Wall leakage effect on nonuniformities in diagonal MHD channels

The effect of wall leakage, symmetric as well as asymmetric, is examined in the linear and nonlinear regimes. It is found that: the range of wavelength in the nonuniformities is reduced and in the asymmetric case splits into two separate passbands; depending on the wavelength, forward waves can propagate both upstream and downstream, and backward waves only upstream; the growth rate is minimal when the leakage at the cathode wall is four times that of the anode wall; and in all cases, a resistance introduced in the diagonal bars reduces the growth rate by a constant. Nomenclature h - width of the channel h' =/*tan0 H = electrode segmentation pitch Ie (k) =k mode component of the fluctuating current Ie (x) = total fluctuating current in the diagonal bars 70 = background dc current k = wave number Se = externally connected resistance in the diagonal bars x = longitudinal coordinate y = transverse coordinate 6 = angle of the diagonal link