Theoretical analysis of planar and non‐planar electron ‐ acoustic shock waves in electron‐positron‐ion plasma

Abstract

The propagation properties of planar and non‐planar electron acoustic shock waves composed of stationary ions, cold electrons, and q‐non‐extensive hot electrons and positrons are studied in unmagnetized electron‐positron‐ion plasma. In this model, the Korteweg‐de Vries Burgers equation is obtained in the planar and non‐planar coordinates. We have investigated the combined action of the dissipation, non‐extensivity, density ratio of hot to cold electrons, concentration of positrons, and temperature difference of cold electrons, hot electrons, and positrons. It was found that the amplitude of shock wave in e‐p‐i plasma increases when the positron concentration and temperature increase. The same effect is observed in the case of kinematic viscosity η. Furthermore, it is noticed that spherical wave moves faster in comparison to the shock waves in cylindrical geometry. This difference arises due to the presence of the geometry term m/2τ. It should be noted that the contribution of the geometry factor comes through the continuity equation. Results of our work may be helpful to illustrate the different properties of shock wave features in different astrophysical and space environments like supernova, polar regions, and in the vicinity of black holes.

Parametric study of cylindrical and spherical dust ion acoustic shock waves with two temperature electrons in dusty plasma relevant to Saturn's E ring

“…To study the characteristics of shock waves in dusty plasma, we derive the modified Burgers equation by including higher order nonlinearity. For this purpose, we use the stretched coordinates as = 2 (r − t), = 4 t. (20) Using the above stretching coordinates and expansions (9) in Equations ( 6)-( 8), the lowest order terms remain same as Equations ( 10)- (12). To the next higher order ( 4 ), we get the following equations…”

“…Shocks are generated in the plasma when dissipation is more dominant than dispersion in the presence of nonlinearity. 9 Shock waves can be found in a planet's magnetotails and are formed in the solar corona and solar wind. Whenever plasmas and field energy flow, there will be shock waves.…”