit. That 'part' of the VDF is assigned to the (varying) velocity components of the particle all along its orbit (Curran and Goertz, 1989). Thus it is then possible to compute the VDF of both species inside and outside the discontinuity. With a reasonable number of particles the phase space can be quite well populated such that the spatial resolution of the reconstructed VDF can be increased. We illustrate the results obtained by a study of the variations introduced by the non-uniformities of the electromagnetic field. We were particularly interested to simulate non-gyrotropic VDFs as those observed in the plasmasheet by Wilber et al. (2004) and to understand the mechanism of remote sensing of thin current sheets (Lee et al., 2004) as the TD distribution considered in our simulations. This project is on development and is carried on in collaboration with the Faculty of Physics of the University of Bucharest.
Echim, M., Test-particle trajectories in ''sheared'' stationary field: Newton-Lorenz and first order drift numerical simulations, Cosmic Research, 40, 534-547, 2002
Curran, D.B. and Goertz, C.K., Particle distributions in a two-dimensional reconnection field geometry, J. Geophys. Res., 94, 272-286, 1989
Delcroix, J.L. and Bers, A., Physique des plasmas, Savoirs Actuels - Inter Editions/CNRS, 1994
Lee, E., M. Wilber, Parks, G.K., et al., Modeling of remote sensing of thin current sheet, Geophysical Research Letters, 31, L21806, 2004
Wilber, M., Lee, E., Parks, G., et al., Cluster observationjs of velocity space-restricted ion distributions near the plasma sheet, Geophysical Research Letters, 31, L24802, 2004