Analytical and numerical solution of sausage MHD wave oscillation in a thin magnetic flux tube

Abdulaziz H. Alharbi; Abdulaziz H. Alharbi

doi:10.3934/math.20241273

AIMS Mathematics

2024, Volume 9, Issue 9: 26065-26076. doi: 10.3934/math.20241273

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Analytical and numerical solution of sausage MHD wave oscillation in a thin magnetic flux tube

Abdulaziz H. Alharbi ^,

Department of Mathematics, Jamoum University College, Umm Al-Qura University, Jamoum, 25375 Makkah, Saudi Arabia

Received: 30 July 2024 Revised: 26 August 2024 Accepted: 04 September 2024 Published: 09 September 2024
MSC : 35A09, 35A22, 35B40, 35L05, 76N30

The aim of the present study is to investigate the damping of slow sausage MHD waves propagating in a gravitationally-stratified magnetic cylindrical structure when the plasma is strongly partially ionised. The problem is treated as an initial value problem and the analysis deals with the temporal evolution of waves in an asymptotic sense, i.e., large values of time compared to the period of waves. The plasma is assumed to be collision-dominated, i.e., we employ a two-fluid approximation. The set of equations describing the plasma dynamics is reduced to a coupled partial differential equations. Our findings show that the slow wave of charged species is affected by the presence of a cut-off. The mode associated with the neutral fluid propagates without any cut-off and decay very quickly due to collisions between particles.
- partial differential equations,
- partial ionisation,
- solar chromosphere,
- MHD waves,
- collision
Citation: Abdulaziz H. Alharbi. Analytical and numerical solution of sausage MHD wave oscillation in a thin magnetic flux tube[J]. AIMS Mathematics, 2024, 9(9): 26065-26076. doi: 10.3934/math.20241273

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Abstract

The aim of the present study is to investigate the damping of slow sausage MHD waves propagating in a gravitationally-stratified magnetic cylindrical structure when the plasma is strongly partially ionised. The problem is treated as an initial value problem and the analysis deals with the temporal evolution of waves in an asymptotic sense, i.e., large values of time compared to the period of waves. The plasma is assumed to be collision-dominated, i.e., we employ a two-fluid approximation. The set of equations describing the plasma dynamics is reduced to a coupled partial differential equations. Our findings show that the slow wave of charged species is affected by the presence of a cut-off. The mode associated with the neutral fluid propagates without any cut-off and decay very quickly due to collisions between particles.

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