  The magnetic field in Hall plasmas is frozen in the electron component and is
advected not only with the plasma motion but also with the electrical current
flow. Its coupling with the plasma may be not as strong as characteristic of
the MHD approximation. The rotation and slipping of the magnetic field result
in a very different and less efficient magnetic field generation by dynamo -
rotating plasma disk in magnetic field. We found a some exact analytical
solutions of nonlinear equations describing the dynamo. In particular, the
dynamo may not dissipate the energy in the steady state limit. The 3-component
magnetic field and magnetic energy are generated and accumulated during the
transition time only. An electrical jet is the other unusual phenomenon for
MHD. It was investigated theoretically and experimentally for laboratory
plasmas during the last 15 years and now is used for fast current switching. We
found periodical or shock-like nonlinear wave traveling along a Hall plasma
column and not associated with plasma motion. A nonlinear equation describing a
possible steady state magnetic field distribution and current flow in Hall
plasma conductor is derived that differs from the Grad-Shafranov equation for
the low pressure MHD plasma. In conclusion we discuss application of our
results to astrophysical plasmas. This physics could be important for
understanding the evolution of dusty plasma disks and jets around new stars.
