Structure of pressure-gradient-driven current singularity in ideal magnetohydrodynamic equilibrium
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866913229954875392 |
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| author | Huang, Yi-Min Zhou, Yao Loizu, Joaquim Hudson, Stuart Bhattacharjee, Amitava |
| author_facet | Huang, Yi-Min Zhou, Yao Loizu, Joaquim Hudson, Stuart Bhattacharjee, Amitava |
| contents | Singular currents typically appear on rational surfaces in non-axisymmetric ideal magnetohydrodynamic equilibria with a continuum of nested flux surfaces and a continuous rotational transform. These currents have two components: a surface current (Dirac $δ$-function in flux surface labeling) that prevents the formation of magnetic islands and an algebraically divergent Pfirsch--Schlüter current density when a pressure gradient is present across the rational surface. At flux surfaces adjacent to the rational surface, the traditional treatment gives the Pfirsch--Schlüter current density scaling as $J\sim1/Δι$, where $Δι$ is the difference of the rotational transform relative to the rational surface. If the distance $s$ between flux surfaces is proportional to $Δι$, the scaling relation $J\sim1/Δι\sim1/s$ will lead to a paradox that the Pfirsch--Schlüter current is not integrable. In this work, we investigate this issue by considering the pressure-gradient-driven singular current in the Hahm\textendash Kulsrud\textendash Taylor problem, which is a prototype for singular currents arising from resonant magnetic perturbations. We show that not only the Pfirsch--Schlüter current density but also the diamagnetic current density are divergent as $\sim1/Δι$. However, due to the formation of a Dirac $δ$-function current sheet at the rational surface, the neighboring flux surfaces are strongly packed with $s\sim(Δι)^{2}$. Consequently, the singular current density $J\sim1/\sqrt{s}$, making the total current finite, thus resolving the paradox. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_02107 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Structure of pressure-gradient-driven current singularity in ideal magnetohydrodynamic equilibrium Huang, Yi-Min Zhou, Yao Loizu, Joaquim Hudson, Stuart Bhattacharjee, Amitava Plasma Physics Fluid Dynamics Singular currents typically appear on rational surfaces in non-axisymmetric ideal magnetohydrodynamic equilibria with a continuum of nested flux surfaces and a continuous rotational transform. These currents have two components: a surface current (Dirac $δ$-function in flux surface labeling) that prevents the formation of magnetic islands and an algebraically divergent Pfirsch--Schlüter current density when a pressure gradient is present across the rational surface. At flux surfaces adjacent to the rational surface, the traditional treatment gives the Pfirsch--Schlüter current density scaling as $J\sim1/Δι$, where $Δι$ is the difference of the rotational transform relative to the rational surface. If the distance $s$ between flux surfaces is proportional to $Δι$, the scaling relation $J\sim1/Δι\sim1/s$ will lead to a paradox that the Pfirsch--Schlüter current is not integrable. In this work, we investigate this issue by considering the pressure-gradient-driven singular current in the Hahm\textendash Kulsrud\textendash Taylor problem, which is a prototype for singular currents arising from resonant magnetic perturbations. We show that not only the Pfirsch--Schlüter current density but also the diamagnetic current density are divergent as $\sim1/Δι$. However, due to the formation of a Dirac $δ$-function current sheet at the rational surface, the neighboring flux surfaces are strongly packed with $s\sim(Δι)^{2}$. Consequently, the singular current density $J\sim1/\sqrt{s}$, making the total current finite, thus resolving the paradox. |
| title | Structure of pressure-gradient-driven current singularity in ideal magnetohydrodynamic equilibrium |
| topic | Plasma Physics Fluid Dynamics |
| url | https://arxiv.org/abs/2303.02107 |