Linear instability of Z-pinch in plasma: Inviscid case

Dongfen Bian; Yan Guo; Ian Tice

doi:10.1142/S0218202521500093

Linear instability of Z-pinch in plasma: Inviscid case

Dongfen Bian^*, Yan Guo, Ian Tice

^*Corresponding author for this work

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

The z-pinch is a classical steady state for the MHD model, where a confined plasma fluid is separated by vacuum, in the presence of a magnetic field which is generated by a prescribed current along the z direction. We develop a variational framework to study its stability in the absence of viscosity effect, and demonstrate for the first time that such a z-pinch is always unstable. Moreover, we discover a sufficient condition such that the eigenvalues can be unbounded, which leads to ill-posedness of the linearized MHD system.

Original language	English
Pages (from-to)	409-472
Number of pages	64
Journal	Mathematical Models and Methods in Applied Sciences
Volume	31
Issue number	2
DOIs	https://doi.org/10.1142/S0218202521500093
Publication status	Published - Feb 2021

Keywords

Compressible MHD system
linear instability
vacuum
z-pinch plasma

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Bian, D., Guo, Y., & Tice, I. (2021). Linear instability of Z-pinch in plasma: Inviscid case. Mathematical Models and Methods in Applied Sciences, 31(2), 409-472. https://doi.org/10.1142/S0218202521500093

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abstract = "The z-pinch is a classical steady state for the MHD model, where a confined plasma fluid is separated by vacuum, in the presence of a magnetic field which is generated by a prescribed current along the z direction. We develop a variational framework to study its stability in the absence of viscosity effect, and demonstrate for the first time that such a z-pinch is always unstable. Moreover, we discover a sufficient condition such that the eigenvalues can be unbounded, which leads to ill-posedness of the linearized MHD system.",

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T1 - Linear instability of Z-pinch in plasma

T2 - Inviscid case

AU - Bian, Dongfen

AU - Guo, Yan

AU - Tice, Ian

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N2 - The z-pinch is a classical steady state for the MHD model, where a confined plasma fluid is separated by vacuum, in the presence of a magnetic field which is generated by a prescribed current along the z direction. We develop a variational framework to study its stability in the absence of viscosity effect, and demonstrate for the first time that such a z-pinch is always unstable. Moreover, we discover a sufficient condition such that the eigenvalues can be unbounded, which leads to ill-posedness of the linearized MHD system.

AB - The z-pinch is a classical steady state for the MHD model, where a confined plasma fluid is separated by vacuum, in the presence of a magnetic field which is generated by a prescribed current along the z direction. We develop a variational framework to study its stability in the absence of viscosity effect, and demonstrate for the first time that such a z-pinch is always unstable. Moreover, we discover a sufficient condition such that the eigenvalues can be unbounded, which leads to ill-posedness of the linearized MHD system.

KW - Compressible MHD system

KW - linear instability

KW - vacuum

KW - z-pinch plasma

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SP - 409

EP - 472

JO - Mathematical Models and Methods in Applied Sciences

JF - Mathematical Models and Methods in Applied Sciences

IS - 2

ER -

Linear instability of Z-pinch in plasma: Inviscid case

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