Skin Effect in Magneto-Fluid Dynamic Traveling Wave Devices

Abstract

Electromagnetic propagation through an infinite circular cylindrical traveling wave tube in which a conducting fluid of constant conductivity is moving axially with uniform speed is studied. Asymptotic solutions valid for |αR0|«1 and |αR0»1, where α is the complex separation constant and R0 the tube radius, are obtained and analyzed. Concentrating specifically on the axial body force per unit tube length induced in the fluid, the |αR0|»1 solution indicates, fixing the current sheet input and geometry, that the magnitude of the induced axial force is a marked function of the dimensionless parameter β, equal to the magnetic Reynolds number based on wavespeed and wavelength multiplied by the slip. The body force rises linearly with β for small β, reaches a peak and then, because of the inability of the electromagnetic field to penetrate into the conductor with increasing β (skin effect), falls like β−1/2 for large β. From the practical viewpoint, the results suggest the adjustment of the electrical and fluid mechanical parameters so that operation occurs at that value of β which optimizes the force. It is further indicated, especially for moderate to high β operation, that for efficient utilization and conservation of working fluid mass and electrical energy, injection and acceleration take place in an annulus close to the coils rather than throughout the entire cross section.