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A Hamiltonian two-field gyrofluid model is used to investigate the dynamicsof an electron-ion collisionless plasma subject to a strong ambient magneticfield, within a spectral range extending from the magnetohydrodynamic (MHD)scales to the electron skin depth. This model isolates Alfv\'en, KineticAlfv\'en and Inertial Kinetic Alfv\'en waves that play a central role in spaceplasmas, and extends standard reduced fluid models to broader ranges of theplasma parameters. Recent numerical results are reviewed, including (i) thereconnection-mediated MHD turbulence developing from the collision ofcounter-propagating Alfv\'en wave packets, (ii) the specific features of thecascade dynamics in strongly imbalanced turbulence, including a possible linkbetween the existence of a spectral transition range and the presence ofco-propagating wave interactions at sub-ion scales, for which new simulationsare reported, (iii) the influence of the ion-to-electron temperature ratio intwo-dimensional collisionless magnetic reconnection. The role of electronfinite Larmor radius corrections is pointed out and the extension of thepresent model to a four-field gyrofluid model is discussed. Such an extendedmodel accurately describes electron finite Larmor radius effects at small ormoderate values of the electron beta parameter, and also retains the couplingto slow magnetosonic waves.

Gyrofluid simulations of turbulence and reconnection in space plasmas