396:. This set forms a hollow tube. The tube follows the field lines, possibly turning, twisting, and changing its cross sectional size and shape as the field lines converge or diverge. Since no field lines pass through the tube walls there is no flux through the walls of the tube, so all the field lines enter and leave through the end surfaces. Thus a flux tube divides all the field lines into two sets; those passing through the inside of the tube, and those outside. Consider the volume bounded by the tube and any two surfaces
2786:
188:
31:
228:
2611:
131:. It is a graphical visual aid for visualizing a magnetic field. Since no magnetic flux passes through the sides of the tube, the flux through any cross section of the tube is equal, and the flux entering the tube at one end is equal to the flux leaving the tube at the other. Both the cross-sectional area of the tube and the magnetic field strength may vary along the length of the tube, but the
568:. In other words, the flux within the tube through any surface intersecting the tube is equal, the tube encloses a constant quantity of flux along its length. The strength (magnitude) of the vector field, and the cross sectional area of the tube varies along its length, but the surface integral of the field over any surface spanning the tube is equal.
1601:
1469:
2737:
pressure in the flux tube to decrease, known as the plasma density depletion region. If there is a significant difference in the temperatures in the flux tube and the surroundings, there is a decrease in plasma pressure as well as a decrease in the plasma density causing some of the magnetic field to
1474:
2484:
1231:
1347:
583:
are divergenceless, magnetic flux tubes have this property, so flux tubes are mainly used as an aid in visualizing magnetic fields. However flux tubes can also be useful for visualizing other vector fields in regions of zero divergence, such as
2757:
and ranges of shapes from the behavior of the magnetic flux tube. These flux tubes confine plasma and are characterized as isolated. The confined magnetic field strength varies from 0.1 to 10 G with diameters ranging from 200 to 300 km.
2343:
663:
If upon any surface which cuts the lines of fluid motion we draw a closed curve, and if from every point of this curve we draw lines of motion, these lines of motion will generate a tubular surface which we may call a
1659:
834:
1167:
1129:
2596:
1872:
1596:{\displaystyle {\frac {d\Phi _{B}}{dt}}=\int _{S}{\boldsymbol {\nabla }}\times (\mathbf {v} \times \mathbf {B} )\cdot d\mathbf {S} +\oint _{C}\mathbf {B} \cdot \mathbf {v} \times d\mathbf {l} }
1826:
2648:. The large flux tube of the sunspot has a field intensity of around 3 kG with a diameter of typically 4000 km. There are extreme cases of when the large flux tubes have diameters of
2208:
880:
755:
508:
2079:
2143:
2693:
within the flux tube can be compressed by decreasing the gas pressure inside and therefore the internal temperature of the tube while maintaining a constant pressure outside.
2727:
2679:
1898:
1342:
2036:
1297:
1275:
1253:
1464:{\displaystyle {\frac {d\Phi _{B}}{dt}}=\int _{S}{\partial \mathbf {B} \over \partial t}\cdot d\mathbf {S} +\oint _{C}\mathbf {B} \cdot \mathbf {v} \times d\mathbf {l} }
953:
2106:
1759:
1779:
2006:
2278:
1978:
1938:
1728:
1697:
1061:
1034:
1007:
980:
566:
539:
448:
421:
394:
340:
110:
83:
2314:
2512:
2338:
2253:
2231:
1958:
1918:
1317:
924:
904:
775:
718:
694:
468:
363:
52:
1610:
3075:
304:
of a volume of liquid in motion, and an imaginary surface within the liquid, the flux is the volume of liquid passing through the surface per unit time.
2992:
Basic Plasma
Processes on the Sun: Proceedings of the 142nd Symposium of the International Astronomical Union Held in Bangalore, India, December 1–5, 1989
2696:
Intense magnetic tubes are isolated flux tubes that have diameters of 100 to 300 km with an overall field strength of 1 to 2 kG and a flux of around
779:
1066:
2517:
3796:
2749:. The plasma inside the loop has a higher temperature than the surroundings causing the pressure and density of the plasma to increase. These
1830:
3801:
2479:{\displaystyle 0={\frac {dp}{dR}}+{\frac {d}{dR}}\left({\frac {B_{\phi }^{2}+B_{z}^{2}}{2\mu }}\right)+{\frac {B_{\phi }^{2}}{\mu R}}}
142:, a flux tube generally means an area of space through which a strong magnetic field passes, in which the behavior of matter (usually
3517:
1784:
2160:
1703:
and the density of the tube increase with the same proportionality. If a flux tube with a configuration of a magnetic field of
3322:
3058:
2833:
gathering at high altitudes of the ionosphere on the sun side of the planets and causing the flux tubes to distort along the
1157:
fluid is conserved. In other words, the magnetic field is constrained to move with the fluid or is "frozen-in" to the fluid.
3464:
Bhardwaj, A.; Gladstone, G. R.; Zarka, P. (2001). "An
Overview of Io Flux Tube Footpoints in Juptier's Auroral Ionosphere".
1153:, Alfvén's theorem states that the magnetic flux through a surface, such as the surface of a flux tube, moving along with a
1226:{\displaystyle {\frac {\partial \mathbf {B} }{\partial t}}={\boldsymbol {\nabla }}\times (\mathbf {v} \times \mathbf {B} )}
3389:
3943:
3818:
3747:
3416:
3123:
275:
1277:
is the velocity field of the fluid. The change in magnetic flux over time through any open surface of the flux tube
257:
3813:
3086:
2875:-like configuration around the planet where plasma flow occurs. An example of this case is the flux tube between
851:
17:
727:
3168:
253:
2955:
Parker, E. N. (1979). "Sunspots and the
Physics of Magnetic Flux Tubes. I The General Nature of the Sunspot".
3674:
3616:
3510:
2317:
599:
particles that make up all matter, such as neutrons and protons, are composed of more basic particles called
481:
514:
the sum of the flux leaving the volume through these two surfaces will be zero, so the flux leaving through
576:
470:
has sources or sinks within the tube the flux out of this volume will be nonzero. However, if the field is
3834:
2041:
845:
3450:
3839:
3679:
3050:
2111:
656:
249:
3550:
3438:
2699:
2651:
2287:
With the magnetohydrostatic equilibrium condition met, a cylindrical flux tube's plasma pressure of
2153:
In magnetohydrostatic equilibrium, the following condition is met for the equation of motion of the
3849:
3631:
3611:
3503:
2789:
Graphic of the magnetosphere of
Jupiter with a flux tube connecting Jupiter and Io shown in yellow.
1877:
1322:
883:
238:
3260:
Peter, H.; et al. (2013). "Structure of Solar
Coronal Loops: from Miniature to Large-Scale".
2014:
1280:
1258:
1236:
588:
in regions where there are no charges and gravitational fields in regions where there is no mass.
3859:
3732:
3727:
3540:
3115:
929:
627:
242:
3854:
3844:
3684:
2491:
2084:
1737:
841:
572:
3145:
1764:
1144:
3654:
2868:
2853:
1983:
3283:
2260:
3689:
3473:
3396:
3351:
3279:
3214:
2964:
2912:
2145:. Reducing the length of the tubes results in a decrease of the magnetic field's strength.
1963:
1923:
1706:
1675:
1669:
1150:
1039:
1012:
985:
958:
882:. the strength is constant at any surface along a flux tube. Under the condition that the
544:
517:
426:
399:
372:
318:
88:
61:
2729:
Wb. These flux tubes are concentrated strong magnetic fields that are found between solar
2644:
occur when small flux tubes combine into a large flux tube that breaks the surface of the
2290:
8:
2918:
2902:
648:
127:, B, such that the cylindrical sides of the tube are everywhere parallel to the magnetic
120:
3477:
3400:
3355:
3218:
2968:
3742:
3426:
3408:
3340:"Evidence for a Magnetic Flux Rope in Observations of a Solar Prominence-Cavity System"
3295:
3269:
3237:
3204:
3192:
2497:
2323:
2238:
2216:
1943:
1903:
1604:
1302:
1161:
909:
889:
760:
703:
679:
511:
453:
348:
37:
3485:
1607:
and an elementary vector identity on the first and second term, respectively, to give
906:, of the flux tube is small enough that the magnetic field is approximately constant,
3774:
3757:
3718:
3664:
3581:
3412:
3318:
3299:
3242:
3164:
3119:
3054:
2907:
2487:
1154:
608:
955:. Therefore, if the cross sectional area of the tube decreases along the tube from
3920:
3905:
3768:
3481:
3404:
3359:
3287:
3232:
3222:
3156:
2972:
2798:
2774:
2770:
2734:
2627:
2154:
1731:
721:
592:
297:
3291:
2785:
300:
of the field over the surface. For example, for a vector field consisting of the
3915:
3910:
652:
2614:
Diagram of coronal loops that consist of plasma confined to magnetic flux tubes.
3869:
3649:
2845:
2841:
2834:
2826:
2802:
2690:
1700:
585:
580:
202:
146:
or plasma) is strongly influenced by the field. They are commonly found around
124:
3160:
3937:
3864:
3699:
3694:
3606:
3601:
3526:
3364:
3339:
2861:
2849:
2810:
2806:
2730:
697:
642:
308:
132:
55:
2494:. The field line's twist around the axis from one end of the tube of length
3895:
3626:
3621:
3596:
3246:
2766:
2750:
2746:
2741:
Plasma that is trapped within magnetic flux tubes that are attached to the
2635:
2631:
604:
343:
293:
139:
162:
are also associated with larger flux tubes of 2500 km diameter. Some
3900:
3806:
3669:
3659:
3227:
2814:
2742:
2645:
2623:
611:
mechanism, why quarks are never seen separately in particle experiments.
1654:{\displaystyle \int _{S}\mathbf {B} \cdot d\mathbf {S} ={\text{const}}.}
632:
Magnetic flux tube that does not have a magnetic field outside the tube.
3641:
3591:
3565:
3560:
2896:
2857:
2838:
2830:
2794:
2754:
837:
475:
471:
366:
312:
143:
128:
1940:
increase and are scaled the same while transverse expansion decreases
3890:
3586:
3555:
2880:
2745:, referred to as footpoints, create a loop-like structure known as a
1009:, then the magnetic field strength must increase proportionally from
607:
field. The flux tube model is important in explaining the so-called
171:
829:{\displaystyle F=\int _{S}\mathbf {B} \cdot \mathbf {\hat {n}} \;dS}
227:
166:
also have flux tubes. A well-known example is the flux tube between
30:
27:
Tube-like region of space with constant magnet flux along its length
2976:
2777:
are modeled using twisted magnetic flux tubes known as flux ropes.
2761:
The result of emerging twisted flux tubes from the interior of the
301:
3495:
3274:
3209:
2685:
can continue to grow as long as there is a constant supply of new
2108:, which then results in the magnetic field strength increasing by
3737:
2884:
2876:
2682:
2641:
2619:
2281:
655:'s work in electrical and magnetic behavior in his paper titled "
167:
159:
1761:
confined to the tube is compressed by a scalar value defined as
3791:
3763:
3545:
2883:
approximately 450 km in diameter at the points closest to
2872:
2610:
596:
163:
3193:"Coronal Loops: Observations and Modeling of Confined Plasma"
2822:
1124:{\displaystyle {\frac {B_{2}}{B_{1}}}={\frac {A_{1}}{A_{2}}}}
600:
2818:
2686:
2591:{\displaystyle \Phi (R)={\frac {LB_{\phi }(R)}{RB_{z}(R)}}}
1699:
is compressed while the length of tube stays the same, the
1160:
This can be shown mathematically for a flux tube using the
289:
155:
147:
2762:
151:
34:
Diagram of a flux tube showing the magnetic field lines
2864:
in opposite field directions get close to one another.
1867:{\displaystyle \rho ={\frac {\rho _{0}}{\lambda ^{2}}}}
158:
tubes from tens to hundreds of kilometers in diameter.
3463:
3112:
Cosmic
Magnetic Fields Their Origin and Their Activity
1063:
in order to satisfy the condition of constant flux F.
3005:
Maxwell, J. C. (1861). "On
Physical Lines of Force".
2702:
2689:
from small flux tubes on the surface of the Sun. The
2654:
2520:
2500:
2346:
2326:
2293:
2263:
2241:
2219:
2163:
2114:
2087:
2044:
2017:
1986:
1966:
1946:
1926:
1906:
1880:
1833:
1787:
1767:
1740:
1709:
1678:
1613:
1477:
1350:
1325:
1305:
1283:
1261:
1239:
1170:
1069:
1042:
1015:
988:
961:
932:
912:
892:
854:
782:
763:
730:
706:
682:
547:
520:
484:
456:
429:
402:
375:
351:
321:
296:
passing through any closed orientable surface is the
91:
64:
40:
651:
gave rise to the concept of a flux tube inspired by
2990:Roberts, B (1990). "Waves in Magnetic Flux Tubes".
1781:, the new magnetic field and density are given by:
2721:
2673:
2590:
2506:
2478:
2332:
2308:
2272:
2247:
2225:
2202:
2137:
2100:
2073:
2030:
2000:
1972:
1952:
1932:
1912:
1892:
1866:
1820:
1773:
1753:
1722:
1691:
1653:
1595:
1463:
1336:
1311:
1291:
1269:
1247:
1225:
1123:
1055:
1028:
1001:
974:
947:
918:
898:
874:
828:
769:
749:
712:
688:
560:
533:
502:
462:
442:
415:
388:
357:
334:
104:
77:
46:
813:
603:, which are bound together by thin flux tubes of
3935:
3146:"Solar Photospheric Magnetic Flux Tubes: Theory"
2486:The second term in the above equation gives the
2081:while the density of the tube remains the same,
3387:
1821:{\displaystyle B={\frac {B_{0}}{\lambda ^{2}}}}
307:A flux tube can be defined passing through any
2316:is given by the following relation written in
3511:
3007:Philosophical Magazine and Journal of Science
3073:
2793:Magnetized planets have an area above their
2203:{\displaystyle 0=-\nabla p+j\times B-\rho g}
1663:
875:{\displaystyle \nabla \cdot \mathbf {B} =0}
541:will be equal to the flux entering through
256:. Unsourced material may be challenged and
3518:
3504:
3153:Encyclopedia of Astronomy and Astrophysics
2490:force while the third term represents the
819:
750:{\displaystyle \mathbf {B} (\mathbf {x} )}
3363:
3344:Frontiers in Astronomy and Space Sciences
3273:
3236:
3226:
3208:
2765:cause twisted magnetic structures in the
2011:Extending the length of the flux tube by
276:Learn how and when to remove this message
2837:creating flux ropes. Particles from the
2784:
2609:
2340:as the distance from the axis radially:
187:
29:
3143:
3004:
2989:
1980:by the same value and proportion where
1672:, if a cylindrical flux tube of length
503:{\displaystyle \operatorname {div} F=0}
54:in the tube walls. The same amount of
14:
3936:
3337:
3109:
3044:
2954:
2856:that occurs when a flux tube from the
3499:
3388:Kivelson, M. G.; Bagenal, F. (2007).
3383:
3381:
3379:
3377:
3375:
3259:
3190:
3074:Priest, E. R.; Forbes, T. G. (2001).
3040:
2618:Examples of solar flux tubes include
1471:. Using the induction equation gives
671:
3186:
3184:
3182:
3180:
3139:
3137:
3135:
3038:
3036:
3034:
3032:
3030:
3028:
3026:
3024:
3022:
3020:
2950:
2948:
2946:
2944:
2942:
2940:
2938:
2936:
2934:
2797:which traps energetic particles and
2255:is the current density of the plasma
1138:
720:intersecting the tube, equal to the
659:". Maxwell described flux tubes as:
254:adding citations to reliable sources
221:
181:
3525:
3312:
2817:is modeled as magnetic flux tubes.
2074:{\displaystyle L=\lambda ^{*}L_{0}}
1900:, known as transverse compression,
85:as leaves the tube through surface
24:
3372:
3338:Jibben, P.R.; et al. (2016).
2681:km with a field strength of 3 kG.
2622:and intense magnetic tubes in the
2521:
2173:
2148:
1485:
1404:
1394:
1358:
1184:
1174:
855:
365:, as the set of all points on the
25:
3955:
3819:Sura Ionospheric Heating Facility
3177:
3132:
3067:
3017:
2983:
2931:
2829:resulting in flux tubes from the
2138:{\displaystyle \lambda ^{*}B_{0}}
1319:with a differential line element
1133:
3409:10.1016/B978-012088589-3/50032-3
2733:. The magnetic field causes the
1636:
1625:
1589:
1578:
1570:
1552:
1538:
1530:
1519:
1457:
1446:
1438:
1420:
1398:
1330:
1285:
1263:
1241:
1216:
1208:
1197:
1178:
1164:of a perfectly conducting fluid
862:
810:
800:
740:
732:
369:passing through the boundary of
226:
186:
58:enters the tube through surface
3457:
3331:
3306:
3197:Living Reviews in Solar Physics
3047:Magnetohydrodynamics of the Sun
123:) region of space containing a
3253:
3103:
2998:
2899:, sometimes called a flux tube
2753:get their characteristic high
2722:{\displaystyle 3\times 10^{9}}
2674:{\displaystyle 6\times 10^{4}}
2582:
2576:
2558:
2552:
2530:
2524:
2514:to the other end is given by:
2303:
2297:
1542:
1526:
1220:
1204:
744:
736:
450:intersecting it. If the field
13:
1:
3675:Interplanetary magnetic field
3617:Magnetosphere particle motion
3486:10.1016/s0273-1177(01)00280-0
2924:
2813:away from the sun known as a
1893:{\displaystyle \lambda <1}
1603:which can be rewritten using
1337:{\displaystyle d\mathbf {l} }
177:
3262:Astronomy & Astrophysics
2780:
2031:{\displaystyle \lambda ^{*}}
1292:{\displaystyle \mathbf {S} }
1270:{\displaystyle \mathbf {v} }
1248:{\displaystyle \mathbf {B} }
836:Since the magnetic field is
197:appears to contradict itself
7:
3292:10.1051/0004-6361/201321826
2890:
2867:Flux tubes that occur from
2600:
2157:confined to the flux tube:
948:{\displaystyle F\approx BA}
623:Twisted magnetic flux tube.
135:inside is always constant.
10:
3960:
3680:Heliospheric current sheet
3466:Advances in Space Research
3390:"Planetary Magnetospheres"
3051:Cambridge University Press
2844:lines can transfer to the
1670:ideal magnetohydrodynamics
1255:is the magnetic field and
1142:
676:The flux tube's strength,
657:On Physical Lines of Force
640:
636:
119:is a generally tube-like (
3878:
3827:
3784:
3708:
3640:
3574:
3533:
2957:The Astrophysical Journal
2860:and a flux tube from the
2852:through the processes of
2626:and the field around the
2101:{\displaystyle \rho _{0}}
1754:{\displaystyle \rho _{0}}
1664:Compression and extension
577:Gauss's law for magnetism
3944:Concepts in astrophysics
3632:Van Allen radiation belt
3612:Magnetosphere chronology
3365:10.3389/fspas.2016.00010
2605:
1774:{\displaystyle \lambda }
846:Gauss' law for magnetism
614:
195:This article or section
3541:Atmospheric circulation
3284:2013A&A...556A.104P
3161:10.1888/0333750888/2255
3116:Oxford University Press
2809:. The extension of the
2318:cylindrical coordinates
2001:{\displaystyle B/\rho }
926:can be approximated as
696:, is defined to be the
3551:Earth's magnetic field
3110:Parker, E. N. (1979).
3076:"Magnetohydrodynamics"
2790:
2723:
2675:
2615:
2592:
2508:
2492:magnetic tension force
2480:
2334:
2310:
2274:
2273:{\displaystyle \rho g}
2249:
2233:is the plasma pressure
2227:
2204:
2139:
2102:
2075:
2038:gives a new length of
2032:
2002:
1974:
1954:
1934:
1914:
1894:
1868:
1822:
1775:
1755:
1724:
1693:
1655:
1597:
1465:
1338:
1313:
1293:
1271:
1249:
1227:
1125:
1057:
1030:
1003:
976:
949:
920:
900:
876:
830:
771:
751:
724:of the magnetic field
714:
690:
669:
562:
535:
504:
464:
444:
417:
390:
359:
336:
112:
106:
79:
48:
3655:Coronal mass ejection
3575:Earth's magnetosphere
2869:magnetic reconnection
2854:magnetic reconnection
2788:
2769:, which then lead to
2724:
2676:
2613:
2593:
2509:
2481:
2335:
2311:
2275:
2250:
2228:
2205:
2140:
2103:
2076:
2033:
2003:
1975:
1973:{\displaystyle \rho }
1955:
1935:
1933:{\displaystyle \rho }
1915:
1895:
1869:
1823:
1776:
1756:
1725:
1723:{\displaystyle B_{0}}
1694:
1692:{\displaystyle L_{0}}
1656:
1598:
1466:
1339:
1314:
1294:
1272:
1250:
1228:
1126:
1058:
1056:{\displaystyle B_{2}}
1031:
1029:{\displaystyle B_{1}}
1004:
1002:{\displaystyle A_{2}}
977:
975:{\displaystyle A_{1}}
950:
921:
901:
877:
831:
772:
752:
715:
691:
666:tube of fluid motion.
661:
563:
561:{\displaystyle S_{1}}
536:
534:{\displaystyle S_{2}}
505:
465:
445:
443:{\displaystyle S_{2}}
418:
416:{\displaystyle S_{1}}
391:
389:{\displaystyle S_{1}}
360:
337:
335:{\displaystyle S_{1}}
205:for more information.
107:
105:{\displaystyle S_{2}}
80:
78:{\displaystyle S_{1}}
49:
33:
3828:Other magnetospheres
3690:Solar particle event
3395:. pp. 519–540.
3228:10.12942/lrsp-2014-4
3144:Roberts, B. (2001).
3053:. pp. 100–103.
2913:Magnetohydrodynamics
2848:lines of a planet's
2835:magnetic field lines
2700:
2652:
2518:
2498:
2344:
2324:
2309:{\displaystyle p(R)}
2291:
2261:
2239:
2217:
2161:
2112:
2085:
2042:
2015:
1984:
1964:
1944:
1924:
1904:
1878:
1831:
1785:
1765:
1738:
1707:
1676:
1611:
1475:
1348:
1323:
1303:
1281:
1259:
1237:
1168:
1155:perfectly conducting
1151:magnetohydrodynamics
1067:
1040:
1013:
986:
959:
930:
910:
890:
884:cross-sectional area
852:
780:
761:
728:
704:
680:
605:strong nuclear force
545:
518:
482:
454:
427:
400:
373:
349:
319:
250:improve this section
89:
62:
38:
3478:2001AdSpR..27.1915B
3401:2007ess..book..519K
3356:2016FrASS...3...10J
3219:2014LRSP...11....4R
3045:Priest, E. (2014).
2969:1979ApJ...230..905P
2919:Marklund convection
2903:Flux transfer event
2738:escape the plasma.
2465:
2430:
2412:
2282:gravitational force
842:Maxwell's equations
649:James Clerk Maxwell
573:Maxwell's equations
3191:Reale, F. (2014).
2791:
2719:
2671:
2616:
2588:
2504:
2476:
2451:
2416:
2398:
2330:
2306:
2270:
2245:
2223:
2200:
2135:
2098:
2071:
2028:
1998:
1970:
1950:
1930:
1910:
1890:
1864:
1818:
1771:
1751:
1720:
1689:
1651:
1593:
1461:
1344:can be written as
1334:
1309:
1289:
1267:
1245:
1223:
1162:induction equation
1121:
1053:
1026:
999:
972:
945:
916:
896:
872:
826:
767:
747:
710:
700:through a surface
686:
672:Flux tube strength
558:
531:
512:divergence theorem
500:
460:
440:
413:
386:
355:
332:
113:
102:
75:
44:
3931:
3930:
3785:Research projects
3753:
3724:
3665:Geomagnetic storm
3582:Birkeland current
3472:(11): 1915–1922.
3445:Missing or empty
3324:978-3-319-10416-4
3315:Solar Prominences
3060:978-0-521-85471-9
2908:Birkeland current
2825:both have strong
2805:, referred to as
2775:Solar prominences
2771:solar prominences
2586:
2507:{\displaystyle L}
2488:magnetic pressure
2474:
2440:
2389:
2371:
2333:{\displaystyle R}
2248:{\displaystyle j}
2226:{\displaystyle p}
1953:{\displaystyle B}
1913:{\displaystyle B}
1862:
1816:
1646:
1503:
1411:
1376:
1312:{\displaystyle C}
1191:
1139:Flux conservation
1119:
1092:
919:{\displaystyle F}
899:{\displaystyle A}
816:
770:{\displaystyle S}
713:{\displaystyle S}
689:{\displaystyle F}
609:color confinement
463:{\displaystyle F}
358:{\displaystyle F}
286:
285:
278:
220:
219:
154:, which has many
47:{\displaystyle B}
16:(Redirected from
3951:
3769:Van Allen Probes
3751:
3722:
3534:Submagnetosphere
3520:
3513:
3506:
3497:
3496:
3490:
3489:
3461:
3455:
3454:
3448:
3442:
3436:
3432:
3430:
3422:
3394:
3385:
3370:
3369:
3367:
3335:
3329:
3328:
3313:Fan, Y. (2015).
3310:
3304:
3303:
3277:
3257:
3251:
3250:
3240:
3230:
3212:
3188:
3175:
3174:
3150:
3141:
3130:
3129:
3107:
3101:
3100:
3098:
3097:
3091:
3085:. Archived from
3080:
3071:
3065:
3064:
3042:
3015:
3014:
3002:
2996:
2995:
2987:
2981:
2980:
2952:
2728:
2726:
2725:
2720:
2718:
2717:
2680:
2678:
2677:
2672:
2670:
2669:
2628:solar prominence
2597:
2595:
2594:
2589:
2587:
2585:
2575:
2574:
2561:
2551:
2550:
2537:
2513:
2511:
2510:
2505:
2485:
2483:
2482:
2477:
2475:
2473:
2464:
2459:
2450:
2445:
2441:
2439:
2431:
2429:
2424:
2411:
2406:
2396:
2390:
2388:
2377:
2372:
2370:
2362:
2354:
2339:
2337:
2336:
2331:
2315:
2313:
2312:
2307:
2279:
2277:
2276:
2271:
2254:
2252:
2251:
2246:
2232:
2230:
2229:
2224:
2209:
2207:
2206:
2201:
2144:
2142:
2141:
2136:
2134:
2133:
2124:
2123:
2107:
2105:
2104:
2099:
2097:
2096:
2080:
2078:
2077:
2072:
2070:
2069:
2060:
2059:
2037:
2035:
2034:
2029:
2027:
2026:
2007:
2005:
2004:
1999:
1994:
1979:
1977:
1976:
1971:
1959:
1957:
1956:
1951:
1939:
1937:
1936:
1931:
1919:
1917:
1916:
1911:
1899:
1897:
1896:
1891:
1873:
1871:
1870:
1865:
1863:
1861:
1860:
1851:
1850:
1841:
1827:
1825:
1824:
1819:
1817:
1815:
1814:
1805:
1804:
1795:
1780:
1778:
1777:
1772:
1760:
1758:
1757:
1752:
1750:
1749:
1729:
1727:
1726:
1721:
1719:
1718:
1698:
1696:
1695:
1690:
1688:
1687:
1660:
1658:
1657:
1652:
1647:
1644:
1639:
1628:
1623:
1622:
1602:
1600:
1599:
1594:
1592:
1581:
1573:
1568:
1567:
1555:
1541:
1533:
1522:
1517:
1516:
1504:
1502:
1494:
1493:
1492:
1479:
1470:
1468:
1467:
1462:
1460:
1449:
1441:
1436:
1435:
1423:
1412:
1410:
1402:
1401:
1392:
1390:
1389:
1377:
1375:
1367:
1366:
1365:
1352:
1343:
1341:
1340:
1335:
1333:
1318:
1316:
1315:
1310:
1298:
1296:
1295:
1290:
1288:
1276:
1274:
1273:
1268:
1266:
1254:
1252:
1251:
1246:
1244:
1232:
1230:
1229:
1224:
1219:
1211:
1200:
1192:
1190:
1182:
1181:
1172:
1145:Alfvén's theorem
1130:
1128:
1127:
1122:
1120:
1118:
1117:
1108:
1107:
1098:
1093:
1091:
1090:
1081:
1080:
1071:
1062:
1060:
1059:
1054:
1052:
1051:
1035:
1033:
1032:
1027:
1025:
1024:
1008:
1006:
1005:
1000:
998:
997:
981:
979:
978:
973:
971:
970:
954:
952:
951:
946:
925:
923:
922:
917:
905:
903:
902:
897:
881:
879:
878:
873:
865:
840:, as defined in
835:
833:
832:
827:
818:
817:
809:
803:
798:
797:
776:
774:
773:
768:
756:
754:
753:
748:
743:
735:
722:surface integral
719:
717:
716:
711:
695:
693:
692:
687:
593:particle physics
567:
565:
564:
559:
557:
556:
540:
538:
537:
532:
530:
529:
510:) then from the
509:
507:
506:
501:
469:
467:
466:
461:
449:
447:
446:
441:
439:
438:
422:
420:
419:
414:
412:
411:
395:
393:
392:
387:
385:
384:
364:
362:
361:
356:
341:
339:
338:
333:
331:
330:
298:surface integral
281:
274:
270:
267:
261:
230:
222:
215:
212:
206:
190:
189:
182:
150:, including the
111:
109:
108:
103:
101:
100:
84:
82:
81:
76:
74:
73:
53:
51:
50:
45:
21:
3959:
3958:
3954:
3953:
3952:
3950:
3949:
3948:
3934:
3933:
3932:
3927:
3874:
3823:
3780:
3704:
3636:
3570:
3529:
3527:Magnetospherics
3524:
3494:
3493:
3462:
3458:
3446:
3444:
3434:
3433:
3424:
3423:
3419:
3392:
3386:
3373:
3336:
3332:
3325:
3311:
3307:
3258:
3254:
3189:
3178:
3171:
3148:
3142:
3133:
3126:
3114:. Bristol, UK:
3108:
3104:
3095:
3093:
3089:
3078:
3072:
3068:
3061:
3043:
3018:
3003:
2999:
2988:
2984:
2953:
2932:
2927:
2893:
2827:magnetic fields
2803:magnetic fields
2783:
2713:
2709:
2701:
2698:
2697:
2665:
2661:
2653:
2650:
2649:
2608:
2603:
2570:
2566:
2562:
2546:
2542:
2538:
2536:
2519:
2516:
2515:
2499:
2496:
2495:
2466:
2460:
2455:
2449:
2432:
2425:
2420:
2407:
2402:
2397:
2395:
2391:
2381:
2376:
2363:
2355:
2353:
2345:
2342:
2341:
2325:
2322:
2321:
2292:
2289:
2288:
2262:
2259:
2258:
2240:
2237:
2236:
2218:
2215:
2214:
2162:
2159:
2158:
2151:
2149:Plasma pressure
2129:
2125:
2119:
2115:
2113:
2110:
2109:
2092:
2088:
2086:
2083:
2082:
2065:
2061:
2055:
2051:
2043:
2040:
2039:
2022:
2018:
2016:
2013:
2012:
1990:
1985:
1982:
1981:
1965:
1962:
1961:
1945:
1942:
1941:
1925:
1922:
1921:
1905:
1902:
1901:
1879:
1876:
1875:
1856:
1852:
1846:
1842:
1840:
1832:
1829:
1828:
1810:
1806:
1800:
1796:
1794:
1786:
1783:
1782:
1766:
1763:
1762:
1745:
1741:
1739:
1736:
1735:
1714:
1710:
1708:
1705:
1704:
1683:
1679:
1677:
1674:
1673:
1666:
1643:
1635:
1624:
1618:
1614:
1612:
1609:
1608:
1605:Stokes' theorem
1588:
1577:
1569:
1563:
1559:
1551:
1537:
1529:
1518:
1512:
1508:
1495:
1488:
1484:
1480:
1478:
1476:
1473:
1472:
1456:
1445:
1437:
1431:
1427:
1419:
1403:
1397:
1393:
1391:
1385:
1381:
1368:
1361:
1357:
1353:
1351:
1349:
1346:
1345:
1329:
1324:
1321:
1320:
1304:
1301:
1300:
1284:
1282:
1279:
1278:
1262:
1260:
1257:
1256:
1240:
1238:
1235:
1234:
1215:
1207:
1196:
1183:
1177:
1173:
1171:
1169:
1166:
1165:
1147:
1141:
1136:
1113:
1109:
1103:
1099:
1097:
1086:
1082:
1076:
1072:
1070:
1068:
1065:
1064:
1047:
1043:
1041:
1038:
1037:
1020:
1016:
1014:
1011:
1010:
993:
989:
987:
984:
983:
966:
962:
960:
957:
956:
931:
928:
927:
911:
908:
907:
891:
888:
887:
861:
853:
850:
849:
808:
807:
799:
793:
789:
781:
778:
777:
762:
759:
758:
739:
731:
729:
726:
725:
705:
702:
701:
681:
678:
677:
674:
653:Michael Faraday
645:
639:
617:
586:electric fields
581:magnetic fields
552:
548:
546:
543:
542:
525:
521:
519:
516:
515:
483:
480:
479:
455:
452:
451:
434:
430:
428:
425:
424:
407:
403:
401:
398:
397:
380:
376:
374:
371:
370:
350:
347:
346:
326:
322:
320:
317:
316:
282:
271:
265:
262:
247:
231:
216:
210:
207:
201:Please see the
200:
191:
180:
96:
92:
90:
87:
86:
69:
65:
63:
60:
59:
39:
36:
35:
28:
23:
22:
18:Flux tube model
15:
12:
11:
5:
3957:
3947:
3946:
3929:
3928:
3926:
3925:
3924:
3923:
3918:
3913:
3908:
3898:
3893:
3888:
3882:
3880:
3879:Related topics
3876:
3875:
3873:
3872:
3867:
3862:
3857:
3852:
3847:
3842:
3837:
3831:
3829:
3825:
3824:
3822:
3821:
3816:
3811:
3810:
3809:
3799:
3794:
3788:
3786:
3782:
3781:
3779:
3778:
3771:
3766:
3761:
3754:
3745:
3740:
3735:
3730:
3725:
3716:
3712:
3710:
3706:
3705:
3703:
3702:
3697:
3692:
3687:
3682:
3677:
3672:
3667:
3662:
3657:
3652:
3650:Magnetic cloud
3646:
3644:
3638:
3637:
3635:
3634:
3629:
3624:
3619:
3614:
3609:
3604:
3599:
3594:
3589:
3584:
3578:
3576:
3572:
3571:
3569:
3568:
3563:
3558:
3553:
3548:
3543:
3537:
3535:
3531:
3530:
3523:
3522:
3515:
3508:
3500:
3492:
3491:
3456:
3435:|journal=
3417:
3371:
3330:
3323:
3305:
3252:
3176:
3169:
3131:
3124:
3102:
3066:
3059:
3016:
2997:
2982:
2977:10.1086/157150
2929:
2928:
2926:
2923:
2922:
2921:
2916:
2910:
2905:
2900:
2892:
2889:
2846:magnetic field
2842:magnetic field
2807:magnetospheres
2782:
2779:
2716:
2712:
2708:
2705:
2691:magnetic field
2668:
2664:
2660:
2657:
2607:
2604:
2602:
2599:
2584:
2581:
2578:
2573:
2569:
2565:
2560:
2557:
2554:
2549:
2545:
2541:
2535:
2532:
2529:
2526:
2523:
2503:
2472:
2469:
2463:
2458:
2454:
2448:
2444:
2438:
2435:
2428:
2423:
2419:
2415:
2410:
2405:
2401:
2394:
2387:
2384:
2380:
2375:
2369:
2366:
2361:
2358:
2352:
2349:
2329:
2305:
2302:
2299:
2296:
2285:
2284:
2269:
2266:
2256:
2244:
2234:
2222:
2199:
2196:
2193:
2190:
2187:
2184:
2181:
2178:
2175:
2172:
2169:
2166:
2150:
2147:
2132:
2128:
2122:
2118:
2095:
2091:
2068:
2064:
2058:
2054:
2050:
2047:
2025:
2021:
1997:
1993:
1989:
1969:
1949:
1929:
1909:
1889:
1886:
1883:
1859:
1855:
1849:
1845:
1839:
1836:
1813:
1809:
1803:
1799:
1793:
1790:
1770:
1748:
1744:
1717:
1713:
1701:magnetic field
1686:
1682:
1665:
1662:
1650:
1642:
1638:
1634:
1631:
1627:
1621:
1617:
1591:
1587:
1584:
1580:
1576:
1572:
1566:
1562:
1558:
1554:
1550:
1547:
1544:
1540:
1536:
1532:
1528:
1525:
1521:
1515:
1511:
1507:
1501:
1498:
1491:
1487:
1483:
1459:
1455:
1452:
1448:
1444:
1440:
1434:
1430:
1426:
1422:
1418:
1415:
1409:
1406:
1400:
1396:
1388:
1384:
1380:
1374:
1371:
1364:
1360:
1356:
1332:
1328:
1308:
1287:
1265:
1243:
1222:
1218:
1214:
1210:
1206:
1203:
1199:
1195:
1189:
1186:
1180:
1176:
1143:Main article:
1140:
1137:
1135:
1134:Plasma physics
1132:
1116:
1112:
1106:
1102:
1096:
1089:
1085:
1079:
1075:
1050:
1046:
1023:
1019:
996:
992:
969:
965:
944:
941:
938:
935:
915:
895:
871:
868:
864:
860:
857:
844:(specifically
825:
822:
815:
812:
806:
802:
796:
792:
788:
785:
766:
746:
742:
738:
734:
709:
685:
673:
670:
641:Main article:
638:
635:
634:
633:
624:
616:
613:
575:(specifically
555:
551:
528:
524:
499:
496:
493:
490:
487:
472:divergenceless
459:
437:
433:
410:
406:
383:
379:
354:
329:
325:
284:
283:
234:
232:
225:
218:
217:
194:
192:
185:
179:
176:
125:magnetic field
99:
95:
72:
68:
43:
26:
9:
6:
4:
3:
2:
3956:
3945:
3942:
3941:
3939:
3922:
3919:
3917:
3914:
3912:
3909:
3907:
3904:
3903:
3902:
3899:
3897:
3894:
3892:
3889:
3887:
3884:
3883:
3881:
3877:
3871:
3868:
3866:
3863:
3861:
3858:
3856:
3853:
3851:
3848:
3846:
3843:
3841:
3838:
3836:
3833:
3832:
3830:
3826:
3820:
3817:
3815:
3812:
3808:
3805:
3804:
3803:
3800:
3798:
3795:
3793:
3790:
3789:
3787:
3783:
3777:
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3700:Space weather
3698:
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3695:Space climate
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3608:
3607:Magnetosphere
3605:
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3602:Magnetosheath
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3125:0-19-851290-2
3121:
3117:
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3092:on 2017-11-09
3088:
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2879:and its moon
2878:
2874:
2871:forms into a
2870:
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2862:magnetosphere
2859:
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2850:magnetosphere
2847:
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2808:
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2751:coronal loops
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2632:coronal loops
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2167:
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2116:
2093:
2089:
2066:
2062:
2056:
2052:
2048:
2045:
2023:
2019:
2009:
2008:is constant.
1995:
1991:
1987:
1967:
1947:
1927:
1907:
1887:
1884:
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1857:
1853:
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1843:
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847:
843:
839:
823:
820:
804:
794:
790:
786:
783:
764:
723:
707:
699:
698:magnetic flux
683:
668:
667:
660:
658:
654:
650:
644:
643:Line of force
631:
629:
625:
622:
619:
618:
612:
610:
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602:
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244:
240:
235:This section
233:
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204:
198:
193:
184:
183:
175:
173:
170:and its moon
169:
165:
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157:
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145:
141:
136:
134:
133:magnetic flux
130:
126:
122:
118:
97:
93:
70:
66:
57:
56:magnetic flux
41:
32:
19:
3901:Ring systems
3896:Lunar swirls
3885:
3773:
3756:
3627:Ring current
3622:Plasmasphere
3597:Magnetopause
3469:
3465:
3459:
3447:|title=
3347:
3343:
3333:
3317:. Springer.
3314:
3308:
3265:
3261:
3255:
3200:
3196:
3152:
3111:
3105:
3094:. Retrieved
3087:the original
3082:
3069:
3046:
3010:
3006:
3000:
2994:. Edition 1.
2991:
2985:
2960:
2956:
2866:
2792:
2760:
2747:coronal loop
2740:
2695:
2640:
2617:
2286:
2152:
2010:
1667:
1299:enclosed by
1159:
1148:
675:
665:
662:
646:
626:
620:
590:
570:
344:vector field
306:
294:vector field
287:
272:
266:January 2023
263:
248:Please help
236:
211:January 2023
208:
196:
140:astrophysics
137:
116:
114:
3807:Unwin Radar
3733:Double Star
3670:Heliosphere
3660:Solar flare
2963:: 905–913.
2815:magnetotail
2795:ionospheres
2743:photosphere
2646:photosphere
2624:photosphere
1734:density of
571:Since from
367:field lines
144:ionized gas
138:As used in
129:field lines
121:cylindrical
3855:Ganymedian
3728:Cluster II
3709:Satellites
3685:Heliopause
3642:Solar wind
3592:Ionosphere
3566:Polar wind
3561:Jet stream
3170:0333750888
3096:2017-04-18
2925:References
2897:QCD string
2858:solar wind
2839:solar wind
2831:solar wind
2755:luminosity
838:solenoidal
621:Flux rope:
476:solenoidal
313:orientable
178:Definition
3891:Gas torus
3886:Flux tube
3870:Neptunian
3860:Saturnian
3814:SuperDARN
3715:Full list
3587:Bow shock
3556:Geosphere
3437:ignored (
3427:cite book
3300:119237311
3275:1306.4685
3210:1010.5927
2781:Planetary
2707:×
2659:×
2548:ϕ
2522:Φ
2468:μ
2457:ϕ
2437:μ
2404:ϕ
2265:ρ
2195:ρ
2192:−
2186:×
2174:∇
2171:−
2121:∗
2117:λ
2090:ρ
2057:∗
2053:λ
2024:∗
2020:λ
1996:ρ
1968:ρ
1928:ρ
1882:λ
1854:λ
1844:ρ
1835:ρ
1808:λ
1769:λ
1743:ρ
1630:⋅
1616:∫
1583:×
1575:⋅
1561:∮
1546:⋅
1535:×
1524:×
1520:∇
1510:∫
1486:Φ
1451:×
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1429:∮
1414:⋅
1405:∂
1395:∂
1383:∫
1359:Φ
1213:×
1202:×
1198:∇
1185:∂
1175:∂
937:≈
859:⋅
856:∇
814:^
805:⋅
791:∫
647:In 1861,
489:
237:does not
203:talk page
117:flux tube
3938:Category
3268:: A104.
3247:27194957
3203:(1): 4.
2891:See also
2731:granules
2683:Sunspots
2642:Sunspots
2620:sunspots
2601:Examples
315:surface
302:velocity
160:Sunspots
3921:Neptune
3906:Jupiter
3865:Uranian
3845:Martian
3835:Hermian
3738:Geotail
3474:Bibcode
3397:Bibcode
3352:Bibcode
3280:Bibcode
3238:4841190
3215:Bibcode
2965:Bibcode
2885:Jupiter
2877:Jupiter
2634:in the
2280:is the
637:History
258:removed
243:sources
168:Jupiter
164:planets
3916:Uranus
3911:Saturn
3850:Jovian
3792:EISCAT
3764:THEMIS
3752:(2015)
3750:
3723:(2016)
3721:
3546:Aurora
3415:
3350:: 10.
3321:
3298:
3245:
3235:
3167:
3122:
3083:Nature
3057:
2873:dipole
2801:along
2799:plasma
2767:corona
2735:plasma
2636:corona
2210:where
2155:plasma
1732:plasma
1730:and a
1233:where
630:field:
628:Fibril
601:quarks
597:hadron
595:, the
309:closed
3840:Lunar
3802:SHARE
3797:HAARP
3758:Polar
3743:IMAGE
3719:Arase
3393:(PDF)
3296:S2CID
3270:arXiv
3205:arXiv
3149:(PDF)
3090:(PDF)
3079:(PDF)
2915:(MHD)
2823:Venus
2606:Solar
2320:with
1645:const
757:over
615:Types
342:in a
292:of a
148:stars
3775:Wind
3451:help
3439:help
3413:ISBN
3319:ISBN
3243:PMID
3165:ISBN
3120:ISBN
3055:ISBN
2821:and
2819:Mars
2687:flux
2630:and
1960:and
1920:and
1885:<
423:and
290:flux
288:The
241:any
239:cite
156:flux
3748:MMS
3482:doi
3405:doi
3360:doi
3288:doi
3266:556
3233:PMC
3223:doi
3157:doi
2973:doi
2961:230
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486:div
252:by
152:Sun
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870:0
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863:B
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