Governing Equations for the Electric Fields within Linear Magnetohydrodynamic Channels

We aim to provide detailed derivation and analytical investigation that lead to closed-form mathematical equations that describe how various plasma properties (such as the electric conductivity and the travel speed) affect the resultant electric behavior of the plasma as a supersonic electrically conductive medium that flows under the influence of an applied magnetic field to produce direct current electricity within a linear channel. This magnetohydrodynamic problem can take four main forms, depending on the geometric design and electric connectivity of electrodes. Starting from basic principles and using informative sketches, we explain the equations governing the performance of this power generation technique, and contrast the operational conditions for the four different channel cases.