Gauss separation algorithm - Revision history

Citation bot: Alter: issue. Add: s2cid, issue, authors 1-1. Removed parameters. Formatted dashes. Some additions/deletions were parameter name changes. | Use this bot. Report bugs. | Suggested by Corvus florensis | #UCB_webform 901/2500

2023-12-08T23:01:59Z

Alter: issue. Add: s2cid, issue, authors 1-1. Removed parameters. Formatted dashes. Some additions/deletions were parameter name changes. | Use this bot. Report bugs. | Suggested by Corvus florensis | #UCB_webform 901/2500

← Previous revision		Revision as of 23:01, 8 December 2023
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	==References==		==References==
	*{{Citation\|last1=Glassmeier\|first1=K.-H.\|last2=Tsurutani\|first2=Bruce T.\|year=2014\|title=Carl Friedrich Gauss – General Theory of Terrestrial Magnetism – a revised translation of the German text\|journal=Hist. Geo Space Sci\|volume=5\|pages=11–62\|doi=10.5194/hgss-5-11-2014\|bibcode = 2014HGSS....5...11G\|doi-access=free}}.		*{{Citation\|last1=Glassmeier\|first1=K.-H.\|last2=Tsurutani\|first2=Bruce T.\|year=2014\|title=Carl Friedrich Gauss – General Theory of Terrestrial Magnetism – a revised translation of the German text\|journal=Hist. Geo Space Sci\|volume=5\|issue=1 \|pages=11–62\|doi=10.5194/hgss-5-11-2014\|bibcode = 2014HGSS....5...11G\|doi-access=free}}.
	*{{Citation\|last1=Olsen\|~~first~~=N.\|last2=Glassmeier\|first2=K.-H.\|last3=Jia\|first3=X.\|year=2010\|title=Separation of the Magnetic Field into External and Internal Parts\|journal=Space Science Reviews\|volume=152\|issue=~~1-4~~\|pages=135–157\|doi=10.1007/s11214-009-9563-0\|bibcode = 2010SSRv..152..135O}}.		*{{Citation\|last1=Olsen\|first1=N.\|last2=Glassmeier\|first2=K.-H.\|last3=Jia\|first3=X.\|year=2010\|title=Separation of the Magnetic Field into External and Internal Parts\|journal=Space Science Reviews\|volume=152\|issue=1–4\|pages=135–157\|doi=10.1007/s11214-009-9563-0\|bibcode = 2010SSRv..152..135O\|s2cid=39056038 }}.

	{{DEFAULTSORT:Magnetic Field}}		{{DEFAULTSORT:Magnetic Field}}

Nempnet: Added authors to footnote

2023-02-21T16:38:44Z

Added authors to footnote

← Previous revision		Revision as of 16:38, 21 February 2023
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	[[Carl Friedrich Gauss]], in his treatise ''Allgemeine Theorie des Erdmagnetismus'',<ref>{{harvnb\|Glassmeier\|2014}}</ref> presented a method, '''the Gauss separation algorithm''', of partitioning the [[magnetic field]] [[Vector (mathematics and physics)\|vector]], '''B'''<math>(r, \theta, \phi)</math>, measured over the surface of a sphere into two components, internal and external, arising from electric currents (per the [[Biot–Savart law]]) flowing in the volumes interior and exterior to the spherical surface, respectively. The method employs [[spherical harmonics]]. When radial currents flow through the surface of interest, the decomposition is more complex, involving the decomposition of the field into [[Poloidal–toroidal decomposition\|poloidal and toroidal]] components. In this case, an additional term (the toroidal component) accounts for the contribution of the radial current to the magnetic field on the surface.<ref>{{harvnb\|Olsen\|2010}}</ref>		[[Carl Friedrich Gauss]], in his treatise ''Allgemeine Theorie des Erdmagnetismus'',<ref>{{harvnb\|Glassmeier\|Tsurutani\|2014}}</ref> presented a method, '''the Gauss separation algorithm''', of partitioning the [[magnetic field]] [[Vector (mathematics and physics)\|vector]], '''B'''<math>(r, \theta, \phi)</math>, measured over the surface of a sphere into two components, internal and external, arising from electric currents (per the [[Biot–Savart law]]) flowing in the volumes interior and exterior to the spherical surface, respectively. The method employs [[spherical harmonics]]. When radial currents flow through the surface of interest, the decomposition is more complex, involving the decomposition of the field into [[Poloidal–toroidal decomposition\|poloidal and toroidal]] components. In this case, an additional term (the toroidal component) accounts for the contribution of the radial current to the magnetic field on the surface.<ref>{{harvnb\|Olsen\|Glassmeier\|Jia\|2010}}</ref>

	The method is commonly used in studies of terrestrial and planetary magnetism, to relate measurements of magnetic fields either at the planetary surface or in orbit above the planet to currents flowing in the planet's interior (internal currents) and its magnetosphere (external currents). Ionospheric currents would be exterior to the planet's surface, but might be internal currents from the vantage point of a satellite orbiting the planent.		The method is commonly used in studies of terrestrial and planetary magnetism, to relate measurements of magnetic fields either at the planetary surface or in orbit above the planet to currents flowing in the planet's interior (internal currents) and its magnetosphere (external currents). Ionospheric currents would be exterior to the planet's surface, but might be internal currents from the vantage point of a satellite orbiting the planent.

OAbot: Open access bot: doi added to citation with #oabot.

2023-01-29T03:10:50Z

Open access bot: doi added to citation with #oabot.

← Previous revision		Revision as of 03:10, 29 January 2023
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	==References==		==References==
	*{{Citation\|last1=Glassmeier\|first1=K.-H.\|last2=Tsurutani\|first2=Bruce T.\|year=2014\|title=Carl Friedrich Gauss – General Theory of Terrestrial Magnetism – a revised translation of the German text\|journal=Hist. Geo Space Sci\|volume=5\|pages=11–62\|doi=10.5194/hgss-5-11-2014\|bibcode = 2014HGSS....5...11G}}.		*{{Citation\|last1=Glassmeier\|first1=K.-H.\|last2=Tsurutani\|first2=Bruce T.\|year=2014\|title=Carl Friedrich Gauss – General Theory of Terrestrial Magnetism – a revised translation of the German text\|journal=Hist. Geo Space Sci\|volume=5\|pages=11–62\|doi=10.5194/hgss-5-11-2014\|bibcode = 2014HGSS....5...11G\|doi-access=free}}.
	*{{Citation\|last1=Olsen\|first=N.\|last2=Glassmeier\|first2=K.-H.\|last3=Jia\|first3=X.\|year=2010\|title=Separation of the Magnetic Field into External and Internal Parts\|journal=Space Science Reviews\|volume=152\|issue=1-4\|pages=135–157\|doi=10.1007/s11214-009-9563-0\|bibcode = 2010SSRv..152..135O}}.		*{{Citation\|last1=Olsen\|first=N.\|last2=Glassmeier\|first2=K.-H.\|last3=Jia\|first3=X.\|year=2010\|title=Separation of the Magnetic Field into External and Internal Parts\|journal=Space Science Reviews\|volume=152\|issue=1-4\|pages=135–157\|doi=10.1007/s11214-009-9563-0\|bibcode = 2010SSRv..152..135O}}.

Brianwelsch: Minor, clarification about status of ionospheric currents being internal or external, depending on observer's vantage.

2022-07-21T17:23:17Z

Minor, clarification about status of ionospheric currents being internal or external, depending on observer's vantage.

← Previous revision		Revision as of 17:23, 21 July 2022
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	[[Carl Friedrich Gauss]], in his treatise ''Allgemeine Theorie des Erdmagnetismus'',<ref>{{harvnb\|Glassmeier\|2014}}</ref> presented a method, '''the Gauss separation algorithm''', of partitioning the [[magnetic field]] [[Vector (mathematics and physics)\|vector]], '''B'''<math>(r, \theta, \phi)</math>, measured over the surface of a sphere into two components, internal and external, arising from electric currents (per the [[Biot–Savart law]]) flowing in the volumes interior and exterior to the spherical surface, respectively. The method employs [[spherical harmonics]]. When radial currents flow through the surface of interest, the decomposition is more complex, involving the decomposition of the field into [[Poloidal–toroidal decomposition\|poloidal and toroidal]] components. In this case, an additional term (the toroidal component) accounts for the contribution of the radial current to the magnetic field on the surface.<ref>{{harvnb\|Olsen\|2010}}</ref>		[[Carl Friedrich Gauss]], in his treatise ''Allgemeine Theorie des Erdmagnetismus'',<ref>{{harvnb\|Glassmeier\|2014}}</ref> presented a method, '''the Gauss separation algorithm''', of partitioning the [[magnetic field]] [[Vector (mathematics and physics)\|vector]], '''B'''<math>(r, \theta, \phi)</math>, measured over the surface of a sphere into two components, internal and external, arising from electric currents (per the [[Biot–Savart law]]) flowing in the volumes interior and exterior to the spherical surface, respectively. The method employs [[spherical harmonics]]. When radial currents flow through the surface of interest, the decomposition is more complex, involving the decomposition of the field into [[Poloidal–toroidal decomposition\|poloidal and toroidal]] components. In this case, an additional term (the toroidal component) accounts for the contribution of the radial current to the magnetic field on the surface.<ref>{{harvnb\|Olsen\|2010}}</ref>

	The method is commonly used in studies of terrestrial and planetary magnetism, to relate measurements of magnetic fields either at the planetary surface or in orbit above the planet to currents flowing in the planet's interior (internal currents) and its magnetosphere ~~and ionosphere~~ (external currents).		The method is commonly used in studies of terrestrial and planetary magnetism, to relate measurements of magnetic fields either at the planetary surface or in orbit above the planet to currents flowing in the planet's interior (internal currents) and its magnetosphere (external currents). Ionospheric currents would be exterior to the planet's surface, but might be internal currents from the vantage point of a satellite orbiting the planent.

	==Notes==		==Notes==

Brianwelsch: Minor, added link to poloidal-toroidal decomposition wiki page, as this technique is needed when radial currents cross the surface of interest.

2022-07-21T16:48:38Z

Minor, added link to poloidal-toroidal decomposition wiki page, as this technique is needed when radial currents cross the surface of interest.

← Previous revision		Revision as of 16:48, 21 July 2022
Line 1:		Line 1:
	[[Carl Friedrich Gauss]], in his treatise ''Allgemeine Theorie des Erdmagnetismus'',<ref>{{harvnb\|Glassmeier\|2014}}</ref> presented a method, '''the Gauss separation algorithm''', of partitioning the [[magnetic field]] [[Vector (mathematics and physics)\|vector]], '''B'''<math>(r, \theta, \phi)</math>, measured over the surface of a sphere into two components, internal and external, arising from electric currents (per the [[Biot–Savart law]]) flowing in the volumes interior and exterior to the spherical surface, respectively. The method employs [[spherical harmonics]]. When radial currents flow through the surface of interest, the decomposition is more complex, and ~~must~~ ~~include~~ an additional term ~~accounting~~ for the contribution of the radial current to the magnetic field on the surface.<ref>{{harvnb\|Olsen\|2010}}</ref>		[[Carl Friedrich Gauss]], in his treatise ''Allgemeine Theorie des Erdmagnetismus'',<ref>{{harvnb\|Glassmeier\|2014}}</ref> presented a method, '''the Gauss separation algorithm''', of partitioning the [[magnetic field]] [[Vector (mathematics and physics)\|vector]], '''B'''<math>(r, \theta, \phi)</math>, measured over the surface of a sphere into two components, internal and external, arising from electric currents (per the [[Biot–Savart law]]) flowing in the volumes interior and exterior to the spherical surface, respectively. The method employs [[spherical harmonics]]. When radial currents flow through the surface of interest, the decomposition is more complex, involving the decomposition of the field into [[Poloidal–toroidal decomposition\|poloidal and toroidal]] components. In this case, an additional term (the toroidal component) accounts for the contribution of the radial current to the magnetic field on the surface.<ref>{{harvnb\|Olsen\|2010}}</ref>

	The method is commonly used in studies of terrestrial and planetary magnetism, to relate measurements of magnetic fields either at the planetary surface or in orbit above the planet to currents flowing in the planet's interior (internal currents) and its magnetosphere and ionosphere (external currents).		The method is commonly used in studies of terrestrial and planetary magnetism, to relate measurements of magnetic fields either at the planetary surface or in orbit above the planet to currents flowing in the planet's interior (internal currents) and its magnetosphere and ionosphere (external currents).

Brianwelsch: Denoted article as a stub, chose electromagnetism as closest stub topic among existing physics stubs, added geomagnetism category

2022-07-21T12:04:37Z

Denoted article as a stub, chose electromagnetism as closest stub topic among existing physics stubs, added geomagnetism category

← Previous revision		Revision as of 12:04, 21 July 2022
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	{{DEFAULTSORT:Magnetic Field}}		{{DEFAULTSORT:Magnetic Field}}
	[[Category:Magnetism]]		[[Category:Magnetism]]
			[[Category:Geomagnetism]]
	[[Category:Physical quantities]]		[[Category:Physical quantities]]
	[[Category:Harmonic analysis]]		[[Category:Harmonic analysis]]


			{{electromagnetism-stub}}

Brianwelsch: Created page to discuss the Gauss separation algorithm, mention its applications, and link to two useful references.

2022-07-21T03:34:16Z

Created page to discuss the Gauss separation algorithm, mention its applications, and link to two useful references.

New page

[[Carl Friedrich Gauss]], in his treatise ''Allgemeine Theorie des Erdmagnetismus'',<ref>{{harvnb|Glassmeier|2014}}</ref> presented a method, '''the Gauss separation algorithm''', of partitioning the [[magnetic field]] [[Vector (mathematics and physics)|vector]], '''B'''<math>(r, \theta, \phi)</math>, measured over the surface of a sphere into two components, internal and external, arising from electric currents (per the [[Biot–Savart law]]) flowing in the volumes interior and exterior to the spherical surface, respectively. The method employs [[spherical harmonics]]. When radial currents flow through the surface of interest, the decomposition is more complex, and must include an additional term accounting for the contribution of the radial current to the magnetic field on the surface.<ref>{{harvnb|Olsen|2010}}</ref>

The method is commonly used in studies of terrestrial and planetary magnetism, to relate measurements of magnetic fields either at the planetary surface or in orbit above the planet to currents flowing in the planet's interior (internal currents) and its magnetosphere and ionosphere (external currents).

==Notes==
<references/>

==References==
*{{Citation|last1=Glassmeier|first1=K.-H.|last2=Tsurutani|first2=Bruce T.|year=2014|title=Carl Friedrich Gauss – General Theory of Terrestrial Magnetism – a revised translation of the German text|journal=Hist. Geo Space Sci|volume=5|pages=11–62|doi=10.5194/hgss-5-11-2014|bibcode = 2014HGSS....5...11G}}.
*{{Citation|last1=Olsen|first=N.|last2=Glassmeier|first2=K.-H.|last3=Jia|first3=X.|year=2010|title=Separation of the Magnetic Field into External and Internal Parts|journal=Space Science Reviews|volume=152|issue=1-4|pages=135–157|doi=10.1007/s11214-009-9563-0|bibcode = 2010SSRv..152..135O}}.

{{DEFAULTSORT:Magnetic Field}}
[[Category:Magnetism]]
[[Category:Physical quantities]]
[[Category:Harmonic analysis]]