It has been shown that in an m.h.d. generator, acoustic waves can grow due to the coupling of fluctuations in electrical conductivity, Hall parameter and thermodynamic properties of the gas, with the ohmic dissipation and electromagnetic body forces. A new analysis of this phenomenon is presented in which waves travelling at an arbitrary angle to the flow direction in a plane perpendicular to the magnetic field are considered. In contrast to McCune’s (1964) treatment the thermodynamic properties are not restricted to perfect gas laws; and the condition for spatially and temporally growing waves is examined using a general dispersion relation which includes both these types of wave. We consider in detail (i) stationary waves in supersonic flow, and (ii) travelling waves in the subsonic flow found in the G.E.G.B. 200 MW thermal input generator being built at Marchwood, and a possible power station m.h.d. generator. It is found that the waves in the 200 MW rig which burns kerosene in oxygen will be damped. But in an oil-air combustion products generator for Hall parameters of order 3 or greater, it is found that stationary waves which grow rapidly may occur at Mach numbers greater than about 1-7; and in subsonic flow waves propagating antiparallel to the steady current vector may be amplified, though the growth rate is not excessive. In noble gas m.h.d. generators these waves are more unstable than in the oil, air combustion products generator.
Anisotropic Choquard problems with Stein–Weiss potential: nonlinear patterns and stationary waves
