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Fourier-Hankel/Bessel space absolute equilibria of 2D gyrokinetics

Two global invariants of two dimensional gyrokinetics are shown to be "rugged" (still conserved by the dynamics) concerning both Fourier and Hankel/Bessel Galerkin truncations. The truncations are made to keep only a finite range of wavenumber $\textbf{k}$ and the Hankel variable $b$ (or $z$ in the Bessel series). The absolute equilibria are used for the discussion of the spectral transfers in the configuration-velocity scale space of kinetic magnetized plasma turbulence. Some interesting aspects of recent numerical results, which were not well understood, are explained with more satisfaction.