Use of the shell model for plasma physics simulation

In problems of interest for plasma physics with a high degree of symmetry (spherical, cylindrical or planar), a particle-based computational technique can be adopted in which the electric field is calculated without using a spatial grid. As an example, referring to the spherical geometry, the electric field can be calculated assuming that each particle behaves like a ``shell'' and therefore $E(r)$ is proportional to the sum of the charges \textit{qi }of the shells with radii \textit{ri$<$r}. The technique has the double advantage of avoiding the use of a spatial grid and of allowing an infinite radial domain. It has been successfully used to study the expansion of spherical and cylindrical plasmas and to analyze the collision of two slabs of plasma with different densities and temperatures.