Time-Dependent Ambipolar Diffusion Waves

A theory for the propagation of a plasma into an ambient gas is proposed. It is an extension of the usual ambipolar diffusion which takes into account the inertia of the particles and predicts a finite velocity for the propagation of the plasma. The equation $${\nabla }^2{n}_{\mathrm{e}}{\text{=(1/u}}^2{\mathrm{)(\partial }}^2{n}_{\mathrm{e}}{\mathrm{/\partial t}}^2{\text{)+(1/D}}_{\mathrm{a}}{\mathrm{)(\partial n}}_{\mathrm{e}}\mathrm{/\partial t)}$$ is obtained for the electron density in the expanding plasma, where u = (D_aν_a)^½, D_a is the ambipolar diffusion coefficient and ν_a is an ``ambipolar collision frequency.'' u gives the speed of propagation of the plasma interface and is equal to the velocity (kT_e/M_i)^½, if the electron temperature T_e is much higher than the ion temperature. This equation is solved in one‐dimensional geometry and some characteristics of the solution discussed. It is shown that the maximum density of the plasma propagates with speed u in the case of low pressure of the gas but with much lower speed in the case of higher pressure.