Gyrokinetic Vlasov-Poisson model for low-frequency electrostatic perturbation derived by pullback transform

抄録

This paper presents a new gyrokinetic Vlasov-Poisson model for low-frequency electrostatic turbulence derived by a rigorously and concisely mathematical method with gyroangle decoupled from this model. TheLagrangian, Vlasov and Poisson equations are firstly transformed to be differential forms defined on real-orbit frame and time. Then, pullback transform is adopted to pulling these differential forms back to versions defined on gyrocenter frame and time. Based on conservation property of phase space density without collision, the time integral of new version of Vlasov differential 1-form along any orbit curve in phase space equalszero. This integral can be approximated by Riemann sum with time slice equaling gyroperiod at local position. Within each time slice, gyroangle can be integrated out with (X, μ,U, t) kept constant due to gyroangle decoupled from them. At last, the new Vlasov equation as a time average over gyroperiod is derived with gyroangle decoupled. The idea of average over gyroperiod is also applied to Poisson equation. With our newmethod, the polarization density of electrons as a new term in the new coordinate frame is introduced to the new model as the result of coordinate transform between real-orbit and gyrocenter frame of ions.