Disentangling the Entangled Linkages of Relative Magnetic Helicity
Magnetic helicity, H , measures magnetic linkages in a volume. The early theoretical development of helicity focused on magnetically closed systems in ${ \mathcal V }$ bounded by $\partial { \mathcal V }$ . For magnetically closed systems, ${ \mathcal V }\in {{\mathbb{R}}}^{3}={ \mathcal V }+{{ \mat...
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| Format: | Article |
| Language: | English |
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IOP Publishing
2024-01-01
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| Series: | The Astrophysical Journal |
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| Online Access: | https://doi.org/10.3847/1538-4357/acf471 |
| _version_ | 1797338627484680192 |
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| author | Peter W. Schuck Mark G. Linton |
| author_facet | Peter W. Schuck Mark G. Linton |
| author_sort | Peter W. Schuck |
| collection | DOAJ |
| description | Magnetic helicity, H , measures magnetic linkages in a volume. The early theoretical development of helicity focused on magnetically closed systems in ${ \mathcal V }$ bounded by $\partial { \mathcal V }$ . For magnetically closed systems, ${ \mathcal V }\in {{\mathbb{R}}}^{3}={ \mathcal V }+{{ \mathcal V }}^{\ast }$ , no magnetic flux threads the boundary, $\hat{{\boldsymbol{n}}}\cdot {\boldsymbol{B}}{| }_{\partial { \mathcal V }}=0$ . Berger & Field and Finn & Antonsen extended the definition of helicity to relative helicity, ${ \mathcal H }$ , for magnetically open systems where magnetic flux may thread the boundary. Berger expressed this relative helicity as two gauge-invariant terms that describe the self-helicity of the magnetic field that closes inside ${ \mathcal V }$ and the mutual helicity between the magnetic field that threads the boundary $\partial { \mathcal V }$ and the magnetic field that closes inside ${ \mathcal V }$ . The total magnetic field that permeates ${ \mathcal V }$ entangles magnetic fields that are produced by current sources J in ${ \mathcal V }$ with magnetic fields that are produced by current sources J ^∗ in ${{ \mathcal V }}^{\ast }$ . Building on this fact, we extend Berger's expressions for relative magnetic helicity to eight gauge-invariant quantities that simultaneously characterize both of these self and mutual helicities and attribute their origins to currents J in ${ \mathcal V }$ and/or J ^∗ in ${{ \mathcal V }}^{\ast }$ , thereby disentangling the domain of origin for these entangled linkages. We arrange these eight terms into novel expressions for internal and external helicity (self) and internal-external helicity (mutual) based on their domain of origin. The implications of these linkages for interpreting magnetic energy are discussed and new boundary observables are proposed for tracking the evolution of the field that threads the boundary. |
| first_indexed | 2024-03-08T09:34:02Z |
| format | Article |
| id | doaj.art-9ddc5a09f58c43c191a813d959299723 |
| institution | Directory Open Access Journal |
| issn | 1538-4357 |
| language | English |
| last_indexed | 2024-03-08T09:34:02Z |
| publishDate | 2024-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | The Astrophysical Journal |
| spelling | doaj.art-9ddc5a09f58c43c191a813d9592997232024-01-30T15:10:07ZengIOP PublishingThe Astrophysical Journal1538-43572024-01-01961215610.3847/1538-4357/acf471Disentangling the Entangled Linkages of Relative Magnetic HelicityPeter W. Schuck0https://orcid.org/0000-0003-1522-4632Mark G. Linton1https://orcid.org/0000-0002-4459-7510Heliophysics Science Division, NASA Goddard Space Flight Center , 8800 Greenbelt Road, Greenbelt, MD 20771, USA ; peter.schuck@nasa.govUnited States Naval Research Laboratory , 4555 Overlook Avenue SW, Washington, DC 20375, USAMagnetic helicity, H , measures magnetic linkages in a volume. The early theoretical development of helicity focused on magnetically closed systems in ${ \mathcal V }$ bounded by $\partial { \mathcal V }$ . For magnetically closed systems, ${ \mathcal V }\in {{\mathbb{R}}}^{3}={ \mathcal V }+{{ \mathcal V }}^{\ast }$ , no magnetic flux threads the boundary, $\hat{{\boldsymbol{n}}}\cdot {\boldsymbol{B}}{| }_{\partial { \mathcal V }}=0$ . Berger & Field and Finn & Antonsen extended the definition of helicity to relative helicity, ${ \mathcal H }$ , for magnetically open systems where magnetic flux may thread the boundary. Berger expressed this relative helicity as two gauge-invariant terms that describe the self-helicity of the magnetic field that closes inside ${ \mathcal V }$ and the mutual helicity between the magnetic field that threads the boundary $\partial { \mathcal V }$ and the magnetic field that closes inside ${ \mathcal V }$ . The total magnetic field that permeates ${ \mathcal V }$ entangles magnetic fields that are produced by current sources J in ${ \mathcal V }$ with magnetic fields that are produced by current sources J ^∗ in ${{ \mathcal V }}^{\ast }$ . Building on this fact, we extend Berger's expressions for relative magnetic helicity to eight gauge-invariant quantities that simultaneously characterize both of these self and mutual helicities and attribute their origins to currents J in ${ \mathcal V }$ and/or J ^∗ in ${{ \mathcal V }}^{\ast }$ , thereby disentangling the domain of origin for these entangled linkages. We arrange these eight terms into novel expressions for internal and external helicity (self) and internal-external helicity (mutual) based on their domain of origin. The implications of these linkages for interpreting magnetic energy are discussed and new boundary observables are proposed for tracking the evolution of the field that threads the boundary.https://doi.org/10.3847/1538-4357/acf471Analytical mathematicsAstrophysical magnetismStellar magnetic fieldsSolar magnetic fieldsSolar magnetic reconnectionMagnetohydrodynamics |
| spellingShingle | Peter W. Schuck Mark G. Linton Disentangling the Entangled Linkages of Relative Magnetic Helicity The Astrophysical Journal Analytical mathematics Astrophysical magnetism Stellar magnetic fields Solar magnetic fields Solar magnetic reconnection Magnetohydrodynamics |
| title | Disentangling the Entangled Linkages of Relative Magnetic Helicity |
| title_full | Disentangling the Entangled Linkages of Relative Magnetic Helicity |
| title_fullStr | Disentangling the Entangled Linkages of Relative Magnetic Helicity |
| title_full_unstemmed | Disentangling the Entangled Linkages of Relative Magnetic Helicity |
| title_short | Disentangling the Entangled Linkages of Relative Magnetic Helicity |
| title_sort | disentangling the entangled linkages of relative magnetic helicity |
| topic | Analytical mathematics Astrophysical magnetism Stellar magnetic fields Solar magnetic fields Solar magnetic reconnection Magnetohydrodynamics |
| url | https://doi.org/10.3847/1538-4357/acf471 |
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