Benchmarking Particle-in-Cell drift wave simulations with Eulerian simulations in a flux-tube

We present the implementation of a flux-tube option in the global turbulence code GEM.\footnote{Y.~Chen and S.~E.~Parker, J. Comp. Phys. 220, 839 (2007)} This is necessary for benchmarking purposes because of the immense complexity involved in comparing global simulations. The global GEM assumes the magnetic equilibrium to be completely given. Our initial flux-tube implementation simply selects a radial location as the center of the flux-tube and a radial size of the flux-tube, sets all equilibrium quantities ($B$, $\nabla B$, $T$, $\nabla T$, the Jacobian etc.) to be equal to their values at the center of the flux-tube, and retains only a linear radial profile of the safety factor needed for boundary conditions. We found good agreement between GEM and GYRO/GS2 for the mode frequency/growth rate in the case of adiabatic electrons, but a difference of $\sim 15\%$ in the growth rates when kinetic electrons are included. Our goal is to understand the origin of this moderate disagreement. An alternative local geometry model based on a local solution of the Grad-Shafranov equation\footnote{J.~Candy, Plasma Phys. Control. Fusion 51, 105009 (2009)} has been implemented and new benchmarking results from this model will be presented.