Plasma kinetic simulation in Eulerian approach (PKSiEA) can yield a dynamic description on plasmas and hence is a popular method in theoretical plasmas physics. Its mathematical model consists of 7 members: 5 partial differential equations (PDEs), a phase space boundary condition of the distribution function (PDF) f, and a mandatory non-negative requirement on f. Because Vlasov equation (VE) is a PDE with variable coefficients and f is mandatory to satisfy the non-negative requirement, when 5 PDEs (4 Maxwell equations and the VE) are treated as an initial-value problem, the temporal evolution of f is difficult to be attacked by existing popular computational mathematics techniques, such as Fourier analysis technique and finite-difference technique, and hence currently these classic methods on PDEs do not yield efficient and reliable schemes of the PKSiEA. In a universal scheme of the PKSiEA presented here, because of the fact that the phase space boundary condition f|r=∞,|υ|=c = 0 causes the VE to yield a conservation of total particle number ∫fd3rd3 , we propose an efficient and strict expression of the f-profile through two classes of functions of phase space coordinates (r; ), and the VE displays a universal relation between two classes. By this new expression, we can express the initial-value problem of 5 PDEs in terms of allowed deformation modes from an initial f-profile, and ensure the PKSiEA fully respecting the non-negative requirement on f.
PACS: 52.65.-y.