Overtaking phenomenon of nonlinear ultra-low frequency multi-shock structures in ultra-relativistic degenerate plasmas

Abstract

Overtaking collisions of nonlinear ultra-low frequency (NULF) shock waves are examined in a degenerate ultra-relativistic plasma, containing inertial mobile heavy-ion fluid and inertialess degenerate light ions and electrons. The well-known reductive perturbation analysis then is used to obtain a Burgers’ equation (BE), which describes the propagation of ultra-low frequency shock waves in the plasma model. The Cole-Hopf transformation and the exponential function have been applied to get NULF multi-shock waves. Here, the findings illustrate that the excitation, amplitude, and steepness of overtaking collisions of NULF multi-shock waves and their electric fields are modified with the influence of heavy-ion kinematic viscosity. It is found that the amplitude and the steepness of NULF multi-shock waves increase with the decrease in the light-to-heavy ion density ratio. The numerical simulation gives rise to significant highlights on the dynamics of overtaking collisions of NULF multi-shock waves in astrophysical plasmas such as white dwarfs.

KEYWORDS:

• Nonlinear ultra-low frequency multi-shock waves
• overtaking collisions
• ultra-relativistic degenerate plasmas

Acknowledgments

The authors extend their appreciation to the Deanship of Scientific Research at King Khalid University for funding this work through a research groups program under grant number KKU R.G.P.1/284/42. The authors also thank the editor and his staff for their kind cooperation.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Notes on contributors

E. F. El-Shamy

E. F. El-Shamy was born in Damietta, Egypt in 1971. He received the Ph.D. degree in theoretical plasma physics from the Faculty of Science, Damietta Branch, Mansoura University, Egypt, in 2002. He is currently Professor of Theoretical Plasma Physics at the Faculty of Science, Damietta University, Egypt. His main research interests include theoretical plasma physics, nonlinear structures in plasmas and fluids, collective processes in space physics, and astrophysics. His present interests involve the physics of degenerate plasmas, wave-wave interaction, and multi-component plasmas. He has authored more than 70 published papers in the best scientific journals on linear and nonlinear waves in plasmas. He has also contributed as a Reviewer in some scientific journals.

E. A. Elghmaz

Ebtehal Elghmaz, Ph.D. in theoretical physics from the Faculty of Science, Damietta University, Egypt in 2017. Currently, she is a lecturer in King Khalid University, Saudi Arabia. She published papers in ISI journals. Her research interests include the solution of the problems related to plasma physics and nonlinear waves.

H. Elhosiny Ali

H. Elhosiny Ali received his Ph.D. degree in advanced materials and nanotechnologies in May 2013, from Universidad Autonoma de Madrid, Madrid, Spain. In 2019, he was promoted to be an Associate Professor of applied physics. He worked at Department of Physics, Faculty of Science, Zagazig University, for more than 10 years as a Demonstrator, assistant lecturer, a Lecturer and associate professor of physics. His research interests include nano-materials films/powder and devices, nano-metal oxide thin films/powders, organic materials, polymer materials, composites, and their characterization.

A. A. Ibraheem

Awad A. Ibraheem was born in Luxor, Egypt, in 1972. He received his PhD in theoretical nuclear physics from Al-Azhar University's Faculty of Science, Assuit Branch in Egypt, in 2005. (Joint supervision between Al-Azhar University and Pisa University Italy). He is currently a Professor of Theoretical Nuclear Physics at the Faculty of Science at Al-Azhar University in Assuit, Egypt. His main research interests include theoretical nuclear physics, radiation physics, direct nuclear reactions, and radioactive beam scattering. He has over 70 papers in the best scientific journals on experimental and theoretical nuclear and radiation research.

M. Mahmoud

Mona Mahmoud, received the M.Sc. and Ph.D. degrees in theoretical physics from the Faculty of Science, Mansoura University, Egypt, in 2004 and 2012, respectively. She is currently an Assistant Professor with the Physics Department, College of Science, King Khalid University, Saudi Arabia. She published several papers in ISI journals and indexed conferences. Her research interests include the solution of the problems related to dusty plasma, soliton theory, and Schrodinger equation and its applications in optics.

M.O. A. El Ghazaly

Prof. Dr M. O. A. El Ghazaly, is a full professor of physics with the two academic ranking qualifications for the ascending titles of Associate professor and Full professor, both earned from the Conseil National des Universités (CNU) in France or French National Board of Universities. Earlier, He earned his PhD from the Catholic University of Louvain in Belgium. He is a research associate at Catholic University of Louvain and a faculty member at the Department of Physics at King Khalid University. His research focuses on interaction between free electron and gas phase ions of astrophysical and fusion plasmas interest, along with charge-exchange in the interaction between solar-wind highly charged ions and neutrals from plasma of molecular could. He publishes about 60 papers in high impact ISI and journals and peer-reviewed international conference proceedings.