ABSTRACT
Two essential approximations were made to derive that equation: the assumption of quasi-neutrality (the “plasma approximation”) and omission of polarization drifts. This chapter elaborates in more detail the consequences of relaxing the latter of the two approximations including the nonlinear corrections. The relaxation of the quasi-neutrality condition implies some formal modifications of the basic equations, which, however, are unlikely to be of physical importance in comparison to the ion polarization drift, which is expected to be more important for most physically realistic conditions. The consequences of including ion polarization drifts are more important, but the quasi-neutral approximation is retained. The Hasegawa-Mima equation describes weakly nonlinear electrostatic fluctuations, in particular also wave interactions. A byproduct of the inverse cascade turns out to be disturbing in numerical simulations. In actual simulations it is difficult to avoid introducing an error at small scales, where the spatial resolution of the numerical code is limited.
