Electron Inertia and Magnetic Reconnection
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912847677620224 |
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| author | Boozer, Allen H |
| author_facet | Boozer, Allen H |
| contents | When electron inertia is the only non-ideal effect in the evolution of a magnetic field $\vec{B}$, the field lines of $\vec{B}$ reconnect, but the lines of a related field $\vec{\mathcal{B}}$ do not. $\vec{\mathcal{B}} \equiv \vec{B} + \vec{\nabla}\times \left( (c/ω_{pe})^2μ_0\vec{j} \right)$ with $ω_{pe}$ the plasma frequency and $\vec{j}$ the current density. Although a full four-dimensional relativistic calculation of $\vec{\mathcal{B}}$ has been made, studies of $\vec{\mathcal{B}}$ have been focused on systems that depend on only two spatial coordinates. Three results are given: (1) A relatively simple demonstration in three dimensional space that the lines of $\vec{\mathcal{B}}$ do not reconnect when electron inertia is the only non-ideal effect. (2) The guiding center motion of charged particles is modified by a term that is proportional to $(c/ω_{pe})^2$, which is smaller than the drifts proportional to the gyroradius unless the current density is extremely large. (3) In three dimensional space, the evolution velocity of $\vec{\mathcal{B}}$ is characteristically chaotic, which means neighboring streamlines separate exponentially on a timescale $τ_u$. $\vec{\mathcal{B}}$ undergoes large scale reconnection on a timescale that is only an order of magnitude or two longer than $τ_u$ unless all diffusive non-ideal effects, such as resistivity, are absolutely zero. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_14400 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Electron Inertia and Magnetic Reconnection Boozer, Allen H Plasma Physics Solar and Stellar Astrophysics When electron inertia is the only non-ideal effect in the evolution of a magnetic field $\vec{B}$, the field lines of $\vec{B}$ reconnect, but the lines of a related field $\vec{\mathcal{B}}$ do not. $\vec{\mathcal{B}} \equiv \vec{B} + \vec{\nabla}\times \left( (c/ω_{pe})^2μ_0\vec{j} \right)$ with $ω_{pe}$ the plasma frequency and $\vec{j}$ the current density. Although a full four-dimensional relativistic calculation of $\vec{\mathcal{B}}$ has been made, studies of $\vec{\mathcal{B}}$ have been focused on systems that depend on only two spatial coordinates. Three results are given: (1) A relatively simple demonstration in three dimensional space that the lines of $\vec{\mathcal{B}}$ do not reconnect when electron inertia is the only non-ideal effect. (2) The guiding center motion of charged particles is modified by a term that is proportional to $(c/ω_{pe})^2$, which is smaller than the drifts proportional to the gyroradius unless the current density is extremely large. (3) In three dimensional space, the evolution velocity of $\vec{\mathcal{B}}$ is characteristically chaotic, which means neighboring streamlines separate exponentially on a timescale $τ_u$. $\vec{\mathcal{B}}$ undergoes large scale reconnection on a timescale that is only an order of magnitude or two longer than $τ_u$ unless all diffusive non-ideal effects, such as resistivity, are absolutely zero. |
| title | Electron Inertia and Magnetic Reconnection |
| topic | Plasma Physics Solar and Stellar Astrophysics |
| url | https://arxiv.org/abs/2509.14400 |