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In [[plasma physics]], '''magnetic helicity''' is the extent to which a [[magnetic field]] "wraps around itself". It is a generalization of the topological concept of [[linking number]] to the differential quantities required to describe the magnetic field. As with many quantities in electromagnetism, magnetic helicity (which describes magnetic field lines) is closely related to fluid mechanical helicity (which describes fluid flow lines).
 
If magnetic field lines follow the strands of a twisted [[rope]], this configuration would have nonzero magnetic helicity; left-handed ropes would have negative values and right-handed ropes would have positive values.{{Clarifyme|date=February 2009}}
 
Formally,
:<math> H = \int {\mathbf A}\cdot{\mathbf B}\,d^3{\mathbf r} </math>
 
where
:<math>{\mathbf B}</math> is the magnetic field strength
:<math>{\mathbf B}=\nabla\times{\mathbf A}</math>;
:<math>\mathbf A</math> is the [[vector potential]] of <math>{\mathbf B}</math>
 
Magnetic helicity has units of Wb<sup>2</sup> ([[Weber (unit)|weber]]s squared).  It is a [[conservation law|conserved quantity]] in electromagnetic fields, even when [[magnetic reconnection]] dissipates [[energy]].   The concept is useful in [[Sun|solar dynamics]] and in [[hydromagnetic dynamo theory]].<ref>
{{cite journal
|last=Brandenburg |first=A.
|year=2009
|title=Hydromagnetic Dynamo Theory
|url=http://www.scholarpedia.org/wiki/index.php?title=Hydromagnetic_dynamo_theory&action=cite&rev=73469
|journal=[[Scholarpedia]]
|volume=2 |issue=3 |pages=2309
  |doi=10.4249/scholarpedia.2309
|id=rev #73469
}}</ref> Magnetic helicity is a gauge-dependent quantity, because <math>\mathbf A</math> can be redefined by adding a gradient to it (gauge transformation). However, for perfectly conducting boundaries or periodic systems without a net magnetic flux, the magnetic helicity is gauge invariant. A gauge-invariant ''relative helicity'' has been defined for volumes with non-zero magnetic flux on their boundary surfaces<ref>
{{cite journal
|last1=Berger |first1=M.A.
|year=1999
|title=Introduction to magnetic helicity
|volume=41 |issue=12B |pages=167
|journal=[[Plasma Physics and Controlled Fusion]]
|bibcode=1999PPCF...41..167B
|doi=10.1088/0741-3335/41/12B/312
}}</ref> If the magnetic field is turbulent and weakly inhomogeneous a magnetic helicity ''density'' and its associated flux can be defined in terms of the density of field line linkages.<ref>
{{cite journal
|last=Subramanian |first=K.
|last2=Brandenburg |first2=A.
|year=2006
|title=Magnetic helicity density and its flux in weakly inhomogeneous turbulence
|journal=[[The Astrophysical Journal Letters]]
|volume= 648 |issue= |pages=L71–L74
|arxiv=astro-ph/0509392
|bibcode=2006ApJ...648L..71S
  |doi=10.1086/507828
}}</ref>
 
==References==
{{reflist}}
==External links==
* A. A. Pevtsov's [http://www4.nso.edu/staff/apevtsov/webhelicity.html Helicity on the Web] Page
* Mitch Berger's [http://emps.exeter.ac.uk/mathematics/staff/mab215/publications Publications] Page
 
[[Category:Physical quantities]]
[[Category:Plasma physics]]

Revision as of 09:03, 6 December 2013

In plasma physics, magnetic helicity is the extent to which a magnetic field "wraps around itself". It is a generalization of the topological concept of linking number to the differential quantities required to describe the magnetic field. As with many quantities in electromagnetism, magnetic helicity (which describes magnetic field lines) is closely related to fluid mechanical helicity (which describes fluid flow lines).

If magnetic field lines follow the strands of a twisted rope, this configuration would have nonzero magnetic helicity; left-handed ropes would have negative values and right-handed ropes would have positive values.Template:Clarifyme

Formally,

H=∫A⋅Bd3r

where

B is the magnetic field strength
B=∇×A;
A is the vector potential of B

Magnetic helicity has units of Wb2 (webers squared). It is a conserved quantity in electromagnetic fields, even when magnetic reconnection dissipates energy. The concept is useful in solar dynamics and in hydromagnetic dynamo theory.[1] Magnetic helicity is a gauge-dependent quantity, because A can be redefined by adding a gradient to it (gauge transformation). However, for perfectly conducting boundaries or periodic systems without a net magnetic flux, the magnetic helicity is gauge invariant. A gauge-invariant relative helicity has been defined for volumes with non-zero magnetic flux on their boundary surfaces[2] If the magnetic field is turbulent and weakly inhomogeneous a magnetic helicity density and its associated flux can be defined in terms of the density of field line linkages.[3]

References

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  2. ↑ One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

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    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
  3. ↑ One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

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