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

Abstract

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 B , ω , and δ. 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 Ω i ω < Ω e. Using a perturbative method (δf), 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.

Particle simulation of radio frequency waves with fully-kinetic ions and gyrokinetic electrons

“…This section briefly presents a closed Vlasov-Maxwell simulation model using fully-kinetic ions and gyrokinetic electrons. This physical model [22] is derived using the modern Lie perturbative Hamiltonian approach. The electromagnetic fields are purely described with scalar potential δφ and vector potentials δA without introducing the intermediate magnetic perturbation δB in the parallel direction.…”

“…Recently, based on Lie-transform gyrokinetic theory, a gyrokinetic electron and fully-kinetic ion simulation model, which is directly closed by using Poisson's equation and Ampere's law, is developed in toroidal geometry [22]. This article will report the code development based on this compact toroidal model for investigating nonlinear effects in toroidally-confined fusion plasma devices, such as tokamaks and stellarators.…”

Pushforward transformation of gyrokinetic moments under electromagnetic fluctuations

“…In this procedure, first, gyrocenter Hamilton's equations are derived from the gyrocenter Hamiltonian using the Lie-transform perturbation method, 10,13,28 which decouples complete particle dynamics into the fast gyromotion part and the slow gyrocenter drift motion part. Then, the gyrokinetic Maxwell equations are obtained through the conventional approach, [11][12][13]29 the purely pullback transformation approach, 30 or the purely pushforward transformation approach.. [31][32][33][34] These three approaches are equivalent in principle.…”

“…In the purely pullback approach, the distribution function is transformed from gyrocenter phase space to guidingcenter phase space and then to particle phase space. This approach has been used to construct the high-frequency simulation model 30 for RF waves, where electrons are treated with a gyrokinetic description and ions are treated with a fully kinetic description.…”

Particle Trajectory Integrator in Guiding Center Phase Space

“…[6−8] A newly developed high-frequency simulation model with fully kinetic ion and gyrokinetic electron provides a clear picture of the relationship between the guiding center's polarization/magnetization and macroscopic flows. [9,10] The concomitant simulation thoroughly discussed the relationship of magnetic moment in configuration space, guiding center space and gyrocenter space. [11,12] Because of the complex toroidal magnetic field structure, it will be convenient to use magnetic coordinates to describe the motion of particles.…”