Ambipolar diffusion as a singular perturbation problem

The effect of a magnetic field on the diffusion of a cylindrical column of ionization, having an initial electron density much greater than that of the ambient weakly ionized plasma in which it is embedded, is examined for the case in which the electron gyro-frequency is much greater than the electron neutral collision frequency V_e. The nonlinear diffusion equations are solved by means of a perturbation expansion based on their exact solution for the case V_e = 0. This approach leads to a singular perturbation problem, and shows that, when the column is not closely aligned with the field the distribution of plasma differs appreciably from that obtained from an ordinary anisotropic diffusion equation.