  The structure of a discharge across a magnetic field in a dusty plasma is
analysed. The dust macroparticles are negatively charged, but are unmagnetized
because of their high mass. The electrons are highly magnetized, and the ions
have intermediate magnetization. This results in different transport rates of
the different species across the magnetic field. Depending on the size of the
magnetic field, and the relative charge on the different species, the dust
grains can be the dominant current carrier. The space charge clouds near the
electrodes will then be determined by the relative mobility of the different
species. The discharge can operate in one of two modes, a positive space charge
(PSC) mode, characterized by a strong cathode fall, and a negative space charge
(NSC) mode, characterized by a broad anode fall. Features unique to the dust
particles can also play a role in the structure of the discharge, such as the
variable equilibrium charge on the grains, dependent on the local potential and
species temperatures, the effect of gravity on the grain dynamics, and the rate
of charging of the grains. The dust grains can also form an ordered structure,
the dust-plasma crystal. A fluid model of the different species is used to
calculate the structure of the resulting discharge, incorporating the above
effects. The transition from the PSC mode to the NSC mode as the magnetic
field, pressure and dust properties are varied is demonstrated.
