The coordinate metric elements g ij = ∇ x i · ∇ x j are found in the { V, θ, ζ } representation. Then the grid locations s = s$_{k}$ are all given their own members of the family of these field aligned coordinates via Then we have at s = s$_{k}$ . The drift tensor elements are given by that is, F$_{xy}$ is the only independent, nonvanishing component. We have which defines the bracket [ φ, f ] for any scalar field quantities φ and f . With φ the electro- static potential this gives the ExB advection term, for electrons for which FLR corrections are neglected by taking ρ$_{e}$ → 0. For ions this is generalised by the FLR corrections as given above. For local equations as those used here (nonlinearities kept only in advection and magnetic flutter) the geometry model must be modified to retain free energy conservation by the equations. In particular, any function of x such as a radially varying normalised parameter (such as the temperature/charge ration τ$_{z}$ ) multiplying any of the curvature terms will cause them to fail to conserve free energy. The compressibility is already split away from advection and placed into the curvature terms, so the brackets must retain the properties of incompressible advection. This means that the model for F which is used must satisfy α$_{k}$ ( V ) = q s$_{k}$ + ∫ V 0 dV ′ q g V θ − g V ζ g V V ∣ θ $^{=}$s k (35) g xx = a − $^{6}$g V V (36) g xy k = 0 (37) g yy k = q $^{2}$g θθ − 2 q g θζ + g ζζ (38) g xs = a − $^{3}$g V θ (39) g ys k = q g θθ − g θζ (40) g ss = g θθ (41) F = ϵ · B with F$_{xy}$ = χ$_{,V}$ (42) ∇ f · c B $_{2}$B ×∇ φ ≡ ∇ φ · c F B 2 · ∇ f (43) F → F 0 with ∇ · c F 0 B 2 = 0 (44) 11