Charge preserving high order PIC schemes

In this paper we present some new results on our investigation aimed at extending to higher order (HOPIC) the classical PIC framework. After reviewing the basic resolution properties of the Runge–Kutta time integrator, coupled to fourth (sixth) order compact schemes for space derivatives in the Maxwell equations, we focus on the problem of extending charge conservation schemes to a general HOPIC framework. This issue represents the main contribution of the present work. We consider then a few numerical examples of 1D laser-plasma interaction in the under-dense and over-dense regimes relevant for ions acceleration, to test grid convergence and to compare HOPIC results with standard PIC schemes (LOPIC).