Modeling the Magnetic Field of the Inner Corona in a Radially Expanding Solar Wind
The magnetic field in the interplanetary medium is formed by the action of magnetic field sources on the photosphere of the Sun and currents in the expanding atmosphere of the Sun and the solar wind. In turn, the high-speed plasma flow changes the configuration of the magnetic field lines. The probl...
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MDPI AG
2023-01-01
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| Online Access: | https://www.mdpi.com/2624-8174/5/1/12 |
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| author | Andrey G. Tlatov Ivan Berezin |
| author_facet | Andrey G. Tlatov Ivan Berezin |
| author_sort | Andrey G. Tlatov |
| collection | DOAJ |
| description | The magnetic field in the interplanetary medium is formed by the action of magnetic field sources on the photosphere of the Sun and currents in the expanding atmosphere of the Sun and the solar wind. In turn, the high-speed plasma flow changes the configuration of the magnetic field lines. The problem of determining the parameters of the magnetic field near the Sun is thus a three-dimensional problem of the interaction of the magnetic field and the plasma of the solar wind. We present analytical expressions for calculating the total magnetic field vector <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mover accent="true"><mi>B</mi><mo>→</mo></mover><mrow><mo>(</mo><mi>r</mi><mo>,</mo><mi> </mi><mi>θ</mi><mo>,</mo><mi> </mi><mi>ϕ</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> (in spherical coordinates) for a radially expanding solar wind flow of finite conductivity. The parameters of the solar wind are given in the form of a dimensionless magnetic Reynolds number given as an arbitrary function of the radius, <i>r</i>: <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>R</mi><mi mathvariant="normal">m</mi></msub></semantics></math></inline-formula> = <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>r</mi><mi>σ</mi><mi>μ</mi><mi>v</mi><mo>=</mo><mi>ξ</mi><mo>(</mo><mi>r</mi><mo>)</mo></mrow></semantics></math></inline-formula>, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>σ</mi></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>μ</mi></semantics></math></inline-formula>, and <i>v</i> denote, respectively, the conductivity, magnetic permeability, and velocity of the solar wind. The solution for the magnetic field components is obtained in the form of a decomposition in spherical functions and a radial part depending on the distance from the Sun. Examples of calculations of the configuration of magnetic fields and structures of the solar corona for the solar eclipse of 21 August 2017 are given. |
| first_indexed | 2024-03-11T06:01:25Z |
| format | Article |
| id | doaj.art-97052190c24d4427b1fc9097b34004fd |
| institution | Directory Open Access Journal |
| issn | 2624-8174 |
| language | English |
| last_indexed | 2024-03-11T06:01:25Z |
| publishDate | 2023-01-01 |
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| spelling | doaj.art-97052190c24d4427b1fc9097b34004fd2023-11-17T13:20:15ZengMDPI AGPhysics2624-81742023-01-015116116710.3390/physics5010012Modeling the Magnetic Field of the Inner Corona in a Radially Expanding Solar WindAndrey G. Tlatov0Ivan Berezin1Kislovodsk Mountain Astronomical Station of the Pulkovo Observatory, Gagarina Str. 100, 357700 Kislovodsk, RussiaKislovodsk Mountain Astronomical Station of the Pulkovo Observatory, Gagarina Str. 100, 357700 Kislovodsk, RussiaThe magnetic field in the interplanetary medium is formed by the action of magnetic field sources on the photosphere of the Sun and currents in the expanding atmosphere of the Sun and the solar wind. In turn, the high-speed plasma flow changes the configuration of the magnetic field lines. The problem of determining the parameters of the magnetic field near the Sun is thus a three-dimensional problem of the interaction of the magnetic field and the plasma of the solar wind. We present analytical expressions for calculating the total magnetic field vector <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mover accent="true"><mi>B</mi><mo>→</mo></mover><mrow><mo>(</mo><mi>r</mi><mo>,</mo><mi> </mi><mi>θ</mi><mo>,</mo><mi> </mi><mi>ϕ</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> (in spherical coordinates) for a radially expanding solar wind flow of finite conductivity. The parameters of the solar wind are given in the form of a dimensionless magnetic Reynolds number given as an arbitrary function of the radius, <i>r</i>: <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>R</mi><mi mathvariant="normal">m</mi></msub></semantics></math></inline-formula> = <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>r</mi><mi>σ</mi><mi>μ</mi><mi>v</mi><mo>=</mo><mi>ξ</mi><mo>(</mo><mi>r</mi><mo>)</mo></mrow></semantics></math></inline-formula>, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>σ</mi></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>μ</mi></semantics></math></inline-formula>, and <i>v</i> denote, respectively, the conductivity, magnetic permeability, and velocity of the solar wind. The solution for the magnetic field components is obtained in the form of a decomposition in spherical functions and a radial part depending on the distance from the Sun. Examples of calculations of the configuration of magnetic fields and structures of the solar corona for the solar eclipse of 21 August 2017 are given.https://www.mdpi.com/2624-8174/5/1/12solar windsolar coronasolar magnetic field model |
| spellingShingle | Andrey G. Tlatov Ivan Berezin Modeling the Magnetic Field of the Inner Corona in a Radially Expanding Solar Wind Physics solar wind solar corona solar magnetic field model |
| title | Modeling the Magnetic Field of the Inner Corona in a Radially Expanding Solar Wind |
| title_full | Modeling the Magnetic Field of the Inner Corona in a Radially Expanding Solar Wind |
| title_fullStr | Modeling the Magnetic Field of the Inner Corona in a Radially Expanding Solar Wind |
| title_full_unstemmed | Modeling the Magnetic Field of the Inner Corona in a Radially Expanding Solar Wind |
| title_short | Modeling the Magnetic Field of the Inner Corona in a Radially Expanding Solar Wind |
| title_sort | modeling the magnetic field of the inner corona in a radially expanding solar wind |
| topic | solar wind solar corona solar magnetic field model |
| url | https://www.mdpi.com/2624-8174/5/1/12 |
| work_keys_str_mv | AT andreygtlatov modelingthemagneticfieldoftheinnercoronainaradiallyexpandingsolarwind AT ivanberezin modelingthemagneticfieldoftheinnercoronainaradiallyexpandingsolarwind |