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We consider a plasma described by means of a two-dimensional fluid modelacross a constant but non-uniform magnetic field $\mathbf{B} = B(x,y)\mathbf{\hat{z}}$. The dynamical evolution of the density and the vorticitytakes into account the interchange instability and magnetic fieldinhomogeneities. First, in order to described the Finite Larmor Radius effectswe apply the gyromap to build a Hamiltonian model with ion temperature from acold-ion model. Second, we show that the gyromap is justified usingBraginskii's closure for the stress tensor as well as an apt ordering on thefluctuating quantities.

Gyromap for a two-dimensional Hamiltonian fluid model derived from Braginskii's closure for magnetized plasmas