<p>Our findings examine how the instability parameter (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\Delta '$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi mathvariant="normal">Δ</mi> <mo>′</mo> </msup> </math></EquationSource> </InlineEquation>) impacts the evolution of tearing instability in various viscous settings through two-dimensional MHD (magnetohydrodynamics) simulations. Increasing <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$\Delta '$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi mathvariant="normal">Δ</mi> <mo>′</mo> </msup> </math></EquationSource> </InlineEquation> triggers distinct stages of instability dynamics, influencing critical island width, current sheet aspect ratio, and plasmoid characteristics. Conversely, reducing <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$\Delta '$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi mathvariant="normal">Δ</mi> <mo>′</mo> </msup> </math></EquationSource> </InlineEquation> suppresses plasmoid instability beyond a critical Lundquist number, suggesting retardation in plasmoid formation in thin current sheets. Critical island width experiences rapid initial growth with <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$\Delta '$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi mathvariant="normal">Δ</mi> <mo>′</mo> </msup> </math></EquationSource> </InlineEquation>, stabilizing after <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$\Delta ' = 24$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi mathvariant="normal">Δ</mi> <mo>′</mo> </msup> <mo>=</mo> <mn>24</mn> </mrow> </math></EquationSource> </InlineEquation>. Viscosity (<InlineEquation ID="IEq6"> <EquationSource Format="TEX">$P_r$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>P</mi> <mi>r</mi> </msub> </math></EquationSource> </InlineEquation>, Prandtl number) affects critical island width differently in the <InlineEquation ID="IEq7"> <EquationSource Format="TEX">$P_r < 1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>P</mi> <mi>r</mi> </msub> <mo><</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq8"> <EquationSource Format="TEX">$P_r > 1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>P</mi> <mi>r</mi> </msub> <mo>></mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation> regimes, with a transitional shift observed at <InlineEquation ID="IEq9"> <EquationSource Format="TEX">$P_r = 1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>P</mi> <mi>r</mi> </msub> <mo>=</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>. Aspect ratios demonstrate transitional behaviors at <InlineEquation ID="IEq10"> <EquationSource Format="TEX">$P_r = 1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>P</mi> <mi>r</mi> </msub> <mo>=</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>, increasing exponentially with viscosity in <InlineEquation ID="IEq11"> <EquationSource Format="TEX">$P_r < 1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>P</mi> <mi>r</mi> </msub> <mo><</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation> and decreasing in <InlineEquation ID="IEq12"> <EquationSource Format="TEX">$P_r > 1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>P</mi> <mi>r</mi> </msub> <mo>></mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>. Saturated island width declines with <InlineEquation ID="IEq13"> <EquationSource Format="TEX">$\Delta '$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi mathvariant="normal">Δ</mi> <mo>′</mo> </msup> </math></EquationSource> </InlineEquation>, while smaller <InlineEquation ID="IEq14"> <EquationSource Format="TEX">$\Delta '$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi mathvariant="normal">Δ</mi> <mo>′</mo> </msup> </math></EquationSource> </InlineEquation> values maintain lower saturated plasmoid widths. The dependence of island width on <InlineEquation ID="IEq15"> <EquationSource Format="TEX">$\Delta '$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi mathvariant="normal">Δ</mi> <mo>′</mo> </msup> </math></EquationSource> </InlineEquation> diminishes at higher <InlineEquation ID="IEq16"> <EquationSource Format="TEX">$\Delta '$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi mathvariant="normal">Δ</mi> <mo>′</mo> </msup> </math></EquationSource> </InlineEquation> values, contrasting with trends in saturated plasmoid width. These results highlight the intricate interplay of <InlineEquation ID="IEq17"> <EquationSource Format="TEX">$\Delta '$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi mathvariant="normal">Δ</mi> <mo>′</mo> </msup> </math></EquationSource> </InlineEquation>, viscosity, and equilibrium conditions in the dynamics of magnetic reconnection.</p>

Role of instability parameter during the nonlinear evolution of visco-resistive tearing instability

期刊论文
发表日期：

2025年10月7日

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Nisar Ahmad,
Chao Shen,
Abid Ali Abid,
Yong Ji,
Guang-Rui Yao,
Xiao-Jie Li,
Ying-Jie Zhao,
Yan-Fang Ji

摘要

Our findings examine how the instability parameter ( $\Delta '$ $Δ^{'}$ ) impacts the evolution of tearing instability in various viscous settings through two-dimensional MHD (magnetohydrodynamics) simulations. Increasing $\Delta '$ $Δ^{'}$ triggers distinct stages of instability dynamics, influencing critical island width, current sheet aspect ratio, and plasmoid characteristics. Conversely, reducing $\Delta '$ $Δ^{'}$ suppresses plasmoid instability beyond a critical Lundquist number, suggesting retardation in plasmoid formation in thin current sheets. Critical island width experiences rapid initial growth with $\Delta '$ $Δ^{'}$ , stabilizing after $\Delta ' = 24$ $Δ^{'} = 24$ . Viscosity ( $P_r$ $P_{r}$ , Prandtl number) affects critical island width differently in the $P_r < 1$ $P_{r} < 1$ and $P_r > 1$ $P_{r} > 1$ regimes, with a transitional shift observed at $P_r = 1$ $P_{r} = 1$ . Aspect ratios demonstrate transitional behaviors at $P_r = 1$ $P_{r} = 1$ , increasing exponentially with viscosity in $P_r < 1$ $P_{r} < 1$ and decreasing in $P_r > 1$ $P_{r} > 1$ . Saturated island width declines with $\Delta '$ $Δ^{'}$ , while smaller $\Delta '$ $Δ^{'}$ values maintain lower saturated plasmoid widths. The dependence of island width on $\Delta '$ $Δ^{'}$ diminishes at higher $\Delta '$ $Δ^{'}$ values, contrasting with trends in saturated plasmoid width. These results highlight the intricate interplay of $\Delta '$ $Δ^{'}$ , viscosity, and equilibrium conditions in the dynamics of magnetic reconnection.