Kinetic electron closures for electromagnetic simulation of drift and shear-Alfvén waves. I.

<jats:p>The electromagnetic hybrid scheme of Chen and Parker (fluid electrons and gyrokinetic ions) [Phys. Plasmas 8, 441 (2001)] is extended to include a kinetic electron closure valid for βe&gt;me/mi (βe is the ratio of the plasma electron pressure to the magnetic field energy density). The new schemes incorporate partially linearized (δf ) drift-kinetic electrons whose pressure and number density moments are used to close the fluid momentum equation for the electron fluid (Ohm’s law) using the departure of the perturbed δf kinetic pressure from the isothermal perturbed pressure response. Comparisons are made between the results of the hybrid schemes with kinetic electron closure and a conventional δf algorithm for drift-kinetic electrons and gyrokinetic ions in a two-dimensional slab model. The test cases used are small-amplitude kinetic shear-Alfvén waves with electron Landau damping, the ion-temperature-gradient instability, and the collisionless drift instability (universal mode) in an unsheared slab as a function of the plasma βe. The hybrid schemes have the desirable properties that they do not require that the mesh size perpendicular to the applied magnetic field be smaller than the collisionless skin depth c/ωpe and naturally accommodate zonal flow physics (radial modes) with nonadiabatic electron effects. The most successful of the new algorithms introduced gives very good results for βe&gt;me/mi.</jats:p>