We study the Hall effect in diluted plasmas within the two-fluids theory. Composed by two distinct species with opposite charge, such as electrons and ions in fully ionised hydrogen, the plasma is driven by an electric field through a channel in the presence of a transversal magnetic field. As a consequence, a separation of charge is induced producing an electric potential difference. We have found a general relation for the Hall voltage as function of the mass and viscosity ratios, which converges to the usual expression in the limit of solid matter, i.e. when ions are much more massive than electrons. All the simulations have been performed using a three-dimensional Lattice-Boltzmann model, which has been also validated for some relevant applications. Finally, we discuss the importance of our findings in the light of recent developments in plasma physics, in particular in magnetic reconnection.
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