792:
1691:
1504:
516:
2429:
are the minimum and maximum impact parameters. The minimum impact parameter is the closest distance of approach between two particles in a collision. The maximum impact parameter is the largest distance between two particles such that their trajectories are unaltered by the collision. The maximum
2896:
Intrabeam scattering is an important effect in the proposed "ultimate storage ring" light sources and lepton damping rings for
International Linear Collider (ILC) and Compact Linear Collider (CLIC). Experimental studies aimed at understanding intrabeam scattering in beams similar to those used in
58:
in 1983. The
Bjorken-Mtingwa formulation is regarded as being the most general solution. Both of these methods are computationally intensive. Several approximations of these methods have been done that are easier to evaluate, but less general. These approximations are summarized in
1510:
1323:
1317:
504:
368:
2699:
787:{\displaystyle {\frac {1}{T_{i}}}=4\pi A(\operatorname {log} )\left\langle \int _{0}^{\infty }\,d\lambda \ {\frac {\lambda ^{1/2}}{^{1/2}}}\left\{\operatorname {Tr} L^{i}\operatorname {Tr} \left({\frac {1}{L+\lambda I}}\right)-3\operatorname {Tr} \left\right\}\right\rangle }
1109:
232:
2764:. Above transition, with just IBS, this implies that there is no equilibrium. However, for the case of radiation damping and diffusion, there is certainly an equilibrium. The effect of IBS is to cause a change in the equilibrium values of the emittances.
39:, resulting in a new equilibrium beam emittance with a relaxation time on the order of milliseconds. Intrabeam scattering creates an inverse relationship between the smallness of the beam and the number of particles it contains, therefore limiting
2887:
1998:
983:
2545:
115:. The Touschek effect is a lifetime based on intrabeam collisions that result in both particles being ejected from the beam. Intrabeam scattering is a risetime based on intrabeam collisions that result in momentum coupling.
1686:{\displaystyle L^{(v)}={\frac {\beta _{v}}{\epsilon _{v}}}{\begin{pmatrix}0&0&0\\0&{\frac {\gamma ^{2}{\mathcal {H}}_{v}}{\beta _{v}}}&-\gamma \phi _{v}\\0&-\gamma \phi _{v}&1\end{pmatrix}}}
1499:{\displaystyle L^{(h)}={\frac {\beta _{h}}{\epsilon _{h}}}{\begin{pmatrix}1&-\gamma \phi _{h}&0\\-\gamma \phi _{h}&{\frac {\gamma ^{2}{\mathcal {H}}_{h}}{\beta _{h}}}&0\\0&0&0\end{pmatrix}}}
2762:
1194:
375:
239:
2599:
31:
in all three dimensions. This generally causes the beam size to grow. In proton accelerators, intrabeam scattering causes the beam to grow slowly over a period of several hours. This limits the
1873:
989:
129:
1188:
2195:
2266:
2775:
2301:
2463:
102:
2159:
2359:
2330:
2230:
885:
2036:
879:
are the momentum spread, horizontal, and vertical are the betatron growth times. The angle brackets <...> indicate that the integral is averaged around the ring.
2588:
2568:
2427:
2394:
2124:
2102:
877:
850:
823:
1879:
2080:
2058:
2590:, the longitudinal is typically much "colder" than the transverse. Thus, we typically get growth in the longitudinal, and shrinking in the transverse.
2480:
2474:
IBS can be seen as a process in which the different "temperatures" try to equilibrate. The growth rates would be zero in the case that
1312:{\displaystyle L^{(p)}={\frac {\gamma ^{2}}{\sigma _{p}^{2}}}{\begin{pmatrix}0&0&0\\0&1&0\\0&0&0\end{pmatrix}}}
499:{\displaystyle {\frac {1}{T_{v}}}\ {\stackrel {\mathrm {def} }{=}}\ {\frac {1}{\epsilon _{v}^{1/2}}}{\frac {d\epsilon _{v}^{1/2}}{dt}}}
363:{\displaystyle {\frac {1}{T_{h}}}\ {\stackrel {\mathrm {def} }{=}}\ {\frac {1}{\epsilon _{h}^{1/2}}}{\frac {d\epsilon _{h}^{1/2}}{dt}}}
2981:
2772:
In the case of a coupled beam, one must consider the evolution of the coupled eigenemittances. The growth rates are generalized to
2430:
impact parameter should be taken to be the minimum beam size. See for some analysis of the
Coulomb log and support for this result.
2707:
2694:{\displaystyle {\frac {\epsilon _{x}}{\beta _{x}}}+{\frac {\epsilon _{y}}{\beta _{y}}}+\eta _{s}{\frac {\epsilon _{z}}{\beta _{z}}}}
104:
dependence. This means that its effects diminish with increasing beam energy. Other ways of mitigating IBS effects are the use of
3010:
3044:
1697:
1104:{\displaystyle A={\frac {r_{0}^{2}cN}{64\pi ^{2}\beta ^{3}\gamma ^{4}\epsilon _{h}\epsilon _{v}\sigma _{s}\sigma _{p}}}}
227:{\displaystyle {\frac {1}{T_{p}}}\ {\stackrel {\mathrm {def} }{=}}\ {\frac {1}{\sigma _{p}}}{\frac {d\sigma _{p}}{dt}}}
3006:
K. L. F. Bane, H. Hayano, K. Kubo, T. Naito, T. Okugi, and J. Urakawa, Phys. Rev. ST Accel. Beams 5, 084403 (2002).
1115:
2933:
2882:{\displaystyle {\frac {1}{\tau _{1,2,3}}}={\frac {1}{\epsilon _{1,2,3}}}{\frac {d\epsilon _{1,2,3}}{dt}}}
105:
2953:
2273:
978:{\displaystyle (\operatorname {log} )=\ln {\frac {b_{min}}{b_{max}}}=\ln {\frac {2}{\theta _{min}}}}
47:
2435:
2164:
108:, and reducing beam intensity. Transverse intrabeam scattering rates are sensitive to dispersion.
72:
24:
2235:
2131:
2337:
2308:
2202:
2985:
2915:
2916:
Proceedings of the 9th
International Conference on High Energy Accelerators, Stanford, CA, 1974
2009:
2570:
coming from the
Lorentz transformation. From this equation, we see that due to the factor of
36:
2573:
2553:
2399:
2366:
2109:
2087:
1993:{\displaystyle \phi _{h,v}=\eta '_{h,v}-{\frac {1}{2}}\beta '_{h,v}\eta _{h,v}/\beta _{h,v}}
855:
828:
801:
46:
The two principal methods for calculating the effects of intrabeam scattering were done by
3014:
2593:
One may also the express conservation of energy in IBS in terms of the
Piwinski invariant
112:
3026:
3007:
2065:
2043:
55:
28:
3038:
51:
35:
lifetime. In circular lepton accelerators, intrabeam scattering is counteracted by
2982:"SLAC-R-820 -- Analytical Approach to Eigen-Emittance Evolution in Storage Rings"
2540:{\displaystyle {\frac {\sigma _{\delta }}{\gamma }}=\sigma _{x'}=\sigma _{y'}}
40:
32:
2968:, "A New analysis of intrabeam scattering", Conf.Proc. C030512 (2003) 126,
2897:
these types of machines have been conducted at KEK, CesrTA, and elsewhere.
3025:
M. P. Ehrlichman, et al., Phys. Rev. ST Accel. Beams 16, 104401 (2013).
2934:
https://s3.cern.ch/inspire-prod-files-a/a7d86ec1529ba6512d446523cd88c2d5
2969:
2954:
https://journals.aps.org/prab/abstract/10.1103/PhysRevSTAB.8.081001
123:
The betatron growth rates for intrabeam scattering are defined as,
2757:{\displaystyle \eta _{s}={\frac {1}{\gamma ^{2}}}-\alpha _{c}}
1704:
1603:
1442:
2268:
is the dispersion function and its derivative, respectively
2197:
is the betatron function and its derivative, respectively
3027:
http://prst-ab.aps.org/abstract/PRSTAB/v16/i10/e104401
1562:
1375:
1251:
2778:
2710:
2602:
2576:
2556:
2483:
2438:
2402:
2369:
2340:
2311:
2276:
2238:
2205:
2167:
2134:
2112:
2090:
2068:
2046:
2012:
1882:
1700:
1513:
1326:
1197:
1118:
992:
888:
858:
831:
804:
519:
378:
242:
132:
75:
3008:
http://prst-ab.aps.org/abstract/PRSTAB/v5/i8/e084403
61:
Intrabeam scattering formulas for high energy beams
2881:
2756:
2693:
2582:
2562:
2539:
2457:
2421:
2388:
2353:
2324:
2295:
2260:
2224:
2189:
2153:
2118:
2096:
2074:
2052:
2030:
1992:
1868:{\displaystyle {\mathcal {H}}_{h,v}=/\beta _{h,v}}
1867:
1685:
1498:
1311:
1182:
1103:
977:
871:
844:
817:
786:
498:
362:
226:
96:
510:The following is general to all bunched beams,
111:Intrabeam scattering is closely related to the
27:where collisions between particles couple the
8:
1183:{\displaystyle L=L^{(p)}+L^{(h)}+L^{(v)}\,}
2850:
2840:
2820:
2811:
2788:
2779:
2777:
2748:
2733:
2724:
2715:
2709:
2683:
2673:
2667:
2661:
2646:
2636:
2630:
2619:
2609:
2603:
2601:
2575:
2555:
2526:
2508:
2490:
2484:
2482:
2443:
2437:
2407:
2401:
2374:
2368:
2345:
2339:
2316:
2310:
2281:
2275:
2243:
2237:
2210:
2204:
2172:
2166:
2139:
2133:
2111:
2104:is velocity divided by the speed of light
2089:
2067:
2045:
2022:
2017:
2011:
1978:
1969:
1957:
1938:
1924:
1906:
1887:
1881:
1853:
1844:
1835:
1825:
1806:
1792:
1774:
1758:
1742:
1731:
1709:
1703:
1702:
1699:
1664:
1639:
1619:
1608:
1602:
1601:
1594:
1587:
1557:
1549:
1539:
1533:
1518:
1512:
1458:
1447:
1441:
1440:
1433:
1426:
1418:
1393:
1370:
1362:
1352:
1346:
1331:
1325:
1246:
1238:
1233:
1223:
1217:
1202:
1196:
1179:
1167:
1148:
1129:
1117:
1092:
1082:
1072:
1062:
1052:
1042:
1032:
1011:
1006:
999:
991:
961:
952:
929:
913:
907:
887:
863:
857:
836:
830:
809:
803:
744:
734:
688:
672:
644:
640:
598:
594:
588:
578:
572:
567:
529:
520:
518:
475:
471:
466:
456:
444:
440:
435:
426:
408:
407:
402:
400:
399:
388:
379:
377:
339:
335:
330:
320:
308:
304:
299:
290:
272:
271:
266:
264:
263:
252:
243:
241:
207:
197:
189:
180:
162:
161:
156:
154:
153:
142:
133:
131:
88:
79:
74:
2928:J. Bjorken and S. Mtingwa, Part. Accel.
2906:
2038:is the classical radius of the particle
2892:Measurement and comparison with Theory
7:
2470:Equilibrium and growth rate sum rule
2082:is the number of particles per bunch
2970:http://inspirehep.net/record/623294
2919:(SLAC, Stanford, 1974), p. 405
573:
415:
412:
409:
279:
276:
273:
169:
166:
163:
69:Intrabeam scattering rates have a
14:
2465:is the minimum scattering angle.
2296:{\displaystyle \epsilon _{h,v}}
1841:
1832:
1751:
1724:
1525:
1519:
1338:
1332:
1209:
1203:
1174:
1168:
1155:
1149:
1136:
1130:
895:
889:
637:
633:
618:
609:
555:
549:
1:
2948:, Phys. Rev. ST Accel. Beams
2458:{\displaystyle \theta _{min}}
2190:{\displaystyle \beta '_{h,v}}
97:{\displaystyle 1/\gamma ^{4}}
2261:{\displaystyle \eta '_{h,v}}
2154:{\displaystyle \beta _{h,v}}
2354:{\displaystyle \sigma _{p}}
2325:{\displaystyle \sigma _{s}}
2225:{\displaystyle \eta _{h,v}}
119:Bjorken–Mtingwa formulation
3061:
2126:is energy divided by mass
2031:{\displaystyle r_{0}^{2}}
2583:{\displaystyle \gamma }
2563:{\displaystyle \gamma }
2422:{\displaystyle b_{max}}
2389:{\displaystyle b_{min}}
2119:{\displaystyle \gamma }
2883:
2758:
2695:
2584:
2564:
2541:
2459:
2423:
2390:
2361:is the momentum spread
2355:
2326:
2297:
2262:
2226:
2191:
2155:
2120:
2098:
2097:{\displaystyle \beta }
2076:
2054:
2032:
1994:
1869:
1687:
1500:
1313:
1184:
1105:
979:
873:
846:
819:
788:
500:
364:
228:
98:
2884:
2768:Inclusion of coupling
2759:
2696:
2585:
2565:
2542:
2460:
2424:
2391:
2356:
2327:
2298:
2263:
2227:
2192:
2156:
2121:
2099:
2077:
2060:is the speed of light
2055:
2033:
1995:
1870:
1688:
1501:
1314:
1185:
1106:
980:
874:
872:{\displaystyle T_{v}}
847:
845:{\displaystyle T_{h}}
820:
818:{\displaystyle T_{p}}
789:
501:
365:
229:
99:
2776:
2708:
2600:
2574:
2554:
2550:which the factor of
2481:
2436:
2400:
2367:
2338:
2309:
2274:
2236:
2203:
2165:
2132:
2110:
2088:
2066:
2044:
2010:
1880:
1698:
1511:
1324:
1195:
1116:
990:
886:
856:
829:
802:
517:
376:
240:
130:
73:
17:Intrabeam scattering
3045:Accelerator physics
3013:20 May 2009 at the
2332:is the bunch length
2257:
2186:
2027:
1952:
1920:
1820:
1788:
1747:
1243:
1016:
577:
484:
453:
348:
317:
25:accelerator physics
2879:
2754:
2691:
2580:
2560:
2537:
2455:
2419:
2386:
2351:
2322:
2293:
2258:
2239:
2222:
2187:
2168:
2151:
2116:
2094:
2072:
2050:
2028:
2013:
1990:
1934:
1902:
1865:
1802:
1770:
1727:
1683:
1677:
1496:
1490:
1309:
1303:
1229:
1180:
1101:
1002:
975:
869:
842:
815:
784:
563:
496:
462:
431:
360:
326:
295:
224:
94:
23:) is an effect in
2877:
2838:
2806:
2739:
2689:
2652:
2625:
2499:
2075:{\displaystyle N}
2053:{\displaystyle c}
1932:
1800:
1625:
1555:
1464:
1368:
1244:
1099:
973:
941:
763:
707:
655:
587:
535:
494:
454:
425:
420:
398:
394:
358:
318:
289:
284:
262:
258:
222:
195:
179:
174:
152:
148:
37:radiation damping
3052:
3029:
3023:
3017:
3004:
2998:
2997:
2995:
2993:
2984:. Archived from
2978:
2972:
2962:
2956:
2952:, 081001 (2005)
2942:
2936:
2926:
2920:
2913:A. Piwinski, in
2911:
2888:
2886:
2885:
2880:
2878:
2876:
2868:
2867:
2866:
2841:
2839:
2837:
2836:
2812:
2807:
2805:
2804:
2780:
2763:
2761:
2760:
2755:
2753:
2752:
2740:
2738:
2737:
2725:
2720:
2719:
2700:
2698:
2697:
2692:
2690:
2688:
2687:
2678:
2677:
2668:
2666:
2665:
2653:
2651:
2650:
2641:
2640:
2631:
2626:
2624:
2623:
2614:
2613:
2604:
2589:
2587:
2586:
2581:
2569:
2567:
2566:
2561:
2546:
2544:
2543:
2538:
2536:
2535:
2534:
2518:
2517:
2516:
2500:
2495:
2494:
2485:
2464:
2462:
2461:
2456:
2454:
2453:
2428:
2426:
2425:
2420:
2418:
2417:
2395:
2393:
2392:
2387:
2385:
2384:
2360:
2358:
2357:
2352:
2350:
2349:
2331:
2329:
2328:
2323:
2321:
2320:
2303:is the emittance
2302:
2300:
2299:
2294:
2292:
2291:
2267:
2265:
2264:
2259:
2253:
2231:
2229:
2228:
2223:
2221:
2220:
2196:
2194:
2193:
2188:
2182:
2160:
2158:
2157:
2152:
2150:
2149:
2125:
2123:
2122:
2117:
2103:
2101:
2100:
2095:
2081:
2079:
2078:
2073:
2059:
2057:
2056:
2051:
2037:
2035:
2034:
2029:
2026:
2021:
1999:
1997:
1996:
1991:
1989:
1988:
1973:
1968:
1967:
1948:
1933:
1925:
1916:
1898:
1897:
1874:
1872:
1871:
1866:
1864:
1863:
1848:
1840:
1839:
1830:
1829:
1816:
1801:
1793:
1784:
1769:
1768:
1746:
1741:
1720:
1719:
1708:
1707:
1692:
1690:
1689:
1684:
1682:
1681:
1669:
1668:
1644:
1643:
1626:
1624:
1623:
1614:
1613:
1612:
1607:
1606:
1599:
1598:
1588:
1556:
1554:
1553:
1544:
1543:
1534:
1529:
1528:
1505:
1503:
1502:
1497:
1495:
1494:
1465:
1463:
1462:
1453:
1452:
1451:
1446:
1445:
1438:
1437:
1427:
1423:
1422:
1398:
1397:
1369:
1367:
1366:
1357:
1356:
1347:
1342:
1341:
1318:
1316:
1315:
1310:
1308:
1307:
1245:
1242:
1237:
1228:
1227:
1218:
1213:
1212:
1189:
1187:
1186:
1181:
1178:
1177:
1159:
1158:
1140:
1139:
1110:
1108:
1107:
1102:
1100:
1098:
1097:
1096:
1087:
1086:
1077:
1076:
1067:
1066:
1057:
1056:
1047:
1046:
1037:
1036:
1023:
1015:
1010:
1000:
984:
982:
981:
976:
974:
972:
971:
953:
942:
940:
939:
924:
923:
908:
878:
876:
875:
870:
868:
867:
851:
849:
848:
843:
841:
840:
824:
822:
821:
816:
814:
813:
793:
791:
790:
785:
783:
779:
778:
774:
773:
769:
768:
764:
762:
745:
739:
738:
712:
708:
706:
689:
677:
676:
656:
654:
653:
652:
648:
607:
606:
602:
589:
585:
576:
571:
536:
534:
533:
521:
505:
503:
502:
497:
495:
493:
485:
483:
479:
470:
457:
455:
452:
448:
439:
427:
423:
422:
421:
419:
418:
406:
401:
396:
395:
393:
392:
380:
369:
367:
366:
361:
359:
357:
349:
347:
343:
334:
321:
319:
316:
312:
303:
291:
287:
286:
285:
283:
282:
270:
265:
260:
259:
257:
256:
244:
233:
231:
230:
225:
223:
221:
213:
212:
211:
198:
196:
194:
193:
181:
177:
176:
175:
173:
172:
160:
155:
150:
149:
147:
146:
134:
103:
101:
100:
95:
93:
92:
83:
3060:
3059:
3055:
3054:
3053:
3051:
3050:
3049:
3035:
3034:
3033:
3032:
3024:
3020:
3015:Wayback Machine
3005:
3001:
2991:
2989:
2988:on 3 April 2013
2980:
2979:
2975:
2963:
2959:
2943:
2939:
2927:
2923:
2912:
2908:
2903:
2894:
2869:
2846:
2842:
2816:
2784:
2774:
2773:
2770:
2744:
2729:
2711:
2706:
2705:
2679:
2669:
2657:
2642:
2632:
2615:
2605:
2598:
2597:
2572:
2571:
2552:
2551:
2527:
2522:
2509:
2504:
2486:
2479:
2478:
2472:
2439:
2434:
2433:
2403:
2398:
2397:
2370:
2365:
2364:
2341:
2336:
2335:
2312:
2307:
2306:
2277:
2272:
2271:
2234:
2233:
2206:
2201:
2200:
2163:
2162:
2135:
2130:
2129:
2108:
2107:
2086:
2085:
2064:
2063:
2042:
2041:
2008:
2007:
1974:
1953:
1883:
1878:
1877:
1849:
1831:
1821:
1754:
1701:
1696:
1695:
1676:
1675:
1670:
1660:
1652:
1646:
1645:
1635:
1627:
1615:
1600:
1590:
1589:
1585:
1579:
1578:
1573:
1568:
1558:
1545:
1535:
1514:
1509:
1508:
1489:
1488:
1483:
1478:
1472:
1471:
1466:
1454:
1439:
1429:
1428:
1424:
1414:
1405:
1404:
1399:
1389:
1381:
1371:
1358:
1348:
1327:
1322:
1321:
1302:
1301:
1296:
1291:
1285:
1284:
1279:
1274:
1268:
1267:
1262:
1257:
1247:
1219:
1198:
1193:
1192:
1163:
1144:
1125:
1114:
1113:
1088:
1078:
1068:
1058:
1048:
1038:
1028:
1024:
1001:
988:
987:
957:
925:
909:
884:
883:
859:
854:
853:
832:
827:
826:
805:
800:
799:
749:
740:
730:
729:
725:
693:
684:
668:
661:
657:
636:
608:
590:
562:
558:
525:
515:
514:
486:
458:
384:
374:
373:
350:
322:
248:
238:
237:
214:
203:
199:
185:
138:
128:
127:
121:
113:Touschek effect
84:
71:
70:
12:
11:
5:
3058:
3056:
3048:
3047:
3037:
3036:
3031:
3030:
3018:
2999:
2973:
2957:
2937:
2921:
2905:
2904:
2902:
2899:
2893:
2890:
2875:
2872:
2865:
2862:
2859:
2856:
2853:
2849:
2845:
2835:
2832:
2829:
2826:
2823:
2819:
2815:
2810:
2803:
2800:
2797:
2794:
2791:
2787:
2783:
2769:
2766:
2751:
2747:
2743:
2736:
2732:
2728:
2723:
2718:
2714:
2702:
2701:
2686:
2682:
2676:
2672:
2664:
2660:
2656:
2649:
2645:
2639:
2635:
2629:
2622:
2618:
2612:
2608:
2579:
2559:
2548:
2547:
2533:
2530:
2525:
2521:
2515:
2512:
2507:
2503:
2498:
2493:
2489:
2471:
2468:
2467:
2466:
2452:
2449:
2446:
2442:
2431:
2416:
2413:
2410:
2406:
2383:
2380:
2377:
2373:
2362:
2348:
2344:
2333:
2319:
2315:
2304:
2290:
2287:
2284:
2280:
2269:
2256:
2252:
2249:
2246:
2242:
2219:
2216:
2213:
2209:
2198:
2185:
2181:
2178:
2175:
2171:
2148:
2145:
2142:
2138:
2127:
2115:
2105:
2093:
2083:
2071:
2061:
2049:
2039:
2025:
2020:
2016:
2001:
2000:
1987:
1984:
1981:
1977:
1972:
1966:
1963:
1960:
1956:
1951:
1947:
1944:
1941:
1937:
1931:
1928:
1923:
1919:
1915:
1912:
1909:
1905:
1901:
1896:
1893:
1890:
1886:
1875:
1862:
1859:
1856:
1852:
1847:
1843:
1838:
1834:
1828:
1824:
1819:
1815:
1812:
1809:
1805:
1799:
1796:
1791:
1787:
1783:
1780:
1777:
1773:
1767:
1764:
1761:
1757:
1753:
1750:
1745:
1740:
1737:
1734:
1730:
1726:
1723:
1718:
1715:
1712:
1706:
1693:
1680:
1674:
1671:
1667:
1663:
1659:
1656:
1653:
1651:
1648:
1647:
1642:
1638:
1634:
1631:
1628:
1622:
1618:
1611:
1605:
1597:
1593:
1586:
1584:
1581:
1580:
1577:
1574:
1572:
1569:
1567:
1564:
1563:
1561:
1552:
1548:
1542:
1538:
1532:
1527:
1524:
1521:
1517:
1506:
1493:
1487:
1484:
1482:
1479:
1477:
1474:
1473:
1470:
1467:
1461:
1457:
1450:
1444:
1436:
1432:
1425:
1421:
1417:
1413:
1410:
1407:
1406:
1403:
1400:
1396:
1392:
1388:
1385:
1382:
1380:
1377:
1376:
1374:
1365:
1361:
1355:
1351:
1345:
1340:
1337:
1334:
1330:
1319:
1306:
1300:
1297:
1295:
1292:
1290:
1287:
1286:
1283:
1280:
1278:
1275:
1273:
1270:
1269:
1266:
1263:
1261:
1258:
1256:
1253:
1252:
1250:
1241:
1236:
1232:
1226:
1222:
1216:
1211:
1208:
1205:
1201:
1190:
1176:
1173:
1170:
1166:
1162:
1157:
1154:
1151:
1147:
1143:
1138:
1135:
1132:
1128:
1124:
1121:
1111:
1095:
1091:
1085:
1081:
1075:
1071:
1065:
1061:
1055:
1051:
1045:
1041:
1035:
1031:
1027:
1022:
1019:
1014:
1009:
1005:
998:
995:
985:
970:
967:
964:
960:
956:
951:
948:
945:
938:
935:
932:
928:
922:
919:
916:
912:
906:
903:
900:
897:
894:
891:
866:
862:
839:
835:
812:
808:
796:
795:
782:
777:
772:
767:
761:
758:
755:
752:
748:
743:
737:
733:
728:
724:
721:
718:
715:
711:
705:
702:
699:
696:
692:
687:
683:
680:
675:
671:
667:
664:
660:
651:
647:
643:
639:
635:
632:
629:
626:
623:
620:
617:
614:
611:
605:
601:
597:
593:
584:
581:
575:
570:
566:
561:
557:
554:
551:
548:
545:
542:
539:
532:
528:
524:
508:
507:
492:
489:
482:
478:
474:
469:
465:
461:
451:
447:
443:
438:
434:
430:
417:
414:
411:
405:
391:
387:
383:
371:
356:
353:
346:
342:
338:
333:
329:
325:
315:
311:
307:
302:
298:
294:
281:
278:
275:
269:
255:
251:
247:
235:
220:
217:
210:
206:
202:
192:
188:
184:
171:
168:
165:
159:
145:
141:
137:
120:
117:
91:
87:
82:
78:
56:Sekazi Mtingwa
48:Anton Piwinski
29:beam emittance
13:
10:
9:
6:
4:
3:
2:
3057:
3046:
3043:
3042:
3040:
3028:
3022:
3019:
3016:
3012:
3009:
3003:
3000:
2987:
2983:
2977:
2974:
2971:
2967:
2961:
2958:
2955:
2951:
2947:
2941:
2938:
2935:
2932:, 115 (1983)
2931:
2925:
2922:
2918:
2917:
2910:
2907:
2900:
2898:
2891:
2889:
2873:
2870:
2863:
2860:
2857:
2854:
2851:
2847:
2843:
2833:
2830:
2827:
2824:
2821:
2817:
2813:
2808:
2801:
2798:
2795:
2792:
2789:
2785:
2781:
2767:
2765:
2749:
2745:
2741:
2734:
2730:
2726:
2721:
2716:
2712:
2684:
2680:
2674:
2670:
2662:
2658:
2654:
2647:
2643:
2637:
2633:
2627:
2620:
2616:
2610:
2606:
2596:
2595:
2594:
2591:
2577:
2557:
2531:
2528:
2523:
2519:
2513:
2510:
2505:
2501:
2496:
2491:
2487:
2477:
2476:
2475:
2469:
2450:
2447:
2444:
2440:
2432:
2414:
2411:
2408:
2404:
2381:
2378:
2375:
2371:
2363:
2346:
2342:
2334:
2317:
2313:
2305:
2288:
2285:
2282:
2278:
2270:
2254:
2250:
2247:
2244:
2240:
2217:
2214:
2211:
2207:
2199:
2183:
2179:
2176:
2173:
2169:
2146:
2143:
2140:
2136:
2128:
2113:
2106:
2091:
2084:
2069:
2062:
2047:
2040:
2023:
2018:
2014:
2006:
2005:
2004:
2003:Definitions:
1985:
1982:
1979:
1975:
1970:
1964:
1961:
1958:
1954:
1949:
1945:
1942:
1939:
1935:
1929:
1926:
1921:
1917:
1913:
1910:
1907:
1903:
1899:
1894:
1891:
1888:
1884:
1876:
1860:
1857:
1854:
1850:
1845:
1836:
1826:
1822:
1817:
1813:
1810:
1807:
1803:
1797:
1794:
1789:
1785:
1781:
1778:
1775:
1771:
1765:
1762:
1759:
1755:
1748:
1743:
1738:
1735:
1732:
1728:
1721:
1716:
1713:
1710:
1694:
1678:
1672:
1665:
1661:
1657:
1654:
1649:
1640:
1636:
1632:
1629:
1620:
1616:
1609:
1595:
1591:
1582:
1575:
1570:
1565:
1559:
1550:
1546:
1540:
1536:
1530:
1522:
1515:
1507:
1491:
1485:
1480:
1475:
1468:
1459:
1455:
1448:
1434:
1430:
1419:
1415:
1411:
1408:
1401:
1394:
1390:
1386:
1383:
1378:
1372:
1363:
1359:
1353:
1349:
1343:
1335:
1328:
1320:
1304:
1298:
1293:
1288:
1281:
1276:
1271:
1264:
1259:
1254:
1248:
1239:
1234:
1230:
1224:
1220:
1214:
1206:
1199:
1191:
1171:
1164:
1160:
1152:
1145:
1141:
1133:
1126:
1122:
1119:
1112:
1093:
1089:
1083:
1079:
1073:
1069:
1063:
1059:
1053:
1049:
1043:
1039:
1033:
1029:
1025:
1020:
1017:
1012:
1007:
1003:
996:
993:
986:
968:
965:
962:
958:
954:
949:
946:
943:
936:
933:
930:
926:
920:
917:
914:
910:
904:
901:
898:
892:
882:
881:
880:
864:
860:
837:
833:
810:
806:
780:
775:
770:
765:
759:
756:
753:
750:
746:
741:
735:
731:
726:
722:
719:
716:
713:
709:
703:
700:
697:
694:
690:
685:
681:
678:
673:
669:
665:
662:
658:
649:
645:
641:
630:
627:
624:
621:
615:
612:
603:
599:
595:
591:
582:
579:
568:
564:
559:
552:
546:
543:
540:
537:
530:
526:
522:
513:
512:
511:
490:
487:
480:
476:
472:
467:
463:
459:
449:
445:
441:
436:
432:
428:
403:
389:
385:
381:
372:
354:
351:
344:
340:
336:
331:
327:
323:
313:
309:
305:
300:
296:
292:
267:
253:
249:
245:
236:
218:
215:
208:
204:
200:
190:
186:
182:
157:
143:
139:
135:
126:
125:
124:
118:
116:
114:
109:
107:
89:
85:
80:
76:
67:
66:
62:
57:
53:
52:James Bjorken
49:
44:
42:
38:
34:
30:
26:
22:
18:
3021:
3002:
2990:. Retrieved
2986:the original
2976:
2965:
2960:
2949:
2945:
2940:
2929:
2924:
2914:
2909:
2895:
2771:
2703:
2592:
2549:
2473:
2002:
797:
509:
122:
110:
68:
64:
60:
50:in 1974 and
45:
20:
16:
15:
2992:20 February
63:by K. Kubo
2901:References
41:luminosity
33:luminosity
2848:ϵ
2818:ϵ
2786:τ
2746:α
2742:−
2731:γ
2713:η
2681:β
2671:ϵ
2659:η
2644:β
2634:ϵ
2617:β
2607:ϵ
2578:γ
2558:γ
2524:σ
2506:σ
2497:γ
2492:δ
2488:σ
2441:θ
2343:σ
2314:σ
2279:ϵ
2241:η
2208:η
2170:β
2137:β
2114:γ
2092:β
1976:β
1955:η
1936:β
1922:−
1904:η
1885:ϕ
1851:β
1823:η
1804:β
1790:−
1772:η
1756:β
1729:η
1662:ϕ
1658:γ
1655:−
1637:ϕ
1633:γ
1630:−
1617:β
1592:γ
1547:ϵ
1537:β
1456:β
1431:γ
1416:ϕ
1412:γ
1409:−
1391:ϕ
1387:γ
1384:−
1360:ϵ
1350:β
1231:σ
1221:γ
1090:σ
1080:σ
1070:ϵ
1060:ϵ
1050:γ
1040:β
1030:π
959:θ
950:
905:
757:λ
723:
714:−
701:λ
682:
666:
628:λ
616:
592:λ
583:λ
574:∞
565:∫
544:π
464:ϵ
433:ϵ
328:ϵ
297:ϵ
205:σ
187:σ
86:γ
3039:Category
3011:Archived
2964:B. Nash
2944:K. Kubo
2532:′
2514:′
2255:′
2184:′
1950:′
1918:′
1818:′
1786:′
781:⟩
560:⟨
106:wigglers
2966:et al.
2946:et al.
2704:where
852:, and
798:where
586:
424:
397:
288:
261:
178:
151:
65:et al.
2994:2013
2396:and
2232:and
2161:and
54:and
893:log
613:det
553:log
21:IBS
3041::
2930:13
1026:64
947:ln
902:ln
825:,
720:Tr
679:Tr
663:Tr
43:.
2996:.
2950:8
2874:t
2871:d
2864:3
2861:,
2858:2
2855:,
2852:1
2844:d
2834:3
2831:,
2828:2
2825:,
2822:1
2814:1
2809:=
2802:3
2799:,
2796:2
2793:,
2790:1
2782:1
2750:c
2735:2
2727:1
2722:=
2717:s
2685:z
2675:z
2663:s
2655:+
2648:y
2638:y
2628:+
2621:x
2611:x
2529:y
2520:=
2511:x
2502:=
2451:n
2448:i
2445:m
2415:x
2412:a
2409:m
2405:b
2382:n
2379:i
2376:m
2372:b
2347:p
2318:s
2289:v
2286:,
2283:h
2251:v
2248:,
2245:h
2218:v
2215:,
2212:h
2180:v
2177:,
2174:h
2147:v
2144:,
2141:h
2070:N
2048:c
2024:2
2019:0
2015:r
1986:v
1983:,
1980:h
1971:/
1965:v
1962:,
1959:h
1946:v
1943:,
1940:h
1930:2
1927:1
1914:v
1911:,
1908:h
1900:=
1895:v
1892:,
1889:h
1861:v
1858:,
1855:h
1846:/
1842:]
1837:2
1833:)
1827:h
1814:v
1811:,
1808:h
1798:2
1795:1
1782:v
1779:,
1776:h
1766:v
1763:,
1760:h
1752:(
1749:+
1744:2
1739:v
1736:,
1733:h
1725:[
1722:=
1717:v
1714:,
1711:h
1705:H
1679:)
1673:1
1666:v
1650:0
1641:v
1621:v
1610:v
1604:H
1596:2
1583:0
1576:0
1571:0
1566:0
1560:(
1551:v
1541:v
1531:=
1526:)
1523:v
1520:(
1516:L
1492:)
1486:0
1481:0
1476:0
1469:0
1460:h
1449:h
1443:H
1435:2
1420:h
1402:0
1395:h
1379:1
1373:(
1364:h
1354:h
1344:=
1339:)
1336:h
1333:(
1329:L
1305:)
1299:0
1294:0
1289:0
1282:0
1277:1
1272:0
1265:0
1260:0
1255:0
1249:(
1240:2
1235:p
1225:2
1215:=
1210:)
1207:p
1204:(
1200:L
1175:)
1172:v
1169:(
1165:L
1161:+
1156:)
1153:h
1150:(
1146:L
1142:+
1137:)
1134:p
1131:(
1127:L
1123:=
1120:L
1094:p
1084:s
1074:v
1064:h
1054:4
1044:3
1034:2
1021:N
1018:c
1013:2
1008:0
1004:r
997:=
994:A
969:n
966:i
963:m
955:2
944:=
937:x
934:a
931:m
927:b
921:n
918:i
915:m
911:b
899:=
896:)
890:(
865:v
861:T
838:h
834:T
811:p
807:T
794:,
776:}
771:]
766:)
760:I
754:+
751:L
747:1
742:(
736:i
732:L
727:[
717:3
710:)
704:I
698:+
695:L
691:1
686:(
674:i
670:L
659:{
650:2
646:/
642:1
638:]
634:)
631:I
625:+
622:L
619:(
610:[
604:2
600:/
596:1
580:d
569:0
556:)
550:(
547:A
541:4
538:=
531:i
527:T
523:1
506:.
491:t
488:d
481:2
477:/
473:1
468:v
460:d
450:2
446:/
442:1
437:v
429:1
416:f
413:e
410:d
404:=
390:v
386:T
382:1
370:,
355:t
352:d
345:2
341:/
337:1
332:h
324:d
314:2
310:/
306:1
301:h
293:1
280:f
277:e
274:d
268:=
254:h
250:T
246:1
234:,
219:t
216:d
209:p
201:d
191:p
183:1
170:f
167:e
164:d
158:=
144:p
140:T
136:1
90:4
81:/
77:1
19:(
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.