Bounce-averaged kinetic equations and neoclassical polarization density

The rigorous formulation of the bounce-averaged equations is presented based upon the Poincaré–Cartan one-form and Lie perturbation methods. The resulting bounce-averaged Vlasov equation is Hamiltonian, and is thus suitable for the self-consistent simulation of low frequency electrostatic turbulence in the trapped ion mode regime. In the bounce-kinetic Poisson equation, the “neoclassical polarization density” arises from the difference between the bounce-averaged banana center and real trapped particle densities across a field line. This representation of the neoclassical polarization drift as a shielding term provides a systematic way to study the long term behavior of the turbulence driven E×B flow.