128:, allowing the ions to be treated as unmagnetized. Third, the collision frequency between electrons and background neutrals is assumed to be much less than the electron cyclotron frequency. Finally, we only analyze low frequency waves so that we can neglect electron inertia. Because the Buneman instability is electrostatic in nature, only electrostatic perturbations are considered.
526:
1283:
326:
119:
To derive the dispersion relation below, we make the following assumptions. First, quasi-neutrality is assumed. This is appropriate if we restrict ourselves to wavelengths longer than the Debye length. Second, the collision frequency between ions and background
1811:
1956:
902:
as the frequency of collisions between ions and neutrals. We also assume that all perturbed properties, such as species velocity, density, and the electric field, behave as plane waves. In other words, all physical quantities
1545:
2065:
333:
1116:. If we assume that the ambient electric and magnetic fields are perpendicular to one another and only analyze waves propagating perpendicular to both of these fields, the dispersion relation takes the form of:
1122:
1693:
72:
exceeding the ion acoustic speed. It occurs in collisional plasma with neutrals driven by drift current for two stream instability for unmagnetized plasma it becomes ''Buneman instability ''
167:
1599:
1047:
1699:
1828:
836:
783:
1458:
1431:
1401:
1340:
900:
870:
706:
1623:
1110:
1078:
1370:
1314:
655:
607:
559:
981:
961:
941:
921:
754:
732:
675:
627:
579:
89:. In particular, it occurs in the equatorial electrojet due to the drift of electrons relative to ions, and also in the trails behind ablating meteoroids.
1466:
1967:
838:).The collisional term describes the momentum loss frequency of each fluid due to collisions of charged particles with neutral particles in the
521:{\displaystyle m_{i}n{dv_{i} \over dt}=en({\vec {E}}+{\vec {v}}_{i}\times {\vec {B}})-k_{\text{B}}T_{i}\nabla n-m_{i}n\nu _{in}{\vec {v}}_{i}}
2218:
1278:{\displaystyle \omega \left(1+i\psi _{0}{\frac {\omega -i\nu _{in}}{\nu _{in}}}\right)=kv_{E}+i\psi _{0}{\frac {k^{2}c_{i}^{2}}{\nu _{in}}}}
792:
Note that electron inertia has been neglected, and that both species are assumed to have the same number density at every point in space (
1631:
2273:
321:{\displaystyle 0=-en({\vec {E}}+{\vec {v}}_{e}\times {\vec {B}})-k_{\text{B}}T_{e}\nabla n-m_{e}n\nu _{en}{\vec {v}}_{e}}
86:
46:
1562:
993:
1806:{\displaystyle \gamma ={\frac {\psi _{0}}{\nu _{in}}}{\frac {\omega _{r}^{2}-k^{2}c_{i}^{2}}{1+\psi _{0}}}}
145:
108:
61:
1951:{\displaystyle 1-(\omega _{p}^{2}/\omega ^{2})-{\displaystyle (\omega _{p}^{2}/(\omega -k.v_{0})^{2})}=0}
96:
2101:
Farley, D. T. (1963). "Two-Stream Plasma
Instability as a Source of Irregularities in the Ionosphere".
2145:
2110:
795:
125:
2172:
761:
1436:
1409:
1085:
786:
141:
31:
1379:
1319:
875:
845:
681:
2214:
1089:
1608:
1095:
1063:
2247:
2210:
2184:
2153:
2118:
2076:
839:
137:
121:
53:
35:
1348:
1292:
633:
585:
537:
2149:
2114:
1373:
1342:
1113:
966:
946:
926:
906:
739:
717:
660:
612:
564:
57:
2267:
157:
39:
2136:
Buneman, O. (1963). "Excitation of Field
Aligned Sound Waves by Electron Streams".
1054:
80:
2236:"Electrodynamics of meteor trail evolution in the equatorial E-region ionosphere"
2081:
1081:
984:
100:
28:
2157:
2122:
2188:
1540:{\displaystyle \psi _{0}={\frac {\nu _{in}\nu _{en}}{\Omega _{i}\Omega _{e}}}}
1404:
1403:
described the combined effect of electron and ion collisions as well as their
104:
93:
83:
43:
1625:
describes the growth rate of the instability. For FB we have the following:
1058:
709:
2060:{\displaystyle \gamma ={\sqrt {3}}\omega _{p}(Z_{i}.{m_{e}}/{m_{i}})^{1/3}}
2252:
2235:
149:
65:
2234:
Oppenheim, Meers M.; Endt, Axel F. vom; Dyrud, Lars P. (October 2000).
76:
2173:"Instability, Turbulence, and Conductivity in Current-Carrying Plasma"
160:
and collisional terms. The equation of motion for each species is:
872:
as the frequency of collisions between electrons and neutrals, and
153:
69:
1688:{\displaystyle \omega _{r}={\frac {kv_{E}}{1+\psi _{0}}}}
1556:
Solving the dispersion we arrive at frequency given as:
1970:
1878:
1831:
1702:
1634:
1611:
1565:
1469:
1439:
1412:
1382:
1351:
1322:
1295:
1125:
1098:
1066:
996:
969:
949:
929:
909:
878:
848:
798:
764:
742:
720:
712:
of collisions between species s and neutral particles
684:
663:
636:
615:
588:
567:
540:
336:
170:
2059:
1950:
1805:
1687:
1617:
1593:
1539:
1452:
1425:
1395:
1364:
1334:
1308:
1277:
1104:
1072:
1041:
975:
955:
935:
915:
894:
864:
830:
777:
748:
726:
700:
669:
649:
621:
601:
573:
553:
520:
320:
2205:Treumann, Rudolf A; Baumjohann, Wolfgang (1997).
923:will behave as an exponential function of time
8:
1594:{\displaystyle \omega =\omega _{r}+i\gamma }
124:is assumed to be much greater than the ion
2200:
2198:
1042:{\displaystyle f\sim \exp(-i\omega t+ikx)}
2251:
2047:
2043:
2032:
2027:
2022:
2015:
2010:
2001:
1988:
1977:
1969:
1931:
1921:
1897:
1891:
1886:
1877:
1865:
1856:
1850:
1845:
1830:
1794:
1776:
1771:
1761:
1748:
1743:
1736:
1725:
1715:
1709:
1701:
1676:
1658:
1648:
1639:
1633:
1610:
1576:
1564:
1528:
1518:
1503:
1490:
1483:
1474:
1468:
1444:
1438:
1417:
1411:
1387:
1381:
1356:
1350:
1321:
1300:
1294:
1264:
1253:
1248:
1238:
1231:
1225:
1209:
1183:
1169:
1153:
1147:
1124:
1097:
1065:
995:
968:
948:
928:
908:
883:
877:
853:
847:
816:
803:
797:
769:
763:
741:
719:
689:
683:
662:
641:
635:
614:
593:
587:
566:
545:
539:
512:
501:
500:
490:
477:
458:
448:
427:
426:
417:
406:
405:
390:
389:
360:
350:
341:
335:
312:
301:
300:
290:
277:
258:
248:
227:
226:
217:
206:
205:
190:
189:
169:
64:arising from the difference in drifts of
56:with neutral component, and is driven by
2093:
103:can be used to diagnose the state of
60:. It can be thought of as a modified
7:
1525:
1515:
1441:
1414:
464:
264:
14:
2040:
1994:
1937:
1928:
1902:
1879:
1871:
1838:
1036:
1009:
756:is the electron number density
657:is the temperature of species
506:
438:
432:
411:
395:
386:
306:
238:
232:
211:
195:
186:
92:Since the FB fluctuations can
16:Microscopic plasma instability
1:
2207:Advanced space plasma physics
831:{\displaystyle n_{i}=n_{e}=n}
2240:Geophysical Research Letters
778:{\displaystyle k_{\text{B}}}
734:is the charge of an electron
1822:The dispersion relation is
1453:{\displaystyle \Omega _{e}}
1426:{\displaystyle \Omega _{i}}
609:is the velocity of species
47:Rayleigh-Taylor instability
2290:
2158:10.1103/PhysRevLett.10.285
2123:10.1103/PhysRevLett.10.279
21:Farley–Buneman instability
2189:10.1103/PhysRevLett.1.119
1396:{\displaystyle \psi _{0}}
1376:of ions. The coefficient
1335:{\displaystyle E\times B}
895:{\displaystyle \nu _{in}}
865:{\displaystyle \nu _{en}}
701:{\displaystyle \nu _{sn}}
52:It occurs in collisional
2177:Physical Review Letters
2138:Physical Review Letters
2103:Physical Review Letters
1961:and the growth rate is
1618:{\displaystyle \gamma }
1105:{\displaystyle \omega }
1073:{\displaystyle \omega }
561:is the mass of species
42:. It is similar to the
2061:
1952:
1807:
1689:
1619:
1595:
1541:
1454:
1427:
1397:
1366:
1336:
1310:
1279:
1106:
1074:
1043:
977:
957:
937:
917:
896:
866:
832:
779:
750:
728:
702:
671:
651:
623:
603:
575:
555:
522:
322:
146:equation of continuity
109:electromagnetic pulses
62:two-stream instability
2062:
1953:
1808:
1690:
1620:
1596:
1542:
1455:
1428:
1405:cyclotron frequencies
1398:
1367:
1365:{\displaystyle c_{i}}
1337:
1311:
1309:{\displaystyle v_{E}}
1280:
1107:
1075:
1044:
978:
958:
938:
918:
897:
867:
833:
780:
751:
729:
703:
672:
652:
650:{\displaystyle T_{s}}
624:
604:
602:{\displaystyle v_{s}}
576:
556:
554:{\displaystyle m_{s}}
523:
323:
97:electromagnetic waves
75:It is present in the
2274:Plasma instabilities
2253:10.1029/1999GL000013
2171:Buneman, O. (1958).
2082:Plasma Instabilities
1968:
1829:
1700:
1632:
1609:
1563:
1467:
1437:
1410:
1380:
1349:
1320:
1293:
1123:
1096:
1064:
994:
967:
947:
927:
907:
876:
846:
796:
762:
740:
718:
682:
661:
634:
613:
586:
565:
538:
334:
168:
2150:1963PhRvL..10..285B
2115:1963PhRvL..10..279F
1896:
1855:
1818:Buneman instability
1781:
1753:
1258:
132:Dispersion relation
126:cyclotron frequency
2057:
1948:
1940:
1882:
1841:
1803:
1767:
1739:
1685:
1615:
1591:
1537:
1450:
1423:
1393:
1362:
1332:
1306:
1275:
1244:
1102:
1086:exponential growth
1070:
1039:
973:
953:
933:
913:
892:
862:
828:
787:Boltzmann constant
775:
746:
724:
698:
667:
647:
619:
599:
571:
551:
518:
318:
142:equation of motion
136:We use linearized
32:plasma instability
2220:978-1-86094-026-2
1982:
1801:
1734:
1683:
1535:
1273:
1192:
1090:exponential decay
1053:This can lead to
976:{\displaystyle k}
956:{\displaystyle x}
936:{\displaystyle t}
916:{\displaystyle f}
772:
749:{\displaystyle n}
727:{\displaystyle e}
670:{\displaystyle s}
622:{\displaystyle s}
574:{\displaystyle s}
509:
451:
435:
414:
398:
375:
309:
251:
235:
214:
198:
122:neutral particles
2281:
2258:
2257:
2255:
2231:
2225:
2224:
2211:World Scientific
2202:
2193:
2192:
2168:
2162:
2161:
2133:
2127:
2126:
2098:
2077:Plasma stability
2066:
2064:
2063:
2058:
2056:
2055:
2051:
2038:
2037:
2036:
2026:
2021:
2020:
2019:
2006:
2005:
1993:
1992:
1983:
1978:
1957:
1955:
1954:
1949:
1941:
1936:
1935:
1926:
1925:
1901:
1895:
1890:
1870:
1869:
1860:
1854:
1849:
1812:
1810:
1809:
1804:
1802:
1800:
1799:
1798:
1782:
1780:
1775:
1766:
1765:
1752:
1747:
1737:
1735:
1733:
1732:
1720:
1719:
1710:
1694:
1692:
1691:
1686:
1684:
1682:
1681:
1680:
1664:
1663:
1662:
1649:
1644:
1643:
1624:
1622:
1621:
1616:
1600:
1598:
1597:
1592:
1581:
1580:
1546:
1544:
1543:
1538:
1536:
1534:
1533:
1532:
1523:
1522:
1512:
1511:
1510:
1498:
1497:
1484:
1479:
1478:
1459:
1457:
1456:
1451:
1449:
1448:
1432:
1430:
1429:
1424:
1422:
1421:
1402:
1400:
1399:
1394:
1392:
1391:
1371:
1369:
1368:
1363:
1361:
1360:
1341:
1339:
1338:
1333:
1315:
1313:
1312:
1307:
1305:
1304:
1284:
1282:
1281:
1276:
1274:
1272:
1271:
1259:
1257:
1252:
1243:
1242:
1232:
1230:
1229:
1214:
1213:
1198:
1194:
1193:
1191:
1190:
1178:
1177:
1176:
1154:
1152:
1151:
1111:
1109:
1108:
1103:
1079:
1077:
1076:
1071:
1048:
1046:
1045:
1040:
982:
980:
979:
974:
962:
960:
959:
954:
942:
940:
939:
934:
922:
920:
919:
914:
901:
899:
898:
893:
891:
890:
871:
869:
868:
863:
861:
860:
837:
835:
834:
829:
821:
820:
808:
807:
784:
782:
781:
776:
774:
773:
770:
755:
753:
752:
747:
733:
731:
730:
725:
707:
705:
704:
699:
697:
696:
676:
674:
673:
668:
656:
654:
653:
648:
646:
645:
628:
626:
625:
620:
608:
606:
605:
600:
598:
597:
580:
578:
577:
572:
560:
558:
557:
552:
550:
549:
527:
525:
524:
519:
517:
516:
511:
510:
502:
498:
497:
482:
481:
463:
462:
453:
452:
449:
437:
436:
428:
422:
421:
416:
415:
407:
400:
399:
391:
376:
374:
366:
365:
364:
351:
346:
345:
327:
325:
324:
319:
317:
316:
311:
310:
302:
298:
297:
282:
281:
263:
262:
253:
252:
249:
237:
236:
228:
222:
221:
216:
215:
207:
200:
199:
191:
36:Donald T. Farley
2289:
2288:
2284:
2283:
2282:
2280:
2279:
2278:
2264:
2263:
2262:
2261:
2233:
2232:
2228:
2221:
2204:
2203:
2196:
2170:
2169:
2165:
2135:
2134:
2130:
2100:
2099:
2095:
2090:
2073:
2039:
2028:
2011:
1997:
1984:
1966:
1965:
1927:
1917:
1861:
1827:
1826:
1820:
1790:
1783:
1757:
1738:
1721:
1711:
1698:
1697:
1672:
1665:
1654:
1650:
1635:
1630:
1629:
1607:
1606:
1572:
1561:
1560:
1554:
1524:
1514:
1513:
1499:
1486:
1485:
1470:
1465:
1464:
1440:
1435:
1434:
1413:
1408:
1407:
1383:
1378:
1377:
1352:
1347:
1346:
1318:
1317:
1296:
1291:
1290:
1260:
1234:
1233:
1221:
1205:
1179:
1165:
1155:
1143:
1133:
1129:
1121:
1120:
1094:
1093:
1084:, or to either
1062:
1061:
992:
991:
965:
964:
945:
944:
925:
924:
905:
904:
879:
874:
873:
849:
844:
843:
812:
799:
794:
793:
765:
760:
759:
738:
737:
716:
715:
685:
680:
679:
659:
658:
637:
632:
631:
611:
610:
589:
584:
583:
563:
562:
541:
536:
535:
499:
486:
473:
454:
444:
404:
367:
356:
352:
337:
332:
331:
299:
286:
273:
254:
244:
204:
166:
165:
138:fluid equations
134:
117:
17:
12:
11:
5:
2287:
2285:
2277:
2276:
2266:
2265:
2260:
2259:
2226:
2219:
2194:
2163:
2144:(7): 285–287.
2128:
2109:(7): 279–282.
2092:
2091:
2089:
2086:
2085:
2084:
2079:
2072:
2069:
2068:
2067:
2054:
2050:
2046:
2042:
2035:
2031:
2025:
2018:
2014:
2009:
2004:
2000:
1996:
1991:
1987:
1981:
1976:
1973:
1959:
1958:
1947:
1944:
1939:
1934:
1930:
1924:
1920:
1916:
1913:
1910:
1907:
1904:
1900:
1894:
1889:
1885:
1881:
1876:
1873:
1868:
1864:
1859:
1853:
1848:
1844:
1840:
1837:
1834:
1819:
1816:
1815:
1814:
1797:
1793:
1789:
1786:
1779:
1774:
1770:
1764:
1760:
1756:
1751:
1746:
1742:
1731:
1728:
1724:
1718:
1714:
1708:
1705:
1695:
1679:
1675:
1671:
1668:
1661:
1657:
1653:
1647:
1642:
1638:
1614:
1603:
1602:
1590:
1587:
1584:
1579:
1575:
1571:
1568:
1553:
1550:
1549:
1548:
1531:
1527:
1521:
1517:
1509:
1506:
1502:
1496:
1493:
1489:
1482:
1477:
1473:
1447:
1443:
1420:
1416:
1390:
1386:
1374:acoustic speed
1359:
1355:
1331:
1328:
1325:
1303:
1299:
1287:
1286:
1270:
1267:
1263:
1256:
1251:
1247:
1241:
1237:
1228:
1224:
1220:
1217:
1212:
1208:
1204:
1201:
1197:
1189:
1186:
1182:
1175:
1172:
1168:
1164:
1161:
1158:
1150:
1146:
1142:
1139:
1136:
1132:
1128:
1101:
1069:
1051:
1050:
1038:
1035:
1032:
1029:
1026:
1023:
1020:
1017:
1014:
1011:
1008:
1005:
1002:
999:
972:
952:
932:
912:
889:
886:
882:
859:
856:
852:
827:
824:
819:
815:
811:
806:
802:
790:
789:
768:
757:
745:
735:
723:
713:
695:
692:
688:
677:
666:
644:
640:
629:
618:
596:
592:
581:
570:
548:
544:
529:
528:
515:
508:
505:
496:
493:
489:
485:
480:
476:
472:
469:
466:
461:
457:
447:
443:
440:
434:
431:
425:
420:
413:
410:
403:
397:
394:
388:
385:
382:
379:
373:
370:
363:
359:
355:
349:
344:
340:
328:
315:
308:
305:
296:
293:
289:
285:
280:
276:
272:
269:
266:
261:
257:
247:
243:
240:
234:
231:
225:
220:
213:
210:
203:
197:
194:
188:
185:
182:
179:
176:
173:
133:
130:
116:
113:
107:by the use of
58:drift currents
25:FB instability
15:
13:
10:
9:
6:
4:
3:
2:
2286:
2275:
2272:
2271:
2269:
2254:
2249:
2245:
2241:
2237:
2230:
2227:
2222:
2216:
2212:
2208:
2201:
2199:
2195:
2190:
2186:
2182:
2178:
2174:
2167:
2164:
2159:
2155:
2151:
2147:
2143:
2139:
2132:
2129:
2124:
2120:
2116:
2112:
2108:
2104:
2097:
2094:
2087:
2083:
2080:
2078:
2075:
2074:
2070:
2052:
2048:
2044:
2033:
2029:
2023:
2016:
2012:
2007:
2002:
1998:
1989:
1985:
1979:
1974:
1971:
1964:
1963:
1962:
1945:
1942:
1932:
1922:
1918:
1914:
1911:
1908:
1905:
1898:
1892:
1887:
1883:
1874:
1866:
1862:
1857:
1851:
1846:
1842:
1835:
1832:
1825:
1824:
1823:
1817:
1795:
1791:
1787:
1784:
1777:
1772:
1768:
1762:
1758:
1754:
1749:
1744:
1740:
1729:
1726:
1722:
1716:
1712:
1706:
1703:
1696:
1677:
1673:
1669:
1666:
1659:
1655:
1651:
1645:
1640:
1636:
1628:
1627:
1626:
1612:
1588:
1585:
1582:
1577:
1573:
1569:
1566:
1559:
1558:
1557:
1551:
1529:
1519:
1507:
1504:
1500:
1494:
1491:
1487:
1480:
1475:
1471:
1463:
1462:
1461:
1445:
1418:
1406:
1388:
1384:
1375:
1357:
1353:
1344:
1329:
1326:
1323:
1301:
1297:
1268:
1265:
1261:
1254:
1249:
1245:
1239:
1235:
1226:
1222:
1218:
1215:
1210:
1206:
1202:
1199:
1195:
1187:
1184:
1180:
1173:
1170:
1166:
1162:
1159:
1156:
1148:
1144:
1140:
1137:
1134:
1130:
1126:
1119:
1118:
1117:
1115:
1099:
1091:
1087:
1083:
1067:
1060:
1056:
1033:
1030:
1027:
1024:
1021:
1018:
1015:
1012:
1006:
1003:
1000:
997:
990:
989:
988:
986:
970:
950:
943:and position
930:
910:
887:
884:
880:
857:
854:
850:
841:
825:
822:
817:
813:
809:
804:
800:
788:
766:
758:
743:
736:
721:
714:
711:
693:
690:
686:
678:
664:
642:
638:
630:
616:
594:
590:
582:
568:
546:
542:
534:
533:
532:
513:
503:
494:
491:
487:
483:
478:
474:
470:
467:
459:
455:
445:
441:
429:
423:
418:
408:
401:
392:
383:
380:
377:
371:
368:
361:
357:
353:
347:
342:
338:
329:
313:
303:
294:
291:
287:
283:
278:
274:
270:
267:
259:
255:
245:
241:
229:
223:
218:
208:
201:
192:
183:
180:
177:
174:
171:
163:
162:
161:
159:
158:Lorentz force
155:
151:
147:
143:
139:
131:
129:
127:
123:
114:
112:
110:
106:
102:
98:
95:
90:
88:
85:
82:
78:
73:
71:
67:
63:
59:
55:
50:
48:
45:
41:
40:Oscar Buneman
37:
33:
30:
26:
22:
2246:(19): 3173.
2243:
2239:
2229:
2206:
2180:
2176:
2166:
2141:
2137:
2131:
2106:
2102:
2096:
1960:
1821:
1604:
1555:
1288:
1055:oscillations
1052:
842:. We denote
791:
530:
135:
118:
91:
74:
51:
34:named after
24:
20:
18:
1552:Growth rate
1082:real number
985:wave number
164:Electrons:
101:instability
84:ionospheric
44:ionospheric
29:microscopic
2183:(3): 119.
2088:References
115:Conditions
105:ionosphere
77:equatorial
1986:ω
1972:γ
1909:−
1906:ω
1884:ω
1875:−
1863:ω
1843:ω
1836:−
1792:ψ
1755:−
1741:ω
1723:ν
1713:ψ
1704:γ
1674:ψ
1637:ω
1613:γ
1589:γ
1574:ω
1567:ω
1526:Ω
1516:Ω
1501:ν
1488:ν
1472:ψ
1442:Ω
1415:Ω
1385:ψ
1327:×
1262:ν
1223:ψ
1181:ν
1167:ν
1160:−
1157:ω
1145:ψ
1127:ω
1100:ω
1068:ω
1059:frequency
1019:ω
1013:−
1007:
1001:∼
881:ν
851:ν
710:frequency
687:ν
507:→
488:ν
471:−
465:∇
442:−
433:→
424:×
412:→
396:→
307:→
288:ν
271:−
265:∇
242:−
233:→
224:×
212:→
196:→
178:−
150:electrons
87:E-regions
66:electrons
2268:Category
2071:See also
2146:Bibcode
2111:Bibcode
1372:is the
1316:is the
1114:complex
1057:if the
983:is the
963:(where
785:is the
708:is the
94:scatter
27:, is a
2217:
1605:where
1289:where
840:plasma
531:where
330:Ions:
148:) for
99:, the
54:plasma
1343:drift
1080:is a
156:with
81:polar
23:, or
2215:ISBN
1433:and
1345:and
154:ions
152:and
79:and
70:ions
68:and
38:and
19:The
2248:doi
2185:doi
2154:doi
2119:doi
1112:is
1092:if
1088:or
1004:exp
987:):
2270::
2244:27
2242:.
2238:.
2213:.
2209:.
2197:^
2179:.
2175:.
2152:.
2142:10
2140:.
2117:.
2107:10
2105:.
1460::
144:,
111:.
49:.
2256:.
2250::
2223:.
2191:.
2187::
2181:1
2160:.
2156::
2148::
2125:.
2121::
2113::
2053:3
2049:/
2045:1
2041:)
2034:i
2030:m
2024:/
2017:e
2013:m
2008:.
2003:i
1999:Z
1995:(
1990:p
1980:3
1975:=
1946:0
1943:=
1938:)
1933:2
1929:)
1923:0
1919:v
1915:.
1912:k
1903:(
1899:/
1893:2
1888:p
1880:(
1872:)
1867:2
1858:/
1852:2
1847:p
1839:(
1833:1
1813:.
1796:0
1788:+
1785:1
1778:2
1773:i
1769:c
1763:2
1759:k
1750:2
1745:r
1730:n
1727:i
1717:0
1707:=
1678:0
1670:+
1667:1
1660:E
1656:v
1652:k
1646:=
1641:r
1601:,
1586:i
1583:+
1578:r
1570:=
1547:.
1530:e
1520:i
1508:n
1505:e
1495:n
1492:i
1481:=
1476:0
1446:e
1419:i
1389:0
1358:i
1354:c
1330:B
1324:E
1302:E
1298:v
1285:,
1269:n
1266:i
1255:2
1250:i
1246:c
1240:2
1236:k
1227:0
1219:i
1216:+
1211:E
1207:v
1203:k
1200:=
1196:)
1188:n
1185:i
1174:n
1171:i
1163:i
1149:0
1141:i
1138:+
1135:1
1131:(
1049:.
1037:)
1034:x
1031:k
1028:i
1025:+
1022:t
1016:i
1010:(
998:f
971:k
951:x
931:t
911:f
888:n
885:i
858:n
855:e
826:n
823:=
818:e
814:n
810:=
805:i
801:n
771:B
767:k
744:n
722:e
694:n
691:s
665:s
643:s
639:T
617:s
595:s
591:v
569:s
547:s
543:m
514:i
504:v
495:n
492:i
484:n
479:i
475:m
468:n
460:i
456:T
450:B
446:k
439:)
430:B
419:i
409:v
402:+
393:E
387:(
384:n
381:e
378:=
372:t
369:d
362:i
358:v
354:d
348:n
343:i
339:m
314:e
304:v
295:n
292:e
284:n
279:e
275:m
268:n
260:e
256:T
250:B
246:k
239:)
230:B
219:e
209:v
202:+
193:E
187:(
184:n
181:e
175:=
172:0
140:(
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