Non-linear skin effect in a conducting cylinder

The paper examines the penetration into a plasma cylinder of a quasi-stationary electromagnetic field excited by a wave of azimuthal surface current travelling parallel with the cylinder axis and located at some distance from the surface of the plasma. Since in this instance the variable magnetic field is considerably higher than the electric field its influence on the movement of particles in the plasma was taken into account. Within the limits of a hydrodynamic approximation this factor could be reduced to the inclusion of the Hall current in Ohm's law (σ/enc) []. A solution to the resulting system of nonlinear partial differential equations was found by using a computer programme somewhat analogous to the physical process by which field equilibrium distributions are established in a plasma.The dependence of all physical magnitudes on two parameters was studied: the conductivity of the plasma o and the ratio Ω of the Hall current to the conduction current.Allowance for non-linear effects leads to the appearance of a constant component of the longitudinal current (the carrier current), whose density never exceeds, at any point of the cylinder cross-section, the limiting value corresponding to the movement of all electrons at the phase velocity of the wave. A leakage of current towards the inner region of the plasma cylinder takes place and closed lines of current form in the cross-sections φ = const. The depth of field penetration increases with increased non-linearity, while at high plasma conductivity values the penetration depth is determined only by the value of Ω. Dissipation losses in the plasma are to all practical purposes independent of Ω.