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Alfven waves amplitude applied approximation boundary conditions boundary layer Bullard and Gellman Chapter component conducting fluid consider constant convection curl curl0 cylindrical decay define denote density differential discussion disk displacement dissipation div0 duct dynamo action electric field electrodynamic electromagnetic electromagnetic induction equations equilibrium everywhere example field B0 finite flow flux tubes function gauss grad G grad0 gradient harmonic Hartmann layer hydrodynamic hydromagnetic induced instability insulating integral kinetic large compared Lenz's law linear lines of force Lorentz force magnetic diffusivity magnetic energy magnetic field magnetic flux magnetohydrodynamics magnetostatic main stream motion non-zero normal modes obtain Ohm's law ohmic oscillation perfect conductor perfectly conducting perturbation poloidal potential pressure region Reynolds number satisfy scalar solution squeeze film stability steady suppose surface currents term theorem theory toroidal uniform vanishes vector vector potential velocity viscous volume walls z-direction zero