Effect of Viscosity on Highly Relativistic Ion Acoustic Shock Waves in an Electron–Positron-Ion Plasma with the Pressure Variation Equation

Abstract The Korteweg-de Vries–Burgers (KdV–B) equation is developed using the reductive perturbation method (RPM) to investigate the propagation properties of ion acoustic shock waves (IASHWs) in a highly relativistic plasma containing relativistic thermal ions, thermal positrons, and non-thermal electrons. Only fast mode is found to exist in the electron–positron-ion (epi) plasma of IASHWs. The impact of varying plasma parameters on the shock wave amplitude is examined. The behaviour of nonlinear and dispersion coefficients under the influence of relativistic factor $$(\nu )$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>ν</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> and ion to electron temperature ratio $$(\alpha )$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>α</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> has been examined. Shock waves are produced by increasing the values of the relativistic factor, positron concentration $$(\delta )$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>δ</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> , and electron to positron temperature ratio $$(\sigma )$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>σ</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> . It is also found that the presence of the kinematic viscosity $$({\eta }_{i0})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:msub> <mml:mi>η</mml:mi> <mml:mrow> <mml:mi>i</mml:mi> <mml:mn>0</mml:mn> </mml:mrow> </mml:msub> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> generates shock wave structures. Moreover, the shock wave amplitude reduces with a higher order relativistic impact and increases with a lower order relativistic effect. As a result, shock waves appear to have a significantly bigger amplitude in a non-relativistic environment. The findings might be applicable to both inertial confinement fusion plasmas and astrophysical plasmas.