Two electrostatic gyrokinetic models derived by two different perturbative methods

This paper presents two different electrostatic gyrokinetic models derived through two different perturbative methods. One of the two models is just the conventional electrostatic gyrokinetic model, the derivation of which is repeated using the Lie transform perturbative method. One term is rectified in the derivation of the conventional model. To derive the other model, we use a new method, which is based on the covariant transform formula of the differential 1-form. The new method doesn't split the coordinate transform into the guiding-center transform and the gyrocenter transform. It carries out the coordinate transform up to the order equaling that of the amplitude of the perturbative wave. Compared with the conventional model, the finite Larmor radius terms are completely removed from the orbit equations of the new one, making it simpler for the numerical application.