Weak ion-acoustic double layers in a plasma with a q-nonextensive electron velocity distribution

Weak ion-acoustic double-layers (IA-DLs) in a two-component plasma are investigated in the context of the nonextensive statistics proposed by Tsallis. Due to the entropic index q, our plasma model can admit compressive as well as rarefactive IA-DLs. It is shown that the values 5/3 < q < 3 are automatically ruled out from the domain of allowable nonextensive q-parameters for the existence of small-DLs. As long as the Mach number M is less than similar to 1.42, the only admissible q-values which may lead to IA-DLs are all positive. For -1 < q < 1 (1 < q < 5/3), the effect of increasing q is to lower (to shift towards higher values) the critical Mach number M-cr above which only compressive IA-DL are admitted. Beyond q = 3, only compressive small-amplitude ion-acoustic double layers are observed. Furthermore, due to the flexibility of the q-parameter, the obtained results bring a possibility to deal with small-DLs with relatively high Mach numbers. Our investigation may be of wide relevance to astronomers and space scientists working on interstellar plasmas.