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A conservative scheme has been formulated and verified for gyrokineticparticle simulations of electromagnetic waves and instabilities in magnetizedplasmas. An electron continuity equation derived from drift kinetic equation isused to time advance electron density perturbation by using the perturbedmechanical flow calculated from the parallel vector potential, and the parallelvector potential is solved by using the perturbed canonical flow from theperturbed distribution function. In gyrokinetic particle simulations using thisnew scheme, shear Alfv\'en wave dispersion relation in shearless slab andcontinuum damping in sheared cylinder have been recovered. The new schemeovercomes the stringent requirement in conventional perturbative simulationmethod that perpendicular grid size needs to be as small as electroncollisionless skin depth even for the long wavelength Alfv\'en waves. The newscheme also avoids the problem in conventional method that an unphysicallylarge parallel electric field arises due to the inconsistency betweenelectrostatic potential calculated from the perturbed density and vectorpotential calculated from the perturbed canonical flow. Finally, thegyrokinetic particle simulations of the Alfv\'en waves in sheared cylinder havesuperior numerical properties compared with the fluid simulations, which sufferfrom numerical difficulties associated with singular mode structures.

A conservative scheme for electromagnetic simulation of magnetized plasmas with kinetic electrons