<p>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 <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13538_2025_1783_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="23" /> </InlineMediaObject> <EquationSource Format="TEX">$(\nu )$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>ν</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> and ion to electron temperature ratio <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13538_2025_1783_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="25" /> </InlineMediaObject> <EquationSource Format="TEX">$(\alpha )$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>α</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> has been examined. Shock waves are produced by increasing the values of the relativistic factor, positron concentration <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13538_2025_1783_Article_IEq3.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="22" /> </InlineMediaObject> <EquationSource Format="TEX">$(\delta )$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>δ</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>, and electron to positron temperature ratio <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13538_2025_1783_Article_IEq4.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="24" /> </InlineMediaObject> <EquationSource Format="TEX">$(\sigma )$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>σ</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>. It is also found that the presence of the kinematic viscosity <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13538_2025_1783_Article_IEq5.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="33" /> </InlineMediaObject> <EquationSource Format="TEX">$({\eta }_{i0})$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <msub> <mi>η</mi> <mrow> <mi>i</mi> <mn>0</mn> </mrow> </msub> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> 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.</p>

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

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2025年5月9日

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R. Das,
M. Das,
E. Hincal,
K. Hosseini,
F. Alizadeh

摘要

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 $(\nu )$ $(ν)$ and ion to electron temperature ratio $(\alpha )$ $(α)$ has been examined. Shock waves are produced by increasing the values of the relativistic factor, positron concentration $(\delta )$ $(δ)$ , and electron to positron temperature ratio $(\sigma )$ $(σ)$ . It is also found that the presence of the kinematic viscosity $({\eta }_{i0})$ $(η_{i 0})$ 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.