Overtaking Collisions of Ion Acoustic <i>N</i>-Shocks in a Collisionless Plasma with Pair-Ion and (<i>α</i>,<i>q</i>) Distribution Function for Electrons

• Main Authors: Md. Golam Hafez, Parvin Akter, Samsul Ariffin Abdul Karim
• Format: Article
• Language: English
• Published: MDPI AG 2020-09-01
• Series: Applied Sciences
• Subjects: unmagnetized plasma; pair-ion; Burgers equation; multi-shocks
• Online Access: https://www.mdpi.com/2076-3417/10/17/6115

In this work, the effects of plasma parameters on overtaking collisions of ion acoustic multi-shocks are studied in an unmagnetized collisionless plasma with positive and negative ions, and (<inline-formula><math display="inline"><semantics><mrow><mi>α</mi><mo>,</mo><mi>q</mi></mrow></semantics></math></inline-formula>)-distributed electrons. To investigate such phenomena, the reductive perturbation technique is implemented to derive the Burgers equation. The <i>N</i>-shock wave solution is determined for this equation by directly implementing the exponential function. The result reveals that both the amplitudes and thicknesses of overtaking collisions of <i>N</i>-shock wave compressive and rarefactive electrostatic potential are significantly modified with the influences of viscosity coefficients of positive and negative ions. In addition, the density ratios also play an essential role to the formation of overtaking collisions of <i>N</i>-shocks. It is observed from all theoretical and parametric investigations that the outcomes may be very useful in understanding the dynamical behavior of overtaking collisions of multi-shocks in various environments, especially the D- and F-regions of the Earth’s ionosphere and the future experimental investigations in Q-machine laboratory plasmas.