# Electrostatic Ion-Acoustic Shock Waves in a Magnetized Degenerate Quantum Plasma

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## Abstract

**:**

## 1. Introduction

## 2. Model Equations

## 3. Derivation of the Burgers Equation

## 4. Results and Discussion

## 5. Conclusions

- The plasma model only supports positive shock potential under the consideration of both non-relativistic positively charged heavy and light ions (i.e., $\alpha =5/3$), and ultra-relativistically degenerate electrons (i.e., ${\gamma}_{e}=4/3$);
- The increasing number density of ultra-relativistic electrons enhances the amplitude of the IASHWs;
- The increasing charge state and number density of the non-relativistic heavy and light ion species enhance the amplitude of the IASHWs associated with $\mathsf{\Phi}>0$ (i.e., $A>0$);
- The steepness of the shock profile is decreased with the increasing kinematic viscosity ($\eta $) of ions;
- The amplitude of the shock profile is found to increase as the oblique angle increases.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A. First-Order and Second-Order Perturbation Terms

## References

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**Figure 1.**Plot of the nonlinear coefficient A vs. ${\mu}_{4}$ (

**left panel**) and $\mathsf{\Phi}$ vs $\zeta $ for different values of $\delta $ (

**right panel**) when $\alpha =5/3$, $\eta =0.3$, ${\gamma}_{e}=4/3$, $\delta ={20}^{\circ}$, ${Z}_{1}=37$, ${Z}_{2}=6$, ${n}_{10}={10}^{29}\phantom{\rule{3.33333pt}{0ex}}{\mathrm{cm}}^{-3}$, ${n}_{20}={10}^{30}\phantom{\rule{3.33333pt}{0ex}}{\mathrm{cm}}^{-3}$, ${n}_{{e}_{0}}={10}^{33}\phantom{\rule{3.33333pt}{0ex}}{\mathrm{cm}}^{-3}$, ${U}_{0}=0.05$, and ${v}_{p}={v}_{p+}$.

**Figure 2.**Plot of $\mathsf{\Phi}$ vs. $\zeta $ for different values of $\eta $ (

**left panel**) and for different values of ${n}_{{e}_{0}}$ (

**right panel**) when $\alpha =5/3$, $\delta ={20}^{\circ}$, ${\gamma}_{e}=4/3$, $\eta =0.3$, ${Z}_{1}=37$, ${Z}_{2}=6$, ${n}_{10}={10}^{29}\phantom{\rule{3.33333pt}{0ex}}{\mathrm{cm}}^{-3}$, ${n}_{20}={10}^{30}\phantom{\rule{3.33333pt}{0ex}}{\mathrm{cm}}^{-3}$, ${n}_{{e}_{0}}={10}^{33}\phantom{\rule{3.33333pt}{0ex}}{\mathrm{cm}}^{-3}$, ${U}_{0}=0.05$, and ${v}_{p}={v}_{p+}$.

**Figure 3.**Plot of $\mathsf{\Phi}$ vs. $\zeta $ for different values of ${Z}_{1}$ (

**left panel**) and for different values of ${Z}_{2}$ (

**right panel**) when $\alpha =5/3$, $\delta ={20}^{\circ}$, $\eta =0.3$, ${\gamma}_{e}=4/3$, ${Z}_{1}=37$, ${Z}_{2}=6$, ${n}_{10}={10}^{29}\phantom{\rule{3.33333pt}{0ex}}{\mathrm{cm}}^{-3}$, ${n}_{20}={10}^{30}\phantom{\rule{3.33333pt}{0ex}}{\mathrm{cm}}^{-3}$, ${n}_{{e}_{0}}={10}^{33}\phantom{\rule{3.33333pt}{0ex}}{\mathrm{cm}}^{-3}$, ${U}_{0}=0.05$, and ${v}_{p}={v}_{p+}$.

**Figure 4.**Plot of $\mathsf{\Phi}$ vs. $\zeta $ for different values of ${n}_{10}$ (

**left panel**) and for different values of ${n}_{20}$ (

**right panel**) when $\alpha =5/3$, $\delta ={20}^{\circ}$, $\eta =0.3$, ${\gamma}_{e}=4/3$, ${Z}_{1}=37$, ${Z}_{2}=6$, ${n}_{10}={10}^{29}\phantom{\rule{3.33333pt}{0ex}}{\mathrm{cm}}^{-3}$, ${n}_{20}={10}^{30}\phantom{\rule{3.33333pt}{0ex}}{\mathrm{cm}}^{-3}$, ${n}_{{e}_{0}}={10}^{33}\phantom{\rule{3.33333pt}{0ex}}{\mathrm{cm}}^{-3}$, ${U}_{0}=0.05$, and ${v}_{p}={v}_{p+}$.

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**MDPI and ACS Style**

Jahan, S.; Sharmin, B.E.; Chowdhury, N.A.; Mannan, A.; Roy, T.S.; Mamun, A.A.
Electrostatic Ion-Acoustic Shock Waves in a Magnetized Degenerate Quantum Plasma. *Plasma* **2021**, *4*, 426-434.
https://doi.org/10.3390/plasma4030031

**AMA Style**

Jahan S, Sharmin BE, Chowdhury NA, Mannan A, Roy TS, Mamun AA.
Electrostatic Ion-Acoustic Shock Waves in a Magnetized Degenerate Quantum Plasma. *Plasma*. 2021; 4(3):426-434.
https://doi.org/10.3390/plasma4030031

**Chicago/Turabian Style**

Jahan, Sharmin, Booshrat E. Sharmin, Nure Alam Chowdhury, Abdul Mannan, Tanu Shree Roy, and A A Mamun.
2021. "Electrostatic Ion-Acoustic Shock Waves in a Magnetized Degenerate Quantum Plasma" *Plasma* 4, no. 3: 426-434.
https://doi.org/10.3390/plasma4030031