The theory of moving striations in a D-C discharge plasma II. High current approximation

Abstract

The integrodifferential equation of striations, found in the preceding part [1] of this theory, is simplified for the case when the Debye lengthl _D is vanishingly small in comparison with the wave-length of the striations. It then takes the form (51b). The still non-zero space charge field then influences the motion of the charge carriers in such a way that it takes on the character of ambipolar diffusion in the axial direction. This is expressed by the first term on the right-hand side of Eq. (51b). The second and third terms describe the influence of the space charge field on the ionization rate through the changes in the electron temperature. Thus the third (integral) term causes the oscillatory behaviour of the transient process excited by a pulse disturbance, while the second term can lead to growth of the amplitude (i.e. to amplification) of the transient wave.

The transient solution of Eq. (51b) is given by the formula (73). It is in full qualitative agreement with the experiment and the quantitative agreement is also sufficient. This shows that processes found to be decisive for the very nature of moving striations [11] and for their amplification [16] do determine with sufficient accuracy even other finer properties of striations. The choice of optimum wave-length, in the conditions studied in this paper, is fulfilled by the ambipolar diffusion in the axial direction, which damps the short wave-length striations, and by the final value of the relaxation length of the electron temperature [1/a ₁, see Eq. (4)] which limits the long-distance effect of the electric space charge field on the ionization rate.