Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  present a new numerical method to solve the Vlasov-Darwin and Vlasov-Poissll systems which are approximations of the Vlasov-Maxll equation in the asymptotic limit of the infinite speed of light. These systems model low-frequency electromagnetic phenomena in plasmas, and thus "light waves" are somewhat supressed, which in turn allows the numerical discretization to dispense with the Courant-Friedrichs-Lewy condition on the time step.  construct a numerical scheme based on semi-Lagrangian methods and time splitting techniques.  develop a four-dimensional phase space algorithm for the distribution function while the electromagnetic field is solved on a two-dimensional Cartesian grid. Finally,  present two nontrivial test cases: (a) the wave Landau damping and (b) the electromagnetic beam-plasma instability. For these cases our numerical scheme works very ll and is in agreement with analytic kinetic theory.
['Nicolas Besse', 'Norbert J. Mauser', 'Eric Sonnendrücker']
I am writing a research paper on a idea Numerical Approximation of Self-Consistent Vlasov Models for Low-Frequency Electromagnetic Phenomena
[{"from": "human", "value": "I am writing a research paper on a idea Numerical Approximation of Self-Consistent Vlasov Models for Low-Frequency Electromagnetic Phenomena"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  present a new numerical method to solve the Vlasov-Darwin and Vlasov-Poissll systems which are approximations of the Vlasov-Maxll equation in the asymptotic limit of the infinite speed of light. These systems model low-frequency electromagnetic phenomena in plasmas, and thus \"light waves\" are somewhat supressed, which in turn allows the numerical discretization to dispense with the Courant-Friedrichs-Lewy condition on the time step.  construct a numerical scheme based on semi-Lagrangian methods and time splitting techniques.  develop a four-dimensional phase space algorithm for the distribution function while the electromagnetic field is solved on a two-dimensional Cartesian grid. Finally,  present two nontrivial test cases: (a) the wave Landau damping and (b) the electromagnetic beam-plasma instability. For these cases our numerical scheme works very ll and is in agreement with analytic kinetic theory."}]