The Electrical Characteristics of an MHD Generator Connected to an Arbitrary Load Resistance Network and the Experimental Determination of the Internal Conductance Matrix

The electrical characteristics of an MHD generator with an arbitrary electrode configuration and a finite number of electrodes are investigated, taking fully into consideration the end-effects. The influence of Hall effect, ion slip and an arbitrary velocity profile are considered. The potential ∅ of the laboratory co-ordinate system is transformed by an integral relation to the moving frame potential Φ, which satisfies Laplace's equation. With the form of the expression for the conformal transformation of the generator duct onto a plane with homogeneous current density, it is shown that the (2n-l) electrode currents of the n electrode pairs can be expressed as a linear function of each of the (2n-l) electrode potentials. The interrelation of the (2n-l) electrode currents and (2n-l) potentials form an array of elements which is termed the internal conductance matrix. Each element of this internal conductance-matrix can be clearly defined by the generator geometry, the conductivity o' and by the angle a of the conductivity tensor. In contrast to the scalar conductivity case, it is shown that Maxwell's reciprocity theorem is here no longer valid. For tensor conductivity, the internal conductance matrix is not symmetric, so the derivation of an equivalent circuit of the generator under general loading conditions is not possible. All the elements of the internal conductance matrix can be determined by simple terminal measurements on a semi-conducting model of high load carrier mobility subjected to a magnetic field. Channel equivalence is obtained with electrodes set in conformity with the MHD channel geometry. At given plasma parameters the corresponding model parameters are formulated. The experimental procedure is suitable in cases where the geometry of the generator duct can only be evaluated with much calculative effort using conformal mapping. (author)