Instability of ion kinetic waves in a weakly ionized plasma

The fundamental higher-order Landau plasma modes are known to be generally heavily damped. We show that these modes for the ion component in a weakly ionized plasma can be substantially modified by ion-neutral collisions and a dc electric field driving ion flow so that some of them can become unstable. This instability is expected to naturally occur in presheaths of gas discharges at sufficiently small pressures and thus affect sheaths and discharge structures.

Figure 1

Steady-state solution. Shown is the longitudinal velocity distribution $f_{0,z}={\int }_{-\infty }^{\infty }{\int }_{-\infty }^{\infty }{f}_{0}d{v}_{x}d{v}_y$, where the $z$ axis is in the direction of the field. Different lines correspond to different values of the parameter $u=v_{\mathrm{f}}/v_{\mathrm{tn}}$.

Figure 2

Modes in the absence of flow. Shown are the solutions of Eq. (9a) for $u=0$. The left column represents the collisionless case [$\zeta \to 0$; in this case the dispersion relation is reduced to Eq. (1)], and the right column illustrates the effect of collisions for $\zeta =0.1$. The ion Langmuir mode and the first two higher modes are denoted by “L,” “1,” and “2,” respectively. The dashed lines, shown to guide the eye, correspond to $\mathrm{Re}\left(\omega \right)/k=v_{\mathrm{tn}}$.

Figure 3

Modes in the presence of flow. The left and right columns correspond to $u=2$ and 10, respectively, both are for $\zeta =0.1$ and downstream waves. The notation of the modes is the same as in Fig. 2. The right column illustrates the instability of the first higher mode. The upper and lower dashed lines, shown to guide the eye, correspond to $\mathrm{Re}\left(\omega \right)/k=v_{\mathrm{f}}$ and $\mathrm{Re}\left(\omega \right)/k=v_{\mathrm{tn}}$, respectively.

Figure 4

Stability diagram. The instability region is bound within $u\gtrsim 8$ and $\zeta \lesssim 0.3$. Note that in the limit $\zeta \to 0$, $u=\text{const}$ within the instability region, the growth rate of the instability tends to zero, so that a finite collision parameter is essential for the instability.

Figure 5

Effect of the electron response. (a) No response case: The unstable mode for $u=10$, $\zeta =0.1$ (i.e., for the same $u$ and $\zeta$ as in the right column of Fig. 3). (b) The same mode for $T_{\mathrm{e}}/T_{\mathrm{n}}=200$, with $u$ and $\zeta$ as above. (c) The same mode for $u=14$, $\zeta =0.05$ and $T_{\mathrm{e}}/T_{\mathrm{n}}$ as above.