Nonextensive approach to the effect of electron trapping in the presence of quantizing magnetic field on the propagation of ion acoustic waves

Ion acoustic waves (IAWs) are studied for degenerate trapped electron and non-degenerate ion plasma in the presence of quantizing magnetic field in the Tsallis framework. The presence of a magnetic field induces a trapping effect on degenerated electrons, which is studied using the generalized form of the Fermi–Dirac in the non-extensive framework. An appropriate new electron density is reformulated and reexamined in this statistics. The new expression for electron density is used to study the propagation of ion acoustic waves. The linear dispersion relation for IAWs is derived in the presence of the quantizing magnetic field and a small finite temperature in the framework of q-statistics, there influence on the propagation characteristics of the linear ion acoustic wave is discussed. In arbitrary amplitude, we use the Sagdeev potential showing that rarefactive and compressive ion acoustic solitary wave can exist simultaneously under certain conditions of temperature T, quantizing magnetic field η and the entropic index q. In addition, to study the dynamics of small but finite amplitude ion Acoustics solitary waves. Using the reductive perturbation technique the Korteweg de-Vries equation is established. Our results show that both rarefactive and compressive solitary waves may coexist in a certain range of plasma parameters.