Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  deals with the numerical resolution of the Vlasov--Poisson system with a strong external magnetic field by particle-in-cell (PIC) methods. In this regime, classical PIC methods are subject to stability constraints on the time and space steps related to the small Larmor radius and plasma frequency. Here  propose an asymptotic-preserving PIC scheme which is not subjected to these limitations. Our approach is based on first- and higher-order semi-implicit numerical schemes already validated on dissipative systems [S. Boscarino, F. Filbet, and G. Russo, J. Sci. Comput., 2016, doi:10.1007/s10915-016-0168-y]. Additionally, when the magnitude of the external magnetic field becomes large, this method provides a consistent PIC discretization of the guiding-center equation, that is, an incompressible Euler equation in vorticity form.  propose several numerical experiments which provide a solid validation of the method and its underlying concepts.
['Francis Filbet', 'Luis Miguel Rodrigues']
I am writing a research paper on a idea Asymptotically Stable Particle-In-Cell Methods for the Vlasov--Poisson System with a Strong External Magnetic Field
[{"from": "human", "value": "I am writing a research paper on a idea Asymptotically Stable Particle-In-Cell Methods for the Vlasov--Poisson System with a Strong External Magnetic Field"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  deals with the numerical resolution of the Vlasov--Poisson system with a strong external magnetic field by particle-in-cell (PIC) methods. In this regime, classical PIC methods are subject to stability constraints on the time and space steps related to the small Larmor radius and plasma frequency. Here  propose an asymptotic-preserving PIC scheme which is not subjected to these limitations. Our approach is based on first- and higher-order semi-implicit numerical schemes already validated on dissipative systems [S. Boscarino, F. Filbet, and G. Russo, J. Sci. Comput., 2016, doi:10.1007/s10915-016-0168-y]. Additionally, when the magnitude of the external magnetic field becomes large, this method provides a consistent PIC discretization of the guiding-center equation, that is, an incompressible Euler equation in vorticity form.  propose several numerical experiments which provide a solid validation of the method and its underlying concepts."}]