We present a Vlasov-DArwin numerical code (ViDA) specifically designed to address plasma physics problems, where small-scale high accuracy is requested even during the non linear regime to guarantee a clean description of the plasma dynamics at fine
spatial scales. The algorithm provides a low-noise description of proton and electron kinetic dynamics, by splitting in time the multi-advection Vlasov equation in phase space. Maxwell equations for the electric and magnetic fields are reorganized according to Darwin approximation to remove light waves. Several numerical tests show that ViDA successfully reproduces the propagation of linear and nonlinear waves and captures the physics of magnetic reconnection. We also discuss preliminary tests of the parallelization algorithm efficiency, performed at CINECA on the Marconi-KNL cluster. ViDA will allow to run Eulerian simulations of a non-relativistic fully-kinetic collisionless plasma and it is expected to provide relevant insights on important problems of plasma astrophysics such as, for instance, the development of the turbulent cascade at electron scales and the structure and dynamics of electron-scale magnetic reconnection, such as the electron diffusion region.
Turbulence at kinetic scales is an unresolved and ubiquitous phenomenon that characterizes both space and laboratory plasmas. Recently, new theories, {it in-situ} spacecraft observations and numerical simulations suggest a novel scenario for turbulen
ce, characterized by a so-called phase space cascade -- the formation of fine structures, both in physical and velocity space. This new concept is here extended by directly taking into account the role of inter-particle collisions, modeled through the nonlinear Landau operator or the simplified Dougherty operator. The characteristic times, associated with inter-particle correlations, are derived in the above cases. The implications of introducing collisions on the phase space cascade are finally discussed.
