<i>α</i> Effect and Magnetic Diffusivity <i>β</i> in Helical Plasma Under Turbulence Growth

<i>α</i> Effect and Magnetic Diffusivity <i>β</i> in Helical Plasma Under Turbulence Growth

We investigate the transport coefficients <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> and <inline-formula><math xmlns="htt...

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Bibliographic Details
Main Author: Kiwan Park
Format: Article
Language:English
Published: MDPI AG 2025-06-01
Series:Universe
Subjects:
MHD
magnetic field
<i>α</i> effect
magnetic diffusion <i>β</i> effect
helicity
simulation
Online Access:https://www.mdpi.com/2218-1997/11/7/203
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Summary:We investigate the transport coefficients <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>β</mi></semantics></math></inline-formula> in plasma systems with varying Reynolds numbers while maintaining a unit magnetic Prandtl number (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mo form="prefix">Pr</mo><mi mathvariant="normal">M</mi></msub></semantics></math></inline-formula>). The <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>β</mi></semantics></math></inline-formula> tensors parameterize the turbulent electromotive force (EMF) in terms of the large-scale magnetic field <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mover><mi mathvariant="bold">B</mi><mo>¯</mo></mover></semantics></math></inline-formula> and current density as follows: <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mo>⟨</mo><mi mathvariant="bold">u</mi><mo>×</mo><mi mathvariant="bold">b</mi><mo>⟩</mo></mrow><mo>=</mo><mi>α</mi><mover><mi mathvariant="bold">B</mi><mo>¯</mo></mover><mo>−</mo><mi>β</mi><mrow><mo>∇</mo><mo>×</mo><mover><mi mathvariant="bold">B</mi><mo>¯</mo></mover></mrow></mrow></semantics></math></inline-formula>. In astrophysical plasmas, high fluid Reynolds numbers (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mi>e</mi></mrow></semantics></math></inline-formula>) and magnetic Reynolds numbers (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><msub><mi>e</mi><mi mathvariant="normal">M</mi></msub></mrow></semantics></math></inline-formula>) drive turbulence, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mi>e</mi></mrow></semantics></math></inline-formula> governs flow dynamics and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><msub><mi>e</mi><mi mathvariant="normal">M</mi></msub></mrow></semantics></math></inline-formula> controls magnetic field evolution. The coefficients <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>α</mi><mi>semi</mi></msub></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>β</mi><mi>semi</mi></msub></semantics></math></inline-formula> are obtained from large-scale magnetic field data as estimates of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>β</mi></semantics></math></inline-formula> tensors, while <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>β</mi><mi>theo</mi></msub></semantics></math></inline-formula> is derived from turbulent kinetic energy data. The reconstructed large-scale field <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mover><mi>B</mi><mo>¯</mo></mover></semantics></math></inline-formula> agrees with simulations, confirming consistency among <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>β</mi></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mover><mi>B</mi><mo>¯</mo></mover></semantics></math></inline-formula> in weakly nonlinear regimes. This highlights the need to incorporate magnetic effects under strong nonlinearity. To clarify <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>β</mi></semantics></math></inline-formula>, we introduce a field structure model, identifying <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> as the electrodynamic induction effect and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>β</mi></semantics></math></inline-formula> as the fluid-like diffusion effect. The agreement between our method and direct simulations suggests that plasma turbulence and magnetic interactions can be analyzed using fundamental physical quantities. Moreover, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>α</mi><mi>semi</mi></msub></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>β</mi><mi>semi</mi></msub></semantics></math></inline-formula>, which successfully reproduce the numerically obtained magnetic field, provide a benchmark for future theoretical studies.
ISSN:2218-1997

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