en>Quondum: /* Four-vector formulation */ italic variable

2015-01-12T19:58:08Z

Four-vector formulation: italic variable

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	~~[[File:Magnetopause.jpg\|thumb\|350px\| Artistic rendition of the Earth's magnetopause. The magnetopause is where the pressure from the solar wind~~ and ~~the planet's magnetic field are equal. The position of the Sun would be far to the left in this image]]~~

	~~The '''magnetopause'''~~ is ~~the abrupt boundary between a [[magnetosphere]] and the surrounding [[Plasma (physics)\|plasma]]~~. For [[planetary science]], the magnetopause is the boundary between the planet’s magnetic field and the [[solar wind]]. The location of the magnetopause is determined by the balance between the pressure of the dynamic planetary magnetic field and the dynamic pressure of the solar wind. As the solar wind pressure increases and decreases, the magnetopause moves inward and outward in ~~response. Waves~~ (~~ripples and flapping motion~~) ~~along the magnetopause move in the direction of the solar wind flow in response to small scale variations in the solar wind pressure and to [[Kelvin-Helmholtz instability]]~~.

	The solar wind is supersonic and passes through a [[bow shock]] where the direction of flow is changed so that most of the solar wind plasma is deflected to either side of the magnetopause, much like water is deflected before the bow of a ship. The zone of shocked solar wind plasma is the [[magnetosheath]]. At Earth and all the other planets with intrinsic magnetic fields, some solar wind plasma succeeds in entering and becoming trapped within the magnetosphere. At Earth, the solar wind plasma which enters the magnetosphere forms the [[plasma sheet]]. The amount of solar wind plasma and energy which enters the magnetosphere is regulated by the orientation of the [[interplanetary magnetic field]] which is embedded in the solar wind.

	The Sun and other stars with magnetic fields and stellar winds have a solar magnetopause or [[Heliopause (astronomy)\|heliopause]] where the stellar environment is bounded by the interstellar environment.

	~~==Characteristics==~~
	[[File:dipole-and-image-dipole.png\|thumb\|300px\|Schematic representation of a planetary dipole magnetic field in a vacuum (right side) deformed by a region of plasma with infinite conductivity. The Sun is to the left. The configuration is equivalent to an image dipole (green arrow) being placed at twice the distance from the planetary dipole to the interaction boundary.<ref name="CB1940">{{cite book\|title=Geomagnetism, Vol. II\|year=1940\|publisher=Oxford Univ. Press\|author=Sydney Chapman\|coauthors=J. Bartels}}</ref>]]

	Prior to the age of space exploration, interplanetary space was considered to be a vacuum. The coincidence of the [[Carrington super flare]] and the super geomagnetic event of 1859 was evidence that plasma was ejected from the Sun during a flare event. Chapman and Ferraro <~~ref~~>~~{{cite journal\|last=Chapman\|first=Sidney\|coauthors=V. C. A. Ferraro\|title=A new theory of magnetic storms\|journal=Terrestrial Magnetism\|year=1931\|volume=36\|pages=77–97}}~~<~~/ref~~><ref>{{cite journal\|last=Chapman\|first=Sidney\|coauthors=V. C. A. Ferraro\|title=A new theory of magnetic storms\|journal=Terrestrial Magnetism\|year=1931\|volume=36\|pages=171–186}}</ref><ref>{{cite journal\|last=Chapman\|first=Sidney\|coauthors=V. C. A. Ferraro\|title=A new theory of magnetic storms, II. The main phase,\|journal=Terrestrial Magnetism\|year=1933\|volume=38\|pages=79}}</ref><ref>{{cite journal\|last=Chapman\|first=Sidney\|coauthors=V. C. A. Ferraro\|title= The theory of the first phase of the geomagnetic storm \|journal=Terrestrial Magnetism\|year=1940\|volume=45\|pages=245}}</ref> proposed that a plasma was emitted by the Sun in a burst as part of a flare event which disturbed the planet's magnetic field in a manner known as a geomagnetic storm. The collision frequency of particles in the plasma in the interplanetary medium is very low and the electrical conductivity is so high that it could be approximated to an infinite conductor. A magnetic field in a vacuum cannot penetrate a volume with infinite conductivity. Chapman and Bartels (1940)<ref name="CB1940" /> illustrated this concept by postulating a plate with infinite conductivity placed on the dayside of a planet’s dipole as shown in the schematic. The field lines on the dayside are bent. At low latitudes, the magnetic field lines are pushed inward. At high latitudes, the magnetic field lines are push backwards and over the polar regions. The boundary between the region dominated by the planet’s magnetic field (i.e., the [[magnetosphere]]) and the plasma in the interplanetary medium is the magnetopause. The configuration equivalent to a flat, infinitely conductive plate is achieved by placing an image dipole (green arrow at left of schematic) at twice the distance from the planet’s dipole to the magnetopause along the planet-Sun line. Since the solar wind is continuously flowing outward, the magnetopause above, below and to the sides of the planet are swept backward into the geomagnetic tail as shown in the artist’s concept. The region (shown in pink in the schematic) which separates field lines from the planet which pushed inward from those which are pushed backward over the poles is an area of weak magnetic field or day-side cusp. Solar wind particles can enter the planet’s magnetosphere through the cusp region. Because the solar wind exists are all time and not just times of solar flares, the magnetopause is a permanent feature of the space near any planet with a magnetic field.

	The magnetic field lines of the planet’s magnetic field are not stationary. They are continuously joining or merging with magnetic field lines of the interplanetary magnetic field. The joined field lines are swept back over the poles into the planetary magnetic tail. In the tail, the field lines from the planet’s magnetic field are re-joined and start moving toward night-side of the planet. The physics of this process was first explain by Dungey (1961) .<ref>{{cite journal\|last=Dungey\|first=J. W.\|title=Interplanetary Magnetic Field and the Auroral Zones\|journal=Phys. Rev. Lett.\|date=Jan 1961\|volume=6\|issue=2\|pages=47–48\|url=http://~~prl.aps.org/\|accessdate=12 July 2011\|bibcode = 1961PhRvL...6...47D \|doi = 10.1103/PhysRevLett~~.6.~~47 }}<~~/~~ref>~~

	If one assumed that magnetopause was just a boundary between a magnetic field in a vacuum and a plasma with a weak magnetic field embedded in it, then the magnetopause would be defined by electrons and ions penetrating one gyroradius into the magnetic field domain. Since the gyro-~~motion of electrons and ions is in opposite directions, an electric current flows along the boundary~~. The actual magnetopause is much more complex.<ref>Physics of the Magnetopause, Edited by P. Song, B. U. Ö. Sonnerup, M. F. Thomsen, American Geophys. Union, Washington, D.C., Geophysical Monograph Series, Volume 90, 1995. 447 pages, ISBN 0-87590-047-~~X</ref>~~

	~~==Estimating the standoff distance to the magnetopause==~~
	If the pressure from particles within the magnetosphere is neglected, it is possible to estimate the distance to the part of the magnetosphere that faces the [[Sun]]. The condition governing this position is that the dynamic [[ram pressure]] from the [[solar wind]] is equal to the magnetic pressure from the [[Earth]]'s [[magnetic field]].
	:<math>(\rho v^2)_{sw}\approx \left( \frac{4 B(r)^2}{2\mu_0} \right) _m</math><ref group="note">The reason for the factor of 4 is because the magnetic field strength just inside the magnetopause is twice the dipole value for a planar magnetopause</ref> where <math>\rho</math> and <math>v</math> are the [[density]] and [[velocity]] of the [[solar wind]], and
	~~''B''(''r'') is the [[Magnetic field\|Magnetic field strength of the planet]] in [[SI]] units (''B'' in [[Tesla (unit)\|T]], [[Permeability constant\|μ<sub>0</sub>]] in [[Henry (unit)\|H]]/[[metre\|m]])~~

	~~Since the [[dipole]] magnetic field strength varies with distance as <math>1/r^3</math> the magnetic field strength can be written as <math>B(r)=B_0/r^3</math>.~~
	~~:<math>\rho v^2\approx \frac{2 B_0^2}{r^6 \mu_0}</math>~~.
	~~Solving this equation for r leads to an estimate of the distance~~
	~~:<math>r\approx \sqrt[6]{\frac{2 B_0^2}{\mu_0 \rho v^2}}</math>~~

	~~The distance from Earth~~ to ~~the subsolar magnetopause varies over time due to solar activity, but typical distances range from 6 -~~ 15 R<math>_{\oplus}</math>. Empirical models<ref>Magnetopause shape as a bivariate function of interplanetary magnetic field Bz and solar wind Dynamic pressure, E. Roelof and D. Sibeck, J. Geophys. Res., 98, A12, {{doi\|10.1029/93JA02362}}, 1993</ref><ref>A new functional form to study the solar wind control of the magnetopause size and shape, J.‐H. Shue, J. Chao, H. Fu, C. Russell, P. Song, K. Khurana, and H. Singer, J. Geophys. Res., 102, A5, {{doi\|10.1029/97JA00196}}, 1997</ref> using real-time [[solar wind]] data can provide a real-time estimate of the magnetopause location. A [[bow shock]] stands upstream from the magnetopause. It serves to decelerate and deflect the solar wind flow before it reaches the magnetopause <ref>Imke de Pater and Jack J. Lissauer: ''Planetary Sciences'', page 261. Cambridge University Press, 2001. ISBN 0-521-48219-4</ref>

	~~==Solar System magnetopauses==~~
	~~{\| class="wikitable sortable"~~
	\|+ Overview of the Solar System magnetopauses<ref>{{cite book\|title='Planetary Magnetospheres,' in The Encyclopedia of the Solar System\|year=2006\|publisher=Academic Press\|isbn= 978-0-12-088589-3\|author=M. K. Kivelson\|edition=2nd\|coauthors=F. Bagenal\|editor=P. Weissman, L.-A. McFadden, and T. Johnson\|page=477}}</ref>
	\|-
	! Planet!! Number !! Magnetic moment <ref group="note">compared to Earth's magnetic moment (7.906 x 10<sup>31</sup> gauss m<sup>-3</sup>)</ref> !! Magnetopause distance <ref group="note">typical distance between magnetopause and magnetosphere in planet radii</ref>!! Observed size of the [[magnetosphere]]<ref group="note">in planet radii</ref>\|\| variance of [[magnetosphere]]<ref group="note">in planet radii, the [[magnetosphere]] varies mainly in response to solar wind dynamic pressure and interplanetary magnetic field orientation</ref>
	\|-
	~~\| [[Image:Mercury symbol.svg\|25px\|Mercury]] [[Mercury (planet)\|Mercury]] \|\|1\|\|0.0004 \|\| 1.5 \|\| 1.4\|\|0~~
	\|-
	~~\| [[Image:Venus symbol.svg\|25px\|Venus]] [[Venus]] \|\|2\|\| 0 \|\| 0\|\| 0\|\|0~~
	\|-
	~~\| [[Image:Earth symbol.svg\|25px\|Earth]] [[Earth]]\|\|3\|\| 1 \|\| 10 \|\| 10\|\|2~~
	\|-
	~~\| [[Image:Mars symbol.svg\|25px\|Mars]] [[Mars]]\|\|4\|\| 0 \|\| 0 \|\| 0\|\|0~~
	\|-
	~~\| [[Image:Jupiter symbol.svg\|25px\|Jupiter]] [[Jupiter]] \|\|5\|\| 20000 \|\| 42 \|\| 75\|\|25~~
	\|-
	~~\| [[Image:Saturn symbol.svg\|25px\|Saturn]] [[Saturn]] \|\|6\|\| 600 \|\| 19\|\| 19\|\|3~~
	\|-
	~~\| [[Image:Uranus symbol.svg\|25px\|Uranus]] [[Uranus]]\|\|7\|\| 50 \|\| 25 \|\| 18\|\|0~~
	\|-
	~~\| [[Image:Neptune symbol.svg\|25px\|Neptune]] [[Neptune]]\|\|8\|\| 25 \|\| 24 \|\| 24.5\|\|1.5~~
	\|}

	Research on the magnetopause is conducted using the LMN coordinate system (which is set of axes like XYZ). N points normal to the magnetopause outward to the magnetosheath, L lies along the projection of the dipole axis onto the magnetopause (positive northward), and M completes the triad by pointing dawnward.

	Venus and Mars do not have a planetary magnetic field and do not have a magnetopause. The solar wind interacts with the planet’s atmosphere<ref>{{cite book\|title=Venus and Mars: Atmospheres, Ionospheres and Solar Wind Interactions, Geophysical Monograph Series, Volume 66\|year=1992\|publisher=Am. Geophys. Union\|location=Washington, DC\|isbn=0-87590-032-1\|pages=448\|editor=J. Luhmann, M. Tatrallyay, and R. Pepin}}</ref> and a void is created behind the planet. In the case of the Earth’s moon and other bodies without a magnetic field or atmosphere, the body’s surface interacts with the solar wind and a void is created behind the body.

	~~== See also ==~~
	* [[Heliopause (astronomy)\|Heliopause]]
	* [[Shock wave]]
	* [[Solar system]]
	* For applications to [[spacecraft propulsion]], see [[magnetic sail]].
	* [[List of plasma (physics) articles]]

	~~== Notes ==~~
	~~<references group="note" />~~

	~~== References ==~~
	*{{cite book\|title=Planetary Atmospheres}}
	~~{{reflist}}~~

	~~{{Magnetosphere}}~~

	~~[[Category:Space plasmas]]~~
	~~[[Category:Plasma physics]~~]

en>RomanSpa: /* History of the concept */

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History of the concept

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en>Quondum: /* Four-vector formulation */ italic variable

en>RomanSpa: /* History of the concept */

80.187.233.186 at 14:14, 1 September 2012