Plasma kinetic simulation in Eulerian approach fully respecting f≥0 requirement and total particle number conservation

Abstract

Abstract 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 8 members: 5 partial differential equations (PDEs), a phase space boundary condition and an initial condition of the distribution function (PDF) f, and a mandatory non-negativity requirement on f. Because Vlasov equation (VE) is a PDE with variable coefficients and the non-negativity requirement is mandatory, 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 these techniques do not yield efficient and reliable schemes of the PKSiEA. In a universal scheme of the PKSiEA presented here, because the phase space boundary condition f∣ r=∞,∣υ∣=c = 0 causes the VE to yield a conservation of total particle number ∫fd 3 rd 3 υ, we propose an efficient and strict expression of the f-profile in terms of two classes of functions of phase space coordinates r , υ , and the VE displays a universal relation between two classes. By this new expression, we 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-negativity requirement on f.