Phase Space Zonal Structures (PSZSs), obtained by averaging out dependencies on angle-like variables in the energetic particle (EP) distribution function, play a fundamental role in regulating EP transport induced by Alfvén instabilities in burning plasmas, acting as a slowly varying nonlinear equilibrium state. Therefore, they are of great interest for the development of reduced models for the description of EP heat and particle transport on long time scales, comparable with the energy confinement time, for future burning plasma experiments. In this work, we propose an efficient finite element based projection of the time evolution of the PSZS, suited for global particle-in-cell (PIC) gyrokinetic (GK) codes. The resulting algorithm has been implemented in the global GK PIC code ORB5. PSZSs can not only be used for validating reduced models, but also as a diagnostic tool for characterizing the nonlinear interaction in phase space between Alfvén instabilities and EPs in global GK simulations.
