Dispersive MHD turbulence in one dimension

Numerical simulations of dispersive turbulence in magnetized plasmas based on the Hall-MHD description are presented, assuming spatial variations along a unique direction making a prescribed angle with the ambient magnetic field. Main observations concern the energy transfers among the different scales and the various types of MHD waves, together with the conditions for the establishment of pressure-balanced structures. For parallel propagation, Alfv\'en-wave transfer to small scales is strongly inhibited and rather feeds magnetosonic modes, unless the effect of dispersion is strong enough at the energy injection scale. In oblique directions, the dominantly compressible character of the turbulence is pointed out with, for quasi-transverse propagation, the presence of conspicuous kinetic Alfv\'en waves. Preliminary simulations of a Landau fluid model incorporating relevant linear kinetic effects reveal the development of a significant plasma temperature anisotropy leading to recurrent instabilities.