A closed high-frequency Vlasov–Maxwell simulation model in toroidal geometry

A fully-kinetic ion and gyrokinetic electron Vlasov–Maxwell particle simulation model is derived through Lie transform perturbation theory for Hamiltonian systems in terms of four ordering parameters , , and . This model is closed by the field equations of Poisson's equation and Ampere' law. This scheme preserves the phase-space volume, and retains the ion cyclotron motion, while fine scale electron motion is ignored, so that the frequency falls in the range . Using a perturbative method (), and ignoring the high order terms, this model is then formulated in a magnetic flux coordinate system with equilibrium Maxwellian distribution of particles. Thus, this model is especially suitable for the global particle simulation of high-frequency physical processes such as lower hybrid waves and waves in the ion cyclotron range of frequencies.