  Magnetohydrodynamics (MHD) is a subject concerned with the dynamics of
electrically conducting fluids (plasma) and can be applied in electric power
generation. As a unique technology for producing direct-current electricity
without moving parts, it can be utilized within a high-temperature topping
power cycle to be combined with a traditional bottoming power cycle, forming a
combined-cycle MHD system. This study presents governing equations for the
electric field and current density field within a moving plasma subject to an
applied magnetic field. The modeling equations are described at four descending
levels of complexity. Starting with the first level of modeling, which is the
most general case, where no assumptions are made regarding the electric field,
plasma velocity field, applied magnetic field, or electrode geometry. In the
second level of modeling, the magnetic field is treated as one-dimensional. In
the third level of modeling, a specific Faraday-type magnetohydrodynamics
plasma generator channel is considered, having two continuous electrodes acting
as parallel constant-voltage terminals. In the fourth (and simplest) level of
modeling, an additional approximation is made by setting the Hall parameter to
zero and replacing all vector fields with scalar quantities. For that simplest
model, a representative set of operation conditions (electric conductivity 20
S/m, temperature 2800 K, supersonic plasma gas speed 2000 m/s with Mach 2.134,
and magnetic flux density 5 T) shows that the optimum idealized electric power
that can be extracted from a unit volume of plasma is estimated as 500 MW/m3.
This is a much larger volumetric power density than typical values encountered
in reciprocating piston-type engines (0.2 MW/m3) or rotary gas turbine engines
(0.5 MW/m3). Such an extremely high power density enables very compact power
generation units.
