Test-kinetic simulation of ion energy-dispersed structures and of
non-gyrotropic distribution functions formed at the traversal of a 
plasma interface: two-dimensional solutions
 
Gabriel Voitcu(1), Marius Echim(1,2)
(1)Institute for Space Sciences, Magurele, Romania
(2)Belgian Institute for Space Aeronomy, Brussels, Belgium
 
In this paper we discuss the formation of ring-shaped and non-gyrotropic velocity distribution 
functions (VDFs) as well as of energy-dispersed structures at the edges of a proton cloud 
injected into a non-uniform two-dimensional distribution of the electromagnetic field. The 
test-kinetic approach is used to compute the velocity distribution function in various regions 
of a particle cloud moving in the vicinity of a plasma interface with a sharp transition of the 
magnetic field. The electric and magnetic fields are prescribed and steady-state. Their spatial 
variation is confined to a transition region whose scale length is an input parameter of the 
simulation. A sheared distribution of the magnetic field is derived from a one-dimensional 
model of tangential discontinuities (TD). The two-dimensional electric field is everywhere 
normal to the magnetic field and is obtained by solving the Laplace equation on a two dimensional 
rectangular grid, with Neumann boundary conditions compatible with the self-consistent TD solution. 
We integrate numerically the trajectories of test-protons having the initial velocities distributed 
according to a displaced Maxwellian. The initial VDF is Liouville mapped along the integrated 
trajectories and is reconstructed in various spatial regions of the simulation domain, inside 
and outside the plasma interface. We also illustrate the evolution of the cloud's morphology 
while traversing the interface. The numerical results show the formation of an energy-dispersed 
structure at the edges of the cloud, with the energy increasing towards the fringes. Ring-shaped 
VDFs form inside the velocity-dispersed structure. Gyro-phase restricted velocity distribution 
functions are obtained in the front-side and trailing edge of the cloud and are likely due to 
the remote sensing of large Larmor radius particles whose guiding centers rest in the core of the 
cloud. The test-kinetic solutions show properties similar to the in-situ velocity distribution 
functions observed by CLUSTER satellites in the magnetotail, close to the neutral sheet, as 
reported by, e.g., Meziane et al. (2003) and Wilber et al. (2004).