  The three-dimensional inviscid Hasegawa-Mima model is one of the fundamental
models that describe plasma turbulence. The model also appears as a simplified
reduced Rayleigh-B\'enard convection model. The mathematical analysis the
Hasegawa-Mima equation is challenging due to the absence of any smoothing
viscous terms, as well as to the presence of an analogue of the vortex
stretching terms. In this paper, we introduce and study a model which is
inspired by the inviscid Hasegawa-Mima model, which we call a
pseudo-Hasegawa-Mima model. The introduced model is easier to investigate
analytically than the original inviscid Hasegawa-Mima model, as it has a nicer
mathematical structure. The resemblance between this model and the Euler
equations of inviscid incompressible fluids inspired us to adapt the techniques
and ideas introduced for the two-dimensional and the three-dimensional Euler
equations to prove the global existence and uniqueness of solutions for our
model. Moreover, we prove the continuous dependence on initial data of
solutions for the pseudo-Hasegawa-Mima model. These are the first results on
existence and uniqueness of solutions for a model that is related to the
three-dimensional inviscid Hasegawa-Mima equations.
