On the effect of incoherence in a polarized dusty plasma and Wigner stability

We theoretically analysed the effect of incoherence present in the initial density in a homogeneous plasma containing nonthermal ions and Maxwellian electrons under the influence of polarization force. The Krylov-Bogoliubov-Mitropolsky (KBM) method is used to derive the Nonlinear Schrödinger equation. In the next stage the incoherence effect is analysed by studying the equation of motion of the correlation function 〈 n ( x , t ) n * ( x , t )〉 with the help of Wigner quantization and Moyal braket. The modulational stability of the new equation is exhaustively studied with respect to the plasma parameters variation and the effect of polarization force. In the next section, we considered a q -nonextensive distribution of electrons and viewed a more general form of polarization force by following Bentabet et al. The same analysis is again repeated and the modulation stability is analysed.