43:
35:
20:
176:
analyzed the orbits of electrons in a magnetic field, and determined that it was possible to construct an orbit that was radially focused in the plane of the orbit. Particles in such an orbit which moved a small distance away from the orbital radius would experience a force pushing them back to the
152:
next to one another and fired electrons from a gun at the outer edge of the magnetic field. As the field was increased, the electrons accelerated in to strike a target at the center of the field, producing X-rays. This device took a step towards the betatron concept by shaping the magnetic field to
164:
for stable orbits. He determined that in order for the orbit radius to remain constant, the field at the radius must be exactly half of the average field over the area of the magnet. This critical calculation allowed for the development of accelerators in which the particles orbited at a constant
169:. Although Wideroe made valuable contributions to the development of the theory of the Betatron, he was unable to build a device in which the electrons orbited more than one and a half times, as his device had no mechanism to keep the beam focused.
190:
applied in
Germany for a patent on a device that would combine the radial focusing condition of Walton with the vertical focusing used in Breit and Tuve's machine. He later claimed to have built a working machine, but this claim was disputed.
202:
In a betatron, the changing magnetic field from the primary coil accelerates electrons injected into the vacuum torus, causing them to circle around the torus in the same manner as current is induced in the secondary coil of a transformer
480:
505:", a suggestion by a German associate, for "Hard working by golly machine for generating extraordinarily high velocity electrons" or perhaps "Extraordinarily high velocity electron generator, high energy by golly-tron."
926:
556:
The maximum energy that a betatron can impart is limited by the strength of the magnetic field due to the saturation of iron and by practical size of the magnet core. The next generation of accelerators, the
133:
proposed a device in 1922 that would use permanent magnets to steer the beam while it was accelerated by a changing magnetic field. However, he did not pursue the idea past the theoretical stage.
275:
78:
accelerates electrons in the vacuum around a circular path. The betatron was the first machine capable of producing electron beams at energies higher than could be achieved with a simple
194:
The first team unequivocally acknowledged to have built a working betatron was led by Donald Kerst at the
University of Illinois. The accelerator was completed on July 15, 1940.
529:). A small version of a betatron was also used to provide a source of hard X-rays (by deceleration of the electron beam in a target) for prompt initiation of some experimental
308:
393:
366:
337:
501:, a fast electron) was chosen during a departmental contest. Other proposals were "rheotron", "induction accelerator", "induction electron accelerator", and even "
1181:
405:
106:
1106:
981:
952:
717:
1142:
145:
1021:
89:. Through the 1920s and 30s a number of theoretical problems related to the device were considered by scientists including
204:
118:
399:
In other words, the magnetic field at the orbit must be half the average magnetic field over its circular cross section:
1176:
540:
The
Radiation Center, the first private medical center to treat cancer patients with a betatron, was opened by Dr.
216:
165:
radius, rather than spiraling inward, as in the case of Breit and Tuve's machine, or outward, as in the case of the
1082:
148:
constructed a working device that used varying magnetic fields to accelerate electrons. Their device placed two
129:, several scientists speculated that this effect could be used to accelerate charged particles to high energies.
74:, with the electrons in the torus-shaped vacuum chamber as its secondary coil. An alternating current in the
973:
1029:
998:
177:
correct radius. These oscillations about a stable orbit in a circular accelerator are now referred to as
521:. If the electron beam is directed at a metal plate, the betatron can be used as a source of energetic
179:
42:
921:
895:
877:
851:
830:
793:
779:
745:
622:
55:
703:
122:
1118:
809:
761:
684:
646:
545:
541:
526:
286:
1056:
1102:
1064:
977:
948:
713:
638:
1130:
903:
859:
801:
753:
676:
630:
514:
30:
at
University of Illinois, 1940. Its 4-ton magnet could accelerate electrons to 24 MeV.
371:
344:
315:
1087:
886:
842:
784:
75:
664:
475:{\displaystyle \Leftrightarrow H_{0}={\frac {1}{2}}{\frac {\theta _{0}}{\pi r_{0}^{2}}}.}
899:
855:
797:
749:
626:
1161:
834:
736:
Steenbeck, Max (1943). "Beschleunigung von
Electronen durch elektrische Wirbelfelder".
530:
130:
126:
86:
82:, and the first circular accelerator in which particles orbited at a constant radius.
1170:
881:
813:
688:
498:
187:
173:
137:
98:
94:
67:
650:
503:
AuĂźerordentlichehochgeschwindigkeitselektronenentwickelndesschwerarbeitsbeigollitron
46:
A 35 MeV betatron used for photonuclear physics at the
University of Melbourne.
34:
1033:
765:
534:
157:
102:
90:
79:
24:
19:
160:
made the next major contribution to the development of the theory by deriving the
578:
558:
71:
141:
709:
525:, which may be used in industrial and medical applications (historically in
517:
experiments to provide high-energy beams of electrons—up to about 300
166:
1131:
Nuclear
Weapons Archive, Elements of Fission Weapon Design, section 4.1.8.2
805:
642:
613:
Kerst, Donald W. (January 1946). "Historical
Development of the Betatron".
907:
863:
667:(17 Dec 1928). "Ăśber ein neues Prinzip zur Herstellung hoher Spannungen".
66:-shaped vacuum chamber with an electron source. Circling the torus is an
149:
59:
1068:
757:
680:
634:
70:
with a wire winding around it. The device functions similarly to a
522:
85:
The concept of the betatron had been proposed as early as 1922 by
63:
41:
33:
18:
884:(Jul 1941). "Electronic Orbits in the Induction Accelerator".
518:
1061:
Men and Ideas in
Engineering: Twelve Histories from Illinois
782:(1940). "Acceleration of Electrons by Magnetic Induction".
310:
is the flux within the area enclosed by the electron orbit,
945:
An introduction to the physics of high energy accelerators
924:, Joseph Slepian, "X ray tube", published 1927
1119:
Nuclear
Weapons Archive, Tumbler shot series, item George
153:
keep the particles focused in the plane of acceleration.
1063:. Urbana, IL: University of Illinois Press. p. 68.
705:
From nuclear transmutation to nuclear fission, 1932-1939
835:"The Acceleration of Electrons by Magnetic Induction"
408:
374:
347:
318:
289:
219:
1055:R.A. Kingery; R.D. Berg; E.H. Schillinger (1967).
474:
387:
360:
331:
302:
269:
1101:Big Science: The Growth of Large-Scale Research,
999:"Shall New Machine Be Named Betatron or Rheotron"
101:. The first working betatron was constructed by
270:{\displaystyle \theta _{0}=2\pi r_{0}^{2}H_{0},}
608:
606:
604:
602:
600:
598:
970:Particle Accelerator Physics: An Introduction
210:The stable orbit for the electrons satisfies
8:
825:
823:
731:
729:
172:Simultaneously with Wideroe's experiments,
938:
936:
460:
455:
441:
435:
425:
416:
407:
379:
373:
352:
346:
323:
317:
294:
288:
258:
248:
243:
224:
218:
513:Betatrons were historically employed in
497:The name "betatron" (a reference to the
339:is the radius of the electron orbit, and
943:Edwards, D. A.; Syphers, M. J. (1993).
570:
533:by means of photon-induced fission and
107:University of Illinois Urbana-Champaign
1146:, Volume 58, Number 15 (July 25, 1957)
7:
1182:German inventions of the Nazi period
1022:"Physics in the 1940s: The Betatron"
117:After the discovery in the 1800s of
23:One of the first betatrons built by
1083:"The Biggest Betatron in the World"
947:. New York: Wiley. pp. 22–23.
38:A German 6 MeV betatron (1942)
14:
579:"Betatron | particle accelerator"
125:could be generated by a changing
1026:Physics Illinois: Time Capsules
485:This condition is often called
146:Bureau of Terrestrial Magnetism
1091:. March 20, 1950. p. 131.
561:, overcame these limitations.
409:
1:
303:{\displaystyle \theta _{0}}
16:Cyclic particle accelerator
1198:
119:Faraday's law of induction
669:Archiv fĂĽr Elektrotechnik
368:is the magnetic field at
1028:. Urbana-Champaign, IL:
997:Science Service (1942).
974:Oxford University Press
738:Die Naturwissenschaften
583:Encyclopedia Britannica
542:O. Arthur Stiennon
121:, which showed that an
1030:University of Illinois
806:10.1103/PhysRev.58.841
476:
389:
362:
333:
304:
271:
47:
39:
31:
1003:The Chemistry Leaflet
968:Wille, Klaus (2001).
908:10.1103/PhysRev.60.53
864:10.1103/PhysRev.60.47
477:
390:
388:{\displaystyle r_{0}}
363:
361:{\displaystyle H_{0}}
334:
332:{\displaystyle r_{0}}
305:
272:
180:betatron oscillations
68:iron transformer core
45:
37:
22:
1162:The Betatron at UIUC
1057:"Electrons in Orbit"
406:
372:
345:
316:
287:
217:
62:. It consists of a
56:particle accelerator
54:is a type of cyclic
1177:Accelerator physics
900:1941PhRv...60...53K
856:1941PhRv...60...47K
798:1940PhRv...58..841K
750:1943NW.....31..234S
627:1946Natur.157...90K
548:in the late 1950s.
487:Widerøe's condition
465:
253:
198:Operation principle
136:In the late 1920s,
123:electromotive force
758:10.1007/BF01482241
681:10.1007/BF01656341
546:Madison, Wisconsin
537:in the bomb core.
527:radiation oncology
472:
451:
385:
358:
329:
300:
267:
239:
150:solenoidal magnets
48:
40:
32:
1144:Wisconsin alumnus
1107:978-0-8047-1879-0
983:978-0-19-850549-5
954:978-0-471-55163-8
719:978-0-7503-0865-6
702:Dahl, F. (2002).
467:
433:
162:Wideroe Condition
1189:
1149:
1140:
1134:
1128:
1122:
1116:
1110:
1099:
1093:
1092:
1079:
1073:
1072:
1052:
1046:
1045:
1043:
1041:
1036:on 15 April 2012
1032:. Archived from
1017:
1011:
1010:
994:
988:
987:
965:
959:
958:
940:
931:
930:
929:
925:
918:
912:
911:
874:
868:
867:
839:
827:
818:
817:
776:
770:
769:
733:
724:
723:
699:
693:
692:
661:
655:
654:
635:10.1038/157090a0
610:
593:
592:
590:
589:
575:
515:particle physics
481:
479:
478:
473:
468:
466:
464:
459:
446:
445:
436:
434:
426:
421:
420:
394:
392:
391:
386:
384:
383:
367:
365:
364:
359:
357:
356:
338:
336:
335:
330:
328:
327:
309:
307:
306:
301:
299:
298:
276:
274:
273:
268:
263:
262:
252:
247:
229:
228:
1197:
1196:
1192:
1191:
1190:
1188:
1187:
1186:
1167:
1166:
1158:
1153:
1152:
1141:
1137:
1129:
1125:
1117:
1113:
1100:
1096:
1081:
1080:
1076:
1054:
1053:
1049:
1039:
1037:
1019:
1018:
1014:
996:
995:
991:
984:
967:
966:
962:
955:
942:
941:
934:
927:
920:
919:
915:
887:Physical Review
876:
875:
871:
843:Physical Review
837:
829:
828:
821:
785:Physical Review
778:
777:
773:
735:
734:
727:
720:
701:
700:
696:
663:
662:
658:
621:(3978): 90–95.
612:
611:
596:
587:
585:
577:
576:
572:
567:
554:
544:in a suburb of
531:nuclear weapons
511:
495:
447:
437:
412:
404:
403:
375:
370:
369:
348:
343:
342:
319:
314:
313:
290:
285:
284:
254:
220:
215:
214:
200:
115:
28:(visible right)
17:
12:
11:
5:
1195:
1193:
1185:
1184:
1179:
1169:
1168:
1165:
1164:
1157:
1156:External links
1154:
1151:
1150:
1135:
1123:
1111:
1094:
1074:
1047:
1020:Celia Elliot.
1012:
989:
982:
960:
953:
932:
913:
869:
819:
771:
744:(S): 234–235.
725:
718:
694:
675:(4): 387–406.
656:
594:
569:
568:
566:
563:
553:
550:
510:
507:
494:
491:
483:
482:
471:
463:
458:
454:
450:
444:
440:
432:
429:
424:
419:
415:
411:
397:
396:
382:
378:
355:
351:
340:
326:
322:
311:
297:
293:
278:
277:
266:
261:
257:
251:
246:
242:
238:
235:
232:
227:
223:
199:
196:
131:Joseph Slepian
127:magnetic field
114:
111:
87:Joseph Slepian
15:
13:
10:
9:
6:
4:
3:
2:
1194:
1183:
1180:
1178:
1175:
1174:
1172:
1163:
1160:
1159:
1155:
1147:
1145:
1139:
1136:
1132:
1127:
1124:
1120:
1115:
1112:
1108:
1104:
1098:
1095:
1090:
1089:
1084:
1078:
1075:
1070:
1066:
1062:
1058:
1051:
1048:
1035:
1031:
1027:
1023:
1016:
1013:
1008:
1004:
1000:
993:
990:
985:
979:
975:
971:
964:
961:
956:
950:
946:
939:
937:
933:
923:
917:
914:
909:
905:
901:
897:
893:
889:
888:
883:
879:
873:
870:
865:
861:
857:
853:
849:
845:
844:
836:
832:
826:
824:
820:
815:
811:
807:
803:
799:
795:
791:
787:
786:
781:
775:
772:
767:
763:
759:
755:
751:
747:
743:
739:
732:
730:
726:
721:
715:
711:
707:
706:
698:
695:
690:
686:
682:
678:
674:
671:(in German).
670:
666:
660:
657:
652:
648:
644:
640:
636:
632:
628:
624:
620:
616:
609:
607:
605:
603:
601:
599:
595:
584:
580:
574:
571:
564:
562:
560:
551:
549:
547:
543:
538:
536:
532:
528:
524:
520:
516:
508:
506:
504:
500:
499:beta particle
492:
490:
488:
469:
461:
456:
452:
448:
442:
438:
430:
427:
422:
417:
413:
402:
401:
400:
380:
376:
353:
349:
341:
324:
320:
312:
295:
291:
283:
282:
281:
264:
259:
255:
249:
244:
240:
236:
233:
230:
225:
221:
213:
212:
211:
208:
206:
205:Faraday's law
197:
195:
192:
189:
188:Max Steenbeck
184:
182:
181:
175:
174:Ernest Walton
170:
168:
163:
159:
154:
151:
147:
143:
139:
138:Gregory Breit
134:
132:
128:
124:
120:
112:
110:
108:
104:
100:
99:Max Steenbeck
96:
95:Ernest Walton
92:
88:
83:
81:
77:
76:primary coils
73:
69:
65:
61:
57:
53:
44:
36:
29:
26:
21:
1143:
1138:
1126:
1114:
1097:
1086:
1077:
1060:
1050:
1038:. Retrieved
1034:the original
1025:
1015:
1006:
1002:
992:
969:
963:
944:
916:
894:(1): 53–58.
891:
885:
878:Kerst, D. W.
872:
850:(1): 47–53.
847:
841:
831:Kerst, D. W.
789:
783:
780:Kerst, D. W.
774:
741:
737:
704:
697:
672:
668:
659:
618:
614:
586:. Retrieved
582:
573:
559:synchrotrons
555:
539:
535:photofission
512:
509:Applications
502:
496:
486:
484:
398:
279:
209:
201:
193:
185:
178:
171:
161:
158:Rolf Wideroe
155:
135:
116:
103:Donald Kerst
91:Rolf Wideroe
84:
80:electron gun
51:
49:
27:
25:Donald Kerst
922:USA 1645304
665:Wideröe, R.
552:Limitations
72:transformer
1171:Categories
1069:B002V8WB8I
882:Serber, R.
792:(9): 841.
588:2019-01-24
565:References
142:Merle Tuve
814:120616002
710:CRC Press
689:109942448
493:Etymology
449:π
439:θ
410:⇔
292:θ
237:π
222:θ
167:cyclotron
156:In 1929,
109:in 1940.
60:electrons
1040:13 April
833:(1941).
651:42153256
643:21015096
186:In 1935
52:betatron
1009:(7–12).
896:Bibcode
852:Bibcode
794:Bibcode
766:6832156
746:Bibcode
623:Bibcode
144:at the
113:History
105:at the
1105:
1067:
980:
951:
928:
812:
764:
716:
687:
649:
641:
615:Nature
523:x-rays
280:where
97:, and
838:(PDF)
810:S2CID
762:S2CID
685:S2CID
647:S2CID
64:torus
1103:ISBN
1088:Life
1065:ASIN
1042:2012
978:ISBN
949:ISBN
714:ISBN
639:PMID
140:and
58:for
904:doi
860:doi
802:doi
754:doi
677:doi
631:doi
619:157
519:MeV
207:).
1173::
1085:.
1059:.
1024:.
1007:15
1005:.
1001:.
976:.
972:.
935:^
902:.
892:60
890:.
880:;
858:.
848:60
846:.
840:.
822:^
808:.
800:.
790:58
788:.
760:.
752:.
742:31
740:.
728:^
712:.
708:.
683:.
673:21
645:.
637:.
629:.
617:.
597:^
581:.
489:.
183:.
93:,
50:A
1148:.
1133:.
1121:.
1109:.
1071:.
1044:.
986:.
957:.
910:.
906::
898::
866:.
862::
854::
816:.
804::
796::
768:.
756::
748::
722:.
691:.
679::
653:.
633::
625::
591:.
470:.
462:2
457:0
453:r
443:0
431:2
428:1
423:=
418:0
414:H
395:.
381:0
377:r
354:0
350:H
325:0
321:r
296:0
265:,
260:0
256:H
250:2
245:0
241:r
234:2
231:=
226:0
203:(
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
