880:
31:
443:
It is notable that the cyclotron frequency is independent of the radius and velocity and therefore independent of the particle's kinetic energy; all particles with the same charge-to-mass ratio rotate around magnetic field lines with the same frequency. This is only true in the non-relativistic
451:
The cyclotron frequency is also useful in non-uniform magnetic fields, in which (assuming slow variation of magnitude of the magnetic field) the movement is approximately helical - in the direction parallel to the magnetic field, the motion is uniform, whereas in the plane perpendicular to the
437:
587:
362:
206:
151:
724:
For some materials, the motion of electrons follows loops that depend on the applied magnetic field, but not exactly the same way. For these materials, we define a cyclotron effective mass,
507:
797:
700:
278:
617:
643:
749:
719:
945:
921:
378:
219:
Since the motion in an orthogonal and constant magnetic field is always circular, the cyclotron frequency is given by equality of
536:
316:
452:
magnetic field the movement is, as previously circular. The sum of these two motions gives a trajectory in the shape of a
843:
17:
159:
960:
109:
940:
469:
459:
When the charged particle begins to approach relativistic speeds, the centripetal force should be multiplied by the
757:
61:
that utilizes an oscillating electric field tuned to this resonance to add kinetic energy to charged particles.
38:, which is the classical trajectory of a charged particle (here positive charge) under a uniform magnetic field
955:
914:
662:
232:
94:
950:
814:
907:
596:
809:
622:
895:
868:
727:
646:
369:
58:
8:
887:
707:
220:
78:
49:
describes the interaction of external forces with charged particles experiencing a
891:
523:
460:
50:
934:
307:
224:
706:
Note that converting this expression to SI units introduces a factor of the
879:
300:
445:
99:
54:
720:
Effective mass (solid-state physics) § Cyclotron effective mass
519:
81:
moving perpendicular to the direction of a uniform magnetic field
30:
526:. In Gaussian units, the Lorentz force differs by a factor of 1/
432:{\displaystyle f={\frac {\omega }{2\pi }}={\frac {qB}{2\pi m}}}
453:
463:, yielding a corresponding factor in the angular frequency:
833:
Physics by M. Alonso & E. Finn, Addison Wesley 1996.
53:, thus moving on a circular path. It is named after the
582:{\displaystyle \omega ={\frac {v}{r}}={\frac {qB}{mc}}}
444:
limit, and underpins the principle of operation of the
357:{\displaystyle \omega ={\frac {v}{r}}={\frac {qB}{m}}}
34:
Diagram of a cyclotron orbit of a particle with speed
760:
730:
665:
625:
599:
539:
522:. In some cases, the cyclotron frequency is given in
472:
381:
319:
235:
162:
112:
791:
743:
694:
637:
611:
581:
501:
431:
356:
272:
201:{\displaystyle \omega _{\rm {c}}={\frac {qB}{mc}}}
200:
145:
146:{\displaystyle \omega _{\rm {c}}={\frac {qB}{m}}}
932:
869:Calculate Cyclotron frequency with Wolfram Alpha
593:For materials with little or no magnetism (i.e.
64:
855:Ashcroft and Mermin. Solid State Physics. pp12
502:{\displaystyle \omega ={\frac {qB}{\gamma m}}}
915:
792:{\displaystyle \omega ={\frac {qB}{m^{*}}}}
922:
908:
695:{\displaystyle \omega ={\frac {qH}{mc}}}
29:
273:{\displaystyle {\frac {mv^{2}}{r}}=qBv}
14:
946:Electric and magnetic fields in matter
933:
827:
530:, the speed of light, which leads to:
85:(constant magnitude and direction).
874:
645:, so we can use the easily measured
372:(being the cyclotron frequency) as:
844:Introduction to Solid State Physics
24:
169:
119:
25:
972:
862:
713:
513:
878:
295:, and the circular path radius
849:
836:
13:
1:
820:
612:{\displaystyle \mu \approx 1}
214:
65:Cyclotron resonance frequency
894:. You can help Knowledge by
815:Electron cyclotron resonance
7:
803:
27:Motion of charged particles
10:
977:
873:
717:
638:{\displaystyle H\approx B}
961:Accelerator physics stubs
647:magnetic field intensity
98:
93:
941:Condensed matter physics
810:Ion cyclotron resonance
283:with the particle mass
890:-related article is a
846:, 8th edition. pp. 153
793:
745:
696:
639:
613:
583:
503:
433:
358:
274:
202:
147:
77:is the frequency of a
43:
956:Scientific techniques
794:
746:
744:{\displaystyle m^{*}}
697:
640:
614:
584:
504:
434:
359:
275:
203:
148:
33:
758:
728:
663:
623:
597:
537:
470:
379:
370:rotational frequency
317:
233:
160:
110:
89:Cyclotron frequency
59:particle accelerator
951:Accelerator physics
888:accelerator physics
708:vacuum permeability
90:
71:cyclotron frequency
47:Cyclotron resonance
18:Cyclotron frequency
789:
741:
692:
635:
609:
579:
499:
429:
354:
270:
198:
143:
88:
44:
903:
902:
842:Kittel, Charles.
787:
690:
577:
554:
518:The above is for
497:
427:
401:
352:
334:
256:
221:centripetal force
212:
211:
196:
141:
16:(Redirected from
968:
924:
917:
910:
882:
875:
856:
853:
847:
840:
834:
831:
798:
796:
795:
790:
788:
786:
785:
776:
768:
750:
748:
747:
742:
740:
739:
701:
699:
698:
693:
691:
689:
681:
673:
644:
642:
641:
636:
618:
616:
615:
610:
588:
586:
585:
580:
578:
576:
568:
560:
555:
547:
508:
506:
505:
500:
498:
496:
488:
480:
438:
436:
435:
430:
428:
426:
415:
407:
402:
400:
389:
363:
361:
360:
355:
353:
348:
340:
335:
327:
279:
277:
276:
271:
257:
252:
251:
250:
237:
207:
205:
204:
199:
197:
195:
187:
179:
174:
173:
172:
152:
150:
149:
144:
142:
137:
129:
124:
123:
122:
91:
87:
79:charged particle
21:
976:
975:
971:
970:
969:
967:
966:
965:
931:
930:
929:
928:
865:
860:
859:
854:
850:
841:
837:
832:
828:
823:
806:
781:
777:
769:
767:
759:
756:
755:
735:
731:
729:
726:
725:
722:
716:
682:
674:
672:
664:
661:
660:
624:
621:
620:
598:
595:
594:
569:
561:
559:
546:
538:
535:
534:
516:
489:
481:
479:
471:
468:
467:
416:
408:
406:
393:
388:
380:
377:
376:
341:
339:
326:
318:
315:
314:
246:
242:
238:
236:
234:
231:
230:
217:
188:
180:
178:
168:
167:
163:
161:
158:
157:
130:
128:
118:
117:
113:
111:
108:
107:
67:
28:
23:
22:
15:
12:
11:
5:
974:
964:
963:
958:
953:
948:
943:
927:
926:
919:
912:
904:
901:
900:
883:
872:
871:
864:
863:External links
861:
858:
857:
848:
835:
825:
824:
822:
819:
818:
817:
812:
805:
802:
801:
800:
784:
780:
775:
772:
766:
763:
738:
734:
715:
714:Effective mass
712:
704:
703:
688:
685:
680:
677:
671:
668:
634:
631:
628:
608:
605:
602:
591:
590:
575:
572:
567:
564:
558:
553:
550:
545:
542:
524:Gaussian units
515:
514:Gaussian units
512:
511:
510:
495:
492:
487:
484:
478:
475:
461:Lorentz factor
441:
440:
425:
422:
419:
414:
411:
405:
399:
396:
392:
387:
384:
366:
365:
351:
347:
344:
338:
333:
330:
325:
322:
299:, also called
281:
280:
269:
266:
263:
260:
255:
249:
245:
241:
216:
213:
210:
209:
194:
191:
186:
183:
177:
171:
166:
154:
140:
136:
133:
127:
121:
116:
103:
102:
97:
66:
63:
51:magnetic field
26:
9:
6:
4:
3:
2:
973:
962:
959:
957:
954:
952:
949:
947:
944:
942:
939:
938:
936:
925:
920:
918:
913:
911:
906:
905:
899:
897:
893:
889:
884:
881:
877:
876:
870:
867:
866:
852:
845:
839:
830:
826:
816:
813:
811:
808:
807:
782:
778:
773:
770:
764:
761:
754:
753:
752:
736:
732:
721:
711:
709:
686:
683:
678:
675:
669:
666:
659:
658:
657:
655:
651:
650:
632:
629:
626:
606:
603:
600:
573:
570:
565:
562:
556:
551:
548:
543:
540:
533:
532:
531:
529:
525:
521:
493:
490:
485:
482:
476:
473:
466:
465:
464:
462:
457:
455:
449:
447:
423:
420:
417:
412:
409:
403:
397:
394:
390:
385:
382:
375:
374:
373:
371:
349:
345:
342:
336:
331:
328:
323:
320:
313:
312:
311:
309:
308:angular speed
304:
302:
298:
294:
290:
287:, its charge
286:
267:
264:
261:
258:
253:
247:
243:
239:
229:
228:
227:
226:
225:Lorentz force
223:and magnetic
222:
208:
192:
189:
184:
181:
175:
164:
155:
153:
138:
134:
131:
125:
114:
105:
104:
101:
96:
92:
86:
84:
80:
76:
75:gyrofrequency
72:
62:
60:
56:
52:
48:
41:
37:
32:
19:
896:expanding it
885:
851:
838:
829:
723:
705:
653:
648:
592:
527:
517:
458:
450:
442:
367:
305:
296:
292:
288:
284:
282:
218:
156:
106:
82:
74:
70:
68:
46:
45:
39:
35:
652:instead of
368:Giving the
291:, velocity
57:, a cyclic
935:Categories
821:References
718:See also:
301:gyroradius
215:Derivation
783:∗
762:ω
751:so that:
737:∗
667:ω
630:≈
604:≈
601:μ
541:ω
491:γ
474:ω
446:cyclotron
421:π
398:π
391:ω
321:ω
310:is then:
165:ω
115:ω
100:CGS units
55:cyclotron
804:See also
520:SI units
95:SI units
886:This
454:helix
892:stub
306:The
69:The
73:or
937::
710:.
656::
619:)
456:.
448:.
303:.
923:e
916:t
909:v
898:.
799:.
779:m
774:B
771:q
765:=
733:m
702:.
687:c
684:m
679:H
676:q
670:=
654:B
649:H
633:B
627:H
607:1
589:.
574:c
571:m
566:B
563:q
557:=
552:r
549:v
544:=
528:c
509:.
494:m
486:B
483:q
477:=
439:,
424:m
418:2
413:B
410:q
404:=
395:2
386:=
383:f
364:.
350:m
346:B
343:q
337:=
332:r
329:v
324:=
297:r
293:v
289:q
285:m
268:v
265:B
262:q
259:=
254:r
248:2
244:v
240:m
193:c
190:m
185:B
182:q
176:=
170:c
139:m
135:B
132:q
126:=
120:c
83:B
42:.
40:B
36:v
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
