27:
120:
185: motion, and increase if the field decreases, while the components of the velocity transverse to the field increase or decrease so as to keep the magnitude of the total velocity constant. Conservation of energy prevents the transverse velocity from increasing without limit, and eventually the longitudinal component of the velocity becomes zero, while the
189:, of the particle with respect to the field line, becomes 90°. Then the longitudinal motion is stopped and reversed, and the particle is reflected back towards regions of weaker field, the guiding center now retracing its previous motion along the field line, with the particle's transverse velocity decreasing and its longitudinal velocity increasing.
211:
local field line connecting the two mirror points at any moment, slowly sweeps out a surface connecting them as it moves in longitude. Eventually the particle will drift entirely around the Earth, and the surface will be closed upon itself. These drift surfaces, nested like the skin of an onion, are the surfaces of constant
210:
shape, and the guiding center slowly moves perpendicular both to the field line and to the radial direction. The guiding center of the cyclotron orbit, instead of moving exactly along the field line, therefore drifts slowly east or west (depending on the sign of the charge of the particle), and the
180:
enclosed by the orbit constant. Since the
Lorentz force is strictly perpendicular to the velocity, it cannot change the energy of a charged particle moving in it. Thus the particle's kinetic energy remains constant. Then so also must its speed be constant. Then it can be shown that the particle's
205:
However, for particles which mirror at safe altitudes, (in yet a further level of approximation) the fact that the field generally increases towards the center of the Earth means that the curvature on the side of the orbit nearest the Earth is somewhat greater than on the opposite side, so that the
201:
on the field line, it bounces back and forth between the north mirror point and the south mirror point, remaining approximately on the same field line. The particle is therefore endlessly trapped, and cannot escape from the region of the Earth. Particles with too-small pitch angles may strike the
405:
is the strongest planetary field in the solar system. Its magnetic field traps electrons with energies greater than 500 MeV The characteristic L-shells are L=6, where electron distribution undergoes a marked hardening (increase of energy), and L=20-50, where the electron energy decreases to the
410:
regime and the magnetosphere eventually gives way to the solar wind. Because
Jupiter's trapped electrons contain so much energy, they more easily diffuse across L-shells than trapped electrons in Earth's magnetic field. One consequence of this is a more continuous and smoothly-varying
192:
In the (approximately) dipole field of the Earth, the magnitude of the field is greatest near the magnetic poles, and least near the magnetic
Equator. Thus after the particle crosses the Equator, it will again encounter regions of increasing field, until it once again stops at the
99:
lines which cross the Earth's magnetic equator two earth radii from the center of the Earth. L-shell parameters can also describe the magnetic fields of other planets. In such cases, the parameter is renormalized for that planet's radius and magnetic field model.
123:
Map of L-shell field line locations on the surface of the Earth. The real terrestrial field is approximately dipolar, but misaligned with the rotation axis, and offset a few hundred km in the direction opposite to the
148:
of the charged particle orbit is small compared to the spatial scale for changes in the field. Then a charged particle will basically follow a helical path orbiting the local field line. In a local coordinate system
215: in the McIlwain coordinate system. They apply not only for a perfect dipole field, but also for fields that are approximately dipolar. For a given particle, as long as only the Lorentz force is involved,
202:
top of the atmosphere if they are not mirrored before their field line reaches too close to the Earth, in which case they will eventually be scattered by atoms in the air, lose energy, and be lost from the belts.
231:) coordinates provides us with a way of mapping the real, non-dipolar terrestrial or planetary field into coordinates that behave essentially like those of a perfect dipole. The
287:
176:
At the next level of approximation, as the particle orbits and moves along the field line, along which the field changes slowly, the radius of the orbit changes so as to keep the
327:
132:
The motions of low-energy charged particles in the Earth's magnetic field (or in any nearly-dipolar magnetic field) can be usefully described in terms of McIlwain's (
93:
351:
307:
429:
108:
31:
444:
104:
235: parameter is traditionally labeled in Earth-radii, of the point where the shell crosses the magnetic Equator, of the equivalent dipole.
165: line, with the gyroradius and frequency characteristic of cyclotron motion for the field strength, while the simultaneous motion along
584:
474:
570:
107:), it is often used to give a general picture of magnetic phenomena near the Earth, in which case it can be approximated using the
501:
361:
For the Earth, L-shells uniquely define regions of particular geophysical interest. Certain physical phenomena occur in the
103:
Although L-value is formally defined in terms of the Earth's true instantaneous magnetic field (or a high-order model like
250:
186:
412:
30:
Plot showing field lines (which, in three dimensions would describe "shells") for L-values 1.5, 2, 3, 4 and 5 using a
576:
144: is just the magnitude (or length) of the magnetic field vector. This description is most valuable when the
547:, Robert C Haymes, Wiley & sons, 1971. Chapter 7, "Van Allen Radiation" and Chapter 9, "Planetary Magnetism"
482:
424:
96:
402:
378:
656:
125:
651:
194:
50:
510:
454:
439:
330:
58:
19:
This article is about planetary magnetic field lines. For the second electron shell in an atom, see
373:
are most common around L=6, can reach L=4 during moderate disturbances, and during the most severe
54:
370:
580:
496:
374:
312:
247:
In a centered dipole magnetic field model, the path along a given L shell can be described as
66:
611:
526:
518:
62:
72:
514:
181:
velocity parallel to the local field must decrease if the field is increasing along its
157: is along the field, the transverse motion will be nearly a circle, orbiting the "
434:
336:
292:
198:
197:, on the opposite side of the Equator. The result is that, as the particle orbits its
158:
20:
26:
645:
605:
366:
177:
170:
119:
600:
390:
362:
145:
531:
522:
497:"Coordinates for Mapping the Distribution of Magnetically Trapped Particles"
223: remain constant and particles can be trapped indefinitely. Use of (
449:
207:
169: will be at nearly uniform velocity, since the component of the
16:
Mathematical parameter used to describe planetary magnetic field lines
309:
is the radial distance (in planetary radii) to a point on the line,
118:
25:
479:
407:
638:, New York, NY: Cambridge University Press, pp. 166–167
53:) is a parameter describing a particular set of planetary
339:
315:
295:
253:
75:
206:
orbit has a slightly non-circular, with a (prolate)
57:. Colloquially, L-value often describes the set of
634:Margaret Kivelson and Christopher Russell (1995),
345:
321:
301:
281:
87:
572:Introduction to Geomagnetically Trapped Radiation
614:, Volume 163, Issue 2, June 2003, Pages 434-448.
601:Jupiter’s radio spectrum from 74 MHz up to 8 GHz
161:", that is the center of the orbit or the local
411:radio-spectrum emitted by trapped electrons in
8:
369:at characteristic L-shells. For instance,
559:. W. N. Hess, Blaisdell Publishing Co 1968
430:Dipole model of the Earth's magnetic field
115:Charged particle motions in a dipole field
109:dipole model of the Earth's magnetic field
32:dipole model of the Earth's magnetic field
530:
445:International Geomagnetic Reference Field
338:
314:
294:
267:
252:
243:Equation for L in a Dipole Magnetic Field
140:) coordinates, the first of which,
74:
466:
629:Introduction to the Space Environment
7:
557:The Radiation Belt and Magnetosphere
475:Galileo - Glossary of Selected Terms
282:{\displaystyle r=L\cos ^{2}\lambda }
69:equal to the L-value. For example,
14:
631:(2nd ed.), Malabar, FL: Kreiger
502:Journal of Geophysical Research
173:along the field line is zero.
1:
636:Introduction to Space Physics
545:Introduction to Space Science
239: is measured in gauss.
627:Tascione, Thomas F. (1994),
353:is the L-shell of interest.
673:
577:Cambridge University Press
495:McIlwain, Carl E. (1961),
18:
483:Jet Propulsion Laboratory
393:is typically around L=5.
379:Van Allen radiation belts
377:, may approach L=2. The
95:describes the set of the
381:roughly correspond to L=
322:{\displaystyle \lambda }
61:which cross the Earth's
523:10.1029/JZ066i011p03681
425:Earth's magnetic field
371:auroral light displays
347:
323:
303:
283:
129:
126:South Atlantic Anomaly
97:Earth's magnetic field
89:
34:
569:Walt, Martin (1994).
403:Jovian magnetic field
348:
324:
304:
284:
195:magnetic mirror point
122:
90:
29:
455:World Magnetic Model
440:Geomagnetic latitude
337:
331:geomagnetic latitude
313:
293:
251:
73:
59:magnetic field lines
55:magnetic field lines
47:McIlwain L-parameter
515:1961JGR....66.3681M
397:L-shells on Jupiter
88:{\displaystyle L=2}
375:geomagnetic storms
343:
319:
299:
279:
130:
85:
35:
586:978-0-521-61611-9
509:(11): 3681–3691,
357:L-shells on Earth
346:{\displaystyle L}
302:{\displaystyle r}
664:
622:Other references
615:
597:
591:
590:
575:. New York, NY:
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532:2060/20150019302
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63:magnetic equator
51:Carl E. McIlwain
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71:
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65:at a number of
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561:
549:
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487:
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458:
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447:
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437:
435:Guiding center
432:
427:
420:
417:
413:gyro-resonance
398:
395:
358:
355:
342:
318:
298:
278:
275:
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199:guiding center
159:guiding center
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113:
84:
81:
78:
21:electron shell
15:
13:
10:
9:
6:
4:
3:
2:
669:
658:
657:Space physics
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606:Imke de Pater
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367:magnetosphere
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179:
178:magnetic flux
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172:
171:Lorentz force
168:
164:
160:
156:
153: where
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82:
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76:
68:
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33:
28:
22:
652:Geomagnetism
635:
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137:
133:
131:
102:
46:
42:
38:
36:
391:plasmapause
219: and
187:pitch angle
67:Earth-radii
646:Categories
461:References
363:ionosphere
146:gyroradius
485:, (2003).
317:λ
277:λ
274:
208:cycloidal
419:See also
385:, and L=
511:Bibcode
389:. The
383:1.5–2.5
329:is its
151:{x,y,z}
49:(after
43:L-value
39:L-shell
612:Icarus
609:et al.
583:
333:, and
289:where
45:, or
581:ISBN
480:NASA
401:The
365:and
105:IGRF
37:The
604:.
527:hdl
519:doi
450:TEP
408:VHF
387:4–6
265:cos
648::
579:.
525:,
517:,
507:66
505:,
499:,
415:.
111:.
41:,
589:.
529::
521::
513::
477:.
341:L
297:r
269:2
261:L
258:=
255:r
237:B
233:L
229:L
227:,
225:B
221:L
217:B
213:L
183:z
167:z
163:B
155:z
142:B
138:L
136:,
134:B
128:.
83:2
80:=
77:L
23:.
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