Discrete eigenmodes of filamentation instability in the presence of a $q$-nonextensive distribution

Discrete eigenmodes of the filamentation instability in a weakly ionized current-driven plasma in the presence of a $q$-nonextensive electron velocity distribution is investigated. Considering the kinetic theory, Bhatnagar-Gross-Krook collision model, and Lorentz transformation relations, the generalized longitudinal and transverse dielectric permittivities are obtained. Taking into account the long-wavelength limit and diffusion frequency limit, the dispersion relations are obtained. Using the approximation of geometrical optics and linear inhomogeneity of the plasma, the real and imaginary parts of the frequency are discussed in these limits. It is shown that in the long-wavelength limit, when the normalized electron velocity is increased the growth rate of the instability increases. However, when the collision frequency is increased the growth rate of the filamentation instability decreases. In the diffusion frequency limit, results indicate that the effects of the electron velocity and $q$-nonextensive parameter on the growth rate of the instability are similar. Finally, it is found that when the collision frequency is increased the growth rate of the instability increases in the presence of a $q$-nonextensive distribution.

Figure 1

Real part of the frequency ${\mathrm{\Omega }}_r$ for different values of the $n$ parameter.

Figure 2

Real ${\mathrm{\Omega }}_r$ and imaginary $\mathrm{\Gamma }$ parts of the frequency for different values of the $U$ parameter.

Figure 3

Real ${\mathrm{\Omega }}_r$ and imaginary $\mathrm{\Gamma }$ parts of the frequency for different values of the $\nu$ parameter.

Figure 4

Imaginary part of the frequency $\mathrm{\Gamma }$ for different values of the $n$ parameter.

Figure 5

Imaginary part of the frequency $\mathrm{\Gamma }$ for different values of the $U$ parameter.

Figure 6

Imaginary part of the frequency $\mathrm{\Gamma }$ for different values of the $q_e$ parameter.

Figure 7

Imaginary part of the frequency $\mathrm{\Gamma }$ for different values of the $q_e$ parameter.