“Echography” of Vlasov codes

Collisionless simulation of nonlinear plasma dynamics is one of the outstanding problems of plasma physics as well as a strong challenge in computational physics. Here, a crucial test for the theoretical study of collisionless plasmas based on large scale numerical simulations is proposed. Plasma echoes are shown to provide a highly selective benchmark for the algorithms adopted in order to follow the collisionless, Hamiltonian dynamics of high temperature, rarefied plasmas described by the Vlasov–Poisson system of equations. The proposed test is more discriminating than those based on the conservation of (a finite set of) Casimir invariants and gives a deeper insight on the numerical dissipative processes at play.