Screening and sheath formation in a nonequilibrium mixed Cairns-Tsallis electron distribution

The effects of electron nonextensivity for a given nonthermality state, on Debye shielding and electrostatic sheath formation are examined. A physically meaningful Cairns-Tsallis distribution is outlined and a generalized expression for the Debye screening length λDq,α is obtained. It is shown that an increase of the entropic index q causes λDq,α to decrease whatever the amount of plasma nonthermality α. In addition, smaller pertinent values of q along with relatively higher values of α provide larger values of λDq,α. The shielded electrostatic potential falls off as a function of distance more slowly as α increases, a result somewhat analogous to the dynamical shielding decrease (albeit in a different context) of a free charge as it begins to move. Moreover, smaller pertinent values of q along with relatively higher values of α are found to involve higher ion drift speed vi0 for proper sheath formation. As α increases, the sheath electrostatic potential-gradient dΨs/dξ becomes abruptly steep slowing down the energetic electrons leakage to the wall. Moreover, the sheath thickness broadens as the electron nonthermality strengthens.