25:
1208:
621:
1004:
1044:
1612:
to the particle mass and perpendicular velocity, while it is inversely proportional to the particle electric charge and the magnetic field strength. The time it takes the particle to complete one revolution, called the
1536:
1767:
1349:
1680:
1606:
859:
693:
218:
1825:
753:
393:
510:
450:
519:
899:
1411:
1378:
904:
269:
1024:
1449:
1254:
773:
317:
293:
238:
1458:
1689:
1283:
1420:
of the velocity and magnetic field. Thus, the
Lorentz force will always act perpendicular to the direction of motion, causing the particle to
1620:
1203:{\displaystyle r_{g}=\mathrm {3.3~m} \times {\frac {(\gamma mc^{2}/\mathrm {GeV} )\cdot (v_{\perp }/c)}{(|q|/e)\cdot (B/\mathrm {T} )}},}
1541:
628:
156:
1772:
698:
343:
459:
410:
1886:
89:
778:
61:
108:
68:
46:
1918:
1845:
75:
1913:
42:
869:
For relativistic particles the classical equation needs to be interpreted in terms of particle momentum
1908:
57:
872:
35:
1387:
1354:
247:
1683:
1609:
1038:
1009:
1614:
1427:
1034:
8:
336:
82:
1239:
758:
616:{\displaystyle f_{g,e}=(2.8\times 10^{10}\,\mathrm {hertz} /\mathrm {tesla} )\times B.}
302:
278:
223:
1882:
1452:
1257:
327:
1875:
Introduction to Plasma
Physics and Controlled Fusion, Vol. 1: Plasma Physics, 2nd ed
999:{\displaystyle r_{g}={\frac {p_{\perp }}{|q|B}}={\frac {\gamma mv_{\perp }}{|q|B}}}
142:
775:, that is the velocity of light, because the magnetic field is expressed in units
296:
1923:
1027:
320:
146:
1902:
1835:
1417:
1277:
1878:
1850:
1381:
1265:
1233:
1451:, can be determined by equating the magnitude of the Lorentz force to the
407:
It is often useful to give the gyrofrequency a sign with the definition
1840:
513:
24:
1421:
272:
150:
1041:
physics, the formula for the gyroradius can be rearranged to give
396:
1531:{\displaystyle {\frac {mv_{\perp }^{2}}{r_{g}}}=|q|v_{\perp }B.}
1762:{\displaystyle f_{g}={\frac {1}{T_{g}}}={\frac {|q|B}{2\pi m}}}
1215:
138:
1030:. This equation is correct also in the non-relativistic case.
1276:
If the charged particle is moving, then it will experience a
453:
1229:
241:
1344:{\displaystyle {\vec {F}}=q({\vec {v}}\times {\vec {B}}),}
1675:{\displaystyle T_{g}={\frac {2\pi r_{g}}{v_{\perp }}}.}
1416:
Notice that the direction of the force is given by the
275:
perpendicular to the direction of the magnetic field,
1775:
1692:
1623:
1544:
1461:
1430:
1390:
1357:
1286:
1242:
1047:
1012:
907:
875:
781:
761:
701:
631:
522:
462:
413:
346:
305:
281:
250:
226:
159:
49:. Unsourced material may be challenged and removed.
1819:
1761:
1674:
1601:{\displaystyle r_{g}={\frac {mv_{\perp }}{|q|B}}.}
1600:
1530:
1443:
1424:, or move in a circle. The radius of this circle,
1405:
1372:
1343:
1248:
1202:
1018:
998:
893:
854:{\displaystyle =\mathrm {g^{1/2}cm^{-1/2}s^{-1}} }
853:
767:
747:
688:{\displaystyle r_{g}={\frac {mcv_{\perp }}{|q|B}}}
687:
615:
504:
444:
387:
311:
287:
263:
232:
212:
213:{\displaystyle r_{g}={\frac {mv_{\perp }}{|q|B}}}
1900:
1538:Rearranging, the gyroradius can be expressed as
1820:{\displaystyle \omega _{g}={\frac {|q|B}{m}}.}
748:{\displaystyle \omega _{g}={\frac {|q|B}{mc}}}
153:, the non-relativistic gyroradius is given by
388:{\displaystyle \omega _{g}={\frac {|q|B}{m}}}
505:{\displaystyle f_{g}={\frac {qB}{2\pi m}}.}
445:{\displaystyle \omega _{g}={\frac {qB}{m}}}
561:
109:Learn how and when to remove this message
330:of this circular motion is known as the
1901:
1868:
1866:
1872:
864:
695:and the corresponding gyrofrequency
47:adding citations to reliable sources
18:
1863:
13:
1187:
1109:
1106:
1103:
1068:
838:
817:
813:
796:
597:
594:
591:
588:
585:
575:
572:
569:
566:
563:
14:
1935:
23:
1686:of the frequency we have found
34:needs additional citations for
1801:
1793:
1738:
1730:
1585:
1577:
1508:
1500:
1413:is the magnetic field vector.
1397:
1364:
1335:
1329:
1314:
1305:
1293:
1191:
1175:
1169:
1157:
1149:
1145:
1140:
1119:
1113:
1078:
986:
978:
943:
935:
788:
782:
727:
719:
675:
667:
601:
542:
372:
364:
200:
192:
1:
1856:
1846:Magnetosphere particle motion
1271:
145:in the presence of a uniform
625:In cgs-units the gyroradius
141:of the circular motion of a
7:
1829:
894:{\displaystyle p=\gamma mv}
402:
321:magnetic field flux density
10:
1940:
1617:, can be calculated to be
1406:{\displaystyle {\vec {B}}}
1373:{\displaystyle {\vec {v}}}
452:or express it in units of
340:, and can be expressed as
264:{\displaystyle v_{\perp }}
1873:Chen, Francis F. (1983).
16:Radius of particle motion
1682:Since the period is the
1608:Thus, the gyroradius is
271:is the component of the
1224:is the speed of light,
1019:{\displaystyle \gamma }
1821:
1763:
1676:
1602:
1532:
1445:
1407:
1374:
1345:
1250:
1204:
1020:
1000:
895:
855:
769:
749:
689:
617:
506:
446:
389:
313:
289:
265:
234:
214:
1822:
1764:
1677:
1610:directly proportional
1603:
1533:
1446:
1444:{\displaystyle r_{g}}
1408:
1375:
1346:
1251:
1205:
1021:
1001:
896:
856:
770:
750:
690:
618:
507:
447:
390:
314:
299:of the particle, and
290:
266:
235:
215:
1919:Kinematic properties
1877:. New York, NY USA:
1773:
1690:
1621:
1542:
1459:
1428:
1388:
1355:
1284:
1240:
1045:
1033:For calculations in
1010:
905:
873:
779:
759:
699:
629:
520:
512:For electrons, this
460:
411:
344:
303:
279:
248:
224:
157:
43:improve this article
1914:Accelerator physics
1482:
337:cyclotron frequency
1817:
1759:
1672:
1598:
1528:
1468:
1441:
1403:
1370:
1341:
1246:
1200:
1016:
996:
891:
851:
765:
745:
685:
613:
516:can be reduced to
502:
442:
385:
309:
285:
261:
230:
210:
127:radius of gyration
1909:Plasma parameters
1888:978-0-306-41332-2
1812:
1757:
1721:
1667:
1593:
1494:
1453:centripetal force
1400:
1367:
1332:
1317:
1296:
1258:elementary charge
1249:{\displaystyle e}
1195:
1067:
994:
951:
865:Relativistic case
768:{\displaystyle c}
755:include a factor
743:
683:
497:
440:
383:
328:angular frequency
312:{\displaystyle B}
288:{\displaystyle q}
244:of the particle,
233:{\displaystyle m}
208:
119:
118:
111:
93:
1931:
1893:
1892:
1870:
1826:
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1818:
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1534:
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1520:
1511:
1503:
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1492:
1483:
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1476:
1463:
1450:
1448:
1447:
1442:
1440:
1439:
1412:
1410:
1409:
1404:
1402:
1401:
1393:
1380:is the velocity
1379:
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1376:
1371:
1369:
1368:
1360:
1350:
1348:
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1342:
1334:
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1310:
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1263:
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774:
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583:
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511:
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477:
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451:
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441:
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428:
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318:
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203:
195:
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169:
168:
143:charged particle
135:cyclotron radius
114:
107:
103:
100:
94:
92:
51:
27:
19:
1939:
1938:
1934:
1933:
1932:
1930:
1929:
1928:
1899:
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1896:
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1871:
1864:
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1800:
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1770:
1746:
1737:
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1726:
1715:
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1706:
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1687:
1661:
1657:
1650:
1646:
1639:
1637:
1628:
1624:
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1619:
1618:
1584:
1576:
1575:
1568:
1564:
1560:
1558:
1549:
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1543:
1540:
1539:
1516:
1512:
1507:
1499:
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1477:
1472:
1464:
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1460:
1457:
1456:
1435:
1431:
1429:
1426:
1425:
1392:
1391:
1389:
1386:
1385:
1359:
1358:
1356:
1353:
1352:
1324:
1323:
1309:
1308:
1288:
1287:
1285:
1282:
1281:
1274:
1264:is the unit of
1261:
1241:
1238:
1237:
1228:is the unit of
1225:
1219:
1211:
1186:
1181:
1161:
1156:
1148:
1144:
1132:
1126:
1122:
1102:
1097:
1091:
1087:
1077:
1075:
1061:
1052:
1048:
1046:
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1042:
1011:
1008:
1007:
985:
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976:
969:
965:
958:
956:
942:
934:
933:
927:
923:
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912:
908:
906:
903:
902:
874:
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870:
867:
841:
837:
827:
820:
816:
803:
799:
795:
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780:
777:
776:
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757:
756:
735:
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718:
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715:
706:
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696:
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665:
658:
654:
647:
645:
636:
632:
630:
627:
626:
584:
579:
562:
555:
551:
527:
523:
521:
518:
517:
486:
478:
476:
467:
463:
461:
458:
457:
429:
427:
418:
414:
412:
409:
408:
405:
371:
363:
362:
360:
351:
347:
345:
342:
341:
304:
301:
300:
297:electric charge
280:
277:
276:
255:
251:
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246:
245:
225:
222:
221:
199:
191:
190:
183:
179:
175:
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158:
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154:
125:(also known as
115:
104:
98:
95:
52:
50:
40:
28:
17:
12:
11:
5:
1937:
1927:
1926:
1921:
1916:
1911:
1895:
1894:
1887:
1881:. p. 20.
1861:
1860:
1858:
1855:
1854:
1853:
1848:
1843:
1838:
1831:
1828:
1816:
1811:
1807:
1803:
1799:
1795:
1788:
1783:
1779:
1769:and therefore
1755:
1752:
1749:
1744:
1740:
1736:
1732:
1725:
1718:
1714:
1710:
1705:
1700:
1696:
1671:
1664:
1660:
1653:
1649:
1645:
1642:
1636:
1631:
1627:
1597:
1591:
1587:
1583:
1579:
1571:
1567:
1563:
1557:
1552:
1548:
1527:
1524:
1519:
1515:
1510:
1506:
1502:
1498:
1491:
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1480:
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1471:
1467:
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1434:
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1363:
1340:
1337:
1331:
1328:
1322:
1316:
1313:
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1304:
1301:
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1292:
1273:
1270:
1245:
1199:
1193:
1189:
1184:
1180:
1177:
1174:
1171:
1168:
1164:
1159:
1155:
1151:
1147:
1142:
1139:
1135:
1129:
1125:
1121:
1118:
1115:
1111:
1108:
1105:
1100:
1094:
1090:
1086:
1083:
1080:
1074:
1070:
1064:
1060:
1055:
1051:
1028:Lorentz factor
1015:
992:
988:
984:
980:
972:
968:
964:
961:
955:
949:
945:
941:
937:
930:
926:
920:
915:
911:
890:
887:
884:
881:
878:
866:
863:
847:
844:
840:
834:
830:
826:
823:
819:
815:
810:
806:
802:
798:
793:
790:
787:
784:
764:
741:
738:
733:
729:
725:
721:
714:
709:
705:
681:
677:
673:
669:
661:
657:
653:
650:
644:
639:
635:
612:
609:
606:
603:
599:
596:
593:
590:
587:
582:
577:
574:
571:
568:
565:
558:
554:
550:
547:
544:
541:
536:
533:
530:
526:
501:
495:
492:
489:
484:
481:
475:
470:
466:
439:
435:
432:
426:
421:
417:
404:
401:
382:
378:
374:
370:
366:
359:
354:
350:
308:
284:
258:
254:
229:
206:
202:
198:
194:
186:
182:
178:
172:
167:
163:
147:magnetic field
117:
116:
31:
29:
22:
15:
9:
6:
4:
3:
2:
1936:
1925:
1922:
1920:
1917:
1915:
1912:
1910:
1907:
1906:
1904:
1890:
1884:
1880:
1876:
1869:
1867:
1862:
1852:
1849:
1847:
1844:
1842:
1839:
1837:
1836:Beam rigidity
1834:
1833:
1827:
1814:
1809:
1805:
1797:
1786:
1781:
1777:
1753:
1750:
1747:
1742:
1734:
1723:
1716:
1712:
1708:
1703:
1698:
1694:
1685:
1669:
1662:
1658:
1651:
1647:
1643:
1640:
1634:
1629:
1625:
1616:
1611:
1595:
1589:
1581:
1569:
1565:
1561:
1555:
1550:
1546:
1525:
1522:
1517:
1513:
1504:
1496:
1489:
1485:
1478:
1473:
1469:
1465:
1454:
1436:
1432:
1423:
1419:
1418:cross product
1414:
1394:
1383:
1361:
1338:
1326:
1320:
1311:
1302:
1299:
1290:
1279:
1278:Lorentz force
1269:
1267:
1259:
1243:
1235:
1234:electronVolts
1231:
1222:
1217:
1197:
1182:
1178:
1172:
1166:
1162:
1153:
1137:
1133:
1127:
1123:
1116:
1098:
1092:
1088:
1084:
1081:
1072:
1062:
1058:
1053:
1049:
1040:
1039:astroparticle
1036:
1031:
1029:
1013:
990:
982:
970:
966:
962:
959:
953:
947:
939:
928:
924:
918:
913:
909:
888:
885:
882:
879:
876:
862:
845:
842:
832:
828:
824:
821:
808:
804:
800:
791:
785:
762:
739:
736:
731:
723:
712:
707:
703:
679:
671:
659:
655:
651:
648:
642:
637:
633:
623:
610:
607:
604:
580:
556:
552:
548:
545:
539:
534:
531:
528:
524:
515:
499:
493:
490:
487:
482:
479:
473:
468:
464:
455:
437:
433:
430:
424:
419:
415:
400:
398:
380:
376:
368:
357:
352:
348:
339:
338:
333:
332:gyrofrequency
329:
324:
322:
306:
298:
282:
274:
256:
252:
243:
227:
204:
196:
184:
180:
176:
170:
165:
161:
152:
148:
144:
140:
136:
132:
131:Larmor radius
128:
124:
113:
110:
102:
99:December 2023
91:
88:
84:
81:
77:
74:
70:
67:
63:
60: –
59:
55:
54:Find sources:
48:
44:
38:
37:
32:This article
30:
26:
21:
20:
1879:Plenum Press
1874:
1851:Gyrokinetics
1415:
1275:
1220:
1032:
868:
624:
406:
395:in units of
335:
331:
325:
134:
130:
126:
122:
120:
105:
96:
86:
79:
72:
65:
58:"Gyroradius"
53:
41:Please help
36:verification
33:
1035:accelerator
1903:Categories
1857:References
1684:reciprocal
1272:Derivation
123:gyroradius
69:newspapers
1841:Cyclotron
1778:ω
1751:π
1663:⊥
1644:π
1570:⊥
1518:⊥
1474:⊥
1398:→
1365:→
1330:→
1321:×
1315:→
1294:→
1280:given by
1173:⋅
1128:⊥
1117:⋅
1082:γ
1073:×
1014:γ
971:⊥
960:γ
929:⊥
883:γ
843:−
822:−
704:ω
660:⊥
605:×
549:×
514:frequency
491:π
416:ω
399:/second.
349:ω
257:⊥
185:⊥
137:) is the
1830:See also
1214:denotes
403:Variants
319:is the
273:velocity
151:SI units
1256:is the
1026:is the
397:radians
295:is the
240:is the
83:scholar
1885:
1615:period
1422:gyrate
1382:vector
1351:where
1260:, and
1216:metres
1210:where
1066:
1006:where
220:where
139:radius
85:
78:
71:
64:
56:
1924:Radii
1266:tesla
456:with
454:hertz
334:, or
149:. In
90:JSTOR
76:books
1883:ISBN
1384:and
1230:Giga
1037:and
326:The
242:mass
121:The
62:news
1455:as
1226:GeV
1063:3.3
546:2.8
133:or
45:by
1905::
1865:^
1268:.
1236:,
1218:,
901::
861:.
557:10
553:10
323:.
129:,
1891:.
1815:.
1810:m
1806:B
1802:|
1798:q
1794:|
1787:=
1782:g
1754:m
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1743:B
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1724:=
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1713:T
1709:1
1704:=
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1695:f
1670:.
1659:v
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1497:=
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1336:)
1327:B
1312:v
1306:(
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1300:=
1291:F
1262:T
1244:e
1232:-
1221:c
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1198:,
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1188:T
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1176:(
1170:)
1167:e
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1150:|
1146:(
1141:)
1138:c
1134:/
1124:v
1120:(
1114:)
1110:V
1107:e
1104:G
1099:/
1093:2
1089:c
1085:m
1079:(
1069:m
1059:=
1054:g
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991:B
987:|
983:q
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967:v
963:m
954:=
948:B
944:|
940:q
936:|
925:p
919:=
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889:v
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880:=
877:p
846:1
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829:/
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814:c
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805:/
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792:=
789:]
786:B
783:[
763:c
740:c
737:m
732:B
728:|
724:q
720:|
713:=
708:g
680:B
676:|
672:q
668:|
656:v
652:c
649:m
643:=
638:g
634:r
611:.
608:B
602:)
598:a
595:l
592:s
589:e
586:t
581:/
576:z
573:t
570:r
567:e
564:h
543:(
540:=
535:e
532:,
529:g
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500:.
494:m
488:2
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480:q
474:=
469:g
465:f
438:m
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425:=
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381:m
377:B
373:|
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365:|
358:=
353:g
307:B
283:q
253:v
228:m
205:B
201:|
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193:|
181:v
177:m
171:=
166:g
162:r
112:)
106:(
101:)
97:(
87:·
80:·
73:·
66:·
39:.
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