2025:
2775:
97:
occurs. Now the electron pressure gradient acts as the restoring force, creating a propagating wave analogous to a sound wave in non-ionized gases. Combining these two restoring forces (from the electric field and electron pressure gradient) a type of wave, named
Langmuir wave, is excited. The
85:
A plasma consists of charged particles which react to electric fields, in contrast with dielectric matter. When electrons in a uniform, homogeneous plasma are perturbed from their equilibrium position, a charge separation occurs creating an electric field which acts as restoring force on the
1209:
848:
355:
1780:
3149:
2962:
1855:
2514:
2624:
2618:
2422:
462:
891:
658:
696:
203:
181:
The first term on the right-hand side of the dispersion relation is the electron plasma oscillation related to the electric field force and the second term is related to the thermal motion of the electrons, where
2101:
1285:
539:
1502:
177:
2318:
1542:
1537:
1372:
3019:
2832:
3030:
2843:
82:
is a purely longitudinal wave, that is, the wave vector is in the same direction as the E-field. It is an electrostatic wave; as such, it doesn't have an oscillating magnetic field.
2020:{\displaystyle \omega ^{2}={\frac {\omega _{e}^{2}+\omega _{i}^{2}}{2}}\pm {\sqrt {\left({\frac {\omega _{e}^{2}-\omega _{i}^{2}}{2}}\right)^{2}+\omega _{pe}^{2}\omega _{pi}^{2}}}}
65:
wave modified by the plasma. In a magnetized plasma, there are two modes perpendicular to the field, the O and X modes, and two modes parallel to the field, the R and L waves.
2249:
1841:
1810:
1529:
1434:
2133:
1400:
2428:
2770:{\displaystyle {\frac {c^{2}k^{2}}{\omega ^{2}}}=1-{\frac {\omega _{p}^{2}}{\omega ^{2}}}\,{\frac {\omega ^{2}-\omega _{p}^{2}}{\omega ^{2}-\omega _{h}^{2}}}}
2525:
2329:
1204:{\displaystyle n^{2}={\frac {}{(\omega ^{2}-\omega _{ci}^{2})(\omega ^{2}-\omega _{ce}^{2})+\omega _{p}^{2}(\omega _{ce}\omega _{ci}-\omega ^{2})}}}
362:
585:
843:{\displaystyle 1-{\frac {\omega _{pe}^{2}}{\omega ^{2}}}-{\frac {k^{2}c^{2}}{\omega ^{2}}}=0\rightarrow \omega ^{2}=c^{2}k^{2}+\omega _{pe}^{2}}
350:{\displaystyle 1-{\frac {\omega _{pe}^{2}}{\omega ^{2}}}-{\frac {k^{2}c^{2}}{\omega ^{2}}}=0\rightarrow \omega ^{2}=c^{2}k^{2}+\omega _{pe}^{2}}
3210:
2032:
1216:
467:
1439:
86:
electrons. Since electrons have inertia the system behaves as a harmonic oscillator, where the electrons oscillate at a frequency ω
103:
17:
198:
In an unmagnetized plasma, waves above the plasma frequency propagate through the plasma according to the dispersion relation:
3305:
3280:
3233:
2255:
1436:
is reached. As the density is further increased, the wave is evanescent until the resonance at the upper hybrid frequency
2183:
can be written as an expression for the frequency (squared), but it is also common to write it as an expression for the
1775:{\displaystyle {\begin{aligned}\omega _{R}&={\frac {1}{2}}\left\\\omega _{L}&={\frac {1}{2}}\left\end{aligned}}}
93:
When the thermal motion of the electrons is taken into account a shift in frequency from the electron plasma frequency ω
3194:
1309:
3144:{\displaystyle {\frac {c^{2}k^{2}}{\omega ^{2}}}=1-{\frac {\omega _{p}^{2}/\omega ^{2}}{1+\omega _{c}/\omega }}}
2973:
2957:{\displaystyle {\frac {c^{2}k^{2}}{\omega ^{2}}}=1-{\frac {\omega _{p}^{2}/\omega ^{2}}{1-\omega _{c}/\omega }}}
2786:
661:
1813:
2212:
3327:
3165:
1819:
1788:
1507:
1412:
90:, called electron plasma frequency. These oscillations do not propagate—the group velocity is 0.
2151:
are right-hand and left-hand circularly polarized, respectively. The R wave has a cut-off at ω
3187:
Introduction to plasma physics : with space, laboratory and astrophysical applications
3022:
2835:
2106:
675:
In a magnetized plasma, except for the O wave, the cut-off relationships are more complex.
2509:{\displaystyle {\frac {c^{2}k^{2}}{\omega ^{2}}}=1-{\frac {\omega _{p}^{2}}{\omega ^{2}}}}
8:
2184:
2180:
1379:
688:
359:
In an unmagnetized plasma for the high frequency or low electron density limit, i.e. for
3204:
853:
546:
3301:
3276:
3229:
3190:
576:
563:
2613:{\displaystyle {\vec {k}}\perp {\vec {B}}_{0},\ {\vec {E}}_{1}\perp {\vec {B}}_{0}}
1844:
886:
is the "extraordinary" wave because it has a more complicated dispersion relation:
871:
47:
43:
2417:{\displaystyle {\vec {k}}\perp {\vec {B}}_{0},\ {\vec {E}}_{1}\|{\vec {B}}_{0}}
558:
554:
550:
51:
35:
3321:
457:{\displaystyle \omega \gg \omega _{pe}=(n_{e}e^{2}/m_{e}\epsilon _{0})^{1/2}}
79:
28:
653:{\displaystyle n_{c}={\frac {\varepsilon _{o}\,m_{e}}{e^{2}}}\,\omega ^{2}}
187:
61:
In an unmagnetized plasma, an electromagnetic electron wave is simply a
3248:
D. Gary
Swanson, Plasma Waves, Second Edition, Academic Press, 1989.
55:
2096:{\displaystyle \omega _{a}^{2}=\omega _{pa}^{2}+\omega _{ca}^{2}}
1280:{\displaystyle \omega _{p}^{2}=\omega _{pe}^{2}+\omega _{pi}^{2}}
534:{\displaystyle n_{e}\ll m_{e}\omega ^{2}\epsilon _{0}\,/\,e^{2}}
1497:{\displaystyle \omega _{h}^{2}=\omega _{p}^{2}+\omega _{c}^{2}}
3298:
Introduction to Plasma
Physics and Controlled Fusion, Volume 1
3273:
Introduction to Plasma
Physics and Controlled Fusion, Volume 1
3226:
Introduction to Plasma
Physics and Controlled Fusion, Volume 1
2155:(hence the designation of this frequency) and a resonance at ω
62:
3300:(2nd ed.). Plenum Publishing Corporation. p. 131.
3275:(2nd ed.). Plenum Publishing Corporation. p. 127.
3228:(2nd ed.). Plenum Publishing Corporation. p. 116.
172:{\displaystyle \omega ^{2}=\omega _{pe}^{2}+3C_{e}^{2}k^{2}}
1405:
As the density is increased, the phase velocity rises from
1504:. Then it can propagate again until the second cut-off at
668:
If the critical density is exceeded, the plasma is called
691:
is the same as that in an unmagnetized plasma, that is,
2313:{\displaystyle \omega ^{2}=\omega _{p}^{2}+k^{2}c^{2}}
1304:) and partly longitudinal; the E-field is of the form
3033:
2976:
2846:
2789:
2627:
2528:
2431:
2332:
2258:
2215:
2109:
2035:
1858:
1822:
1791:
1540:
1510:
1442:
1415:
1382:
1312:
1219:
894:
699:
588:
470:
365:
206:
106:
3143:
3013:
2956:
2826:
2769:
2612:
2508:
2416:
2312:
2243:
2127:
2095:
2019:
1835:
1804:
1774:
1523:
1496:
1428:
1394:
1366:
1279:
1203:
842:
652:
553:in vacuum. As the electron density increases, the
533:
456:
349:
171:
68:
3319:
2163:and no resonance. R waves at frequencies below ω
1367:{\displaystyle (E_{x},-j{\frac {S}{D}}E_{x},0)}
3189:(Second ed.). Cambridge, United Kingdom.
1850:The resonant frequencies for the X-wave are:
687:is the "ordinary" wave in the sense that its
2989:
2802:
2392:
186:is the electron thermal speed and k is the
3209:: CS1 maint: location missing publisher (
3014:{\displaystyle {\vec {k}}\|{\vec {B}}_{0}}
2827:{\displaystyle {\vec {k}}\|{\vec {B}}_{0}}
2194:Summary of electromagnetic electron waves
2702:
1531:. The cut-off frequencies are given by
639:
615:
520:
514:
3184:
2174:
567:where the light frequency is equal to ω
193:
14:
3320:
54:component and in which primarily the
3295:
3289:
3270:
3264:
3223:
2138:
3217:
24:
25:
3339:
2244:{\displaystyle {\vec {B}}_{0}=0}
579:ω of that wave and is given by
73:
2159:. The L wave has a cut-off at ω
571:. This density is known as the
69:Waves in an unmagnetized plasma
3251:
3242:
3178:
2999:
2983:
2812:
2796:
2598:
2576:
2551:
2535:
2402:
2380:
2355:
2339:
2223:
1361:
1313:
1290:It is partly transverse (with
1195:
1153:
1132:
1098:
1095:
1061:
1056:
1035:
1013:
1010:
988:
985:
982:
961:
939:
936:
914:
911:
783:
437:
388:
290:
13:
1:
3171:
40:electromagnetic electron wave
1814:electron cyclotron resonance
1402:refer to the Stix notation.
7:
3185:Gurnett, Donald A. (2017).
3159:
1836:{\displaystyle \omega _{p}}
1805:{\displaystyle \omega _{c}}
1524:{\displaystyle \omega _{L}}
1429:{\displaystyle \omega _{R}}
10:
3344:
870:. It has a cut-off at the
26:
3166:Appleton-Hartree equation
877:
678:
549:, the wave speed is the
98:dispersion relation is:
27:Not to be confused with
3261:, Academic Press, 1989.
2966:R wave (whistler mode)
18:Critical plasma density
3296:Chen, Francis (1984).
3271:Chen, Francis (1984).
3224:Chen, Francis (1984).
3145:
3015:
2958:
2828:
2771:
2614:
2510:
2418:
2314:
2245:
2129:
2097:
2021:
1837:
1806:
1776:
1525:
1498:
1430:
1396:
1368:
1281:
1205:
844:
654:
535:
458:
351:
173:
3146:
3016:
2959:
2829:
2772:
2615:
2511:
2419:
2315:
2246:
2167:/2 are also known as
2130:
2128:{\displaystyle a=e,i}
2098:
2022:
1838:
1807:
1777:
1526:
1499:
1431:
1409:until the cut-off at
1397:
1369:
1282:
1206:
845:
655:
536:
459:
352:
174:
3031:
2974:
2844:
2787:
2625:
2526:
2429:
2330:
2256:
2213:
2175:Dispersion relations
2107:
2033:
1856:
1820:
1789:
1538:
1508:
1440:
1413:
1380:
1310:
1217:
892:
697:
586:
561:decreases until the
468:
363:
204:
194:Electromagnetic wave
104:
3096:
2909:
2763:
2733:
2689:
2493:
2286:
2202:Dispersion relation
2195:
2185:index of refraction
2181:dispersion relation
2092:
2071:
2050:
2014:
1996:
1959:
1941:
1907:
1889:
1746:
1725:
1631:
1610:
1493:
1475:
1457:
1395:{\displaystyle S,D}
1276:
1255:
1234:
1152:
1131:
1094:
1055:
981:
839:
725:
689:dispersion relation
346:
232:
158:
137:
3141:
3082:
3011:
2954:
2895:
2824:
2767:
2749:
2719:
2675:
2610:
2506:
2479:
2414:
2310:
2272:
2241:
2193:
2125:
2093:
2075:
2054:
2036:
2017:
1997:
1979:
1945:
1927:
1893:
1875:
1833:
1802:
1772:
1770:
1732:
1711:
1617:
1596:
1521:
1494:
1479:
1461:
1443:
1426:
1392:
1364:
1277:
1259:
1238:
1220:
1201:
1138:
1114:
1077:
1041:
967:
840:
822:
708:
650:
557:increases and the
531:
454:
347:
329:
215:
169:
144:
120:
3307:978-0-306-41332-2
3282:978-0-306-41332-2
3257:D. Gary Swanson,
3235:978-0-306-41332-2
3157:
3156:
3139:
3068:
3002:
2986:
2952:
2881:
2815:
2799:
2765:
2700:
2662:
2601:
2579:
2568:
2554:
2538:
2504:
2466:
2405:
2383:
2372:
2358:
2342:
2226:
2139:R wave and L wave
2015:
1964:
1912:
1760:
1682:
1645:
1570:
1343:
1199:
775:
736:
637:
577:angular frequency
564:cut-off frequency
282:
243:
16:(Redirected from
3335:
3328:Waves in plasmas
3312:
3311:
3293:
3287:
3286:
3268:
3262:
3255:
3249:
3246:
3240:
3239:
3221:
3215:
3214:
3208:
3200:
3182:
3150:
3148:
3147:
3142:
3140:
3138:
3134:
3129:
3128:
3112:
3111:
3110:
3101:
3095:
3090:
3080:
3069:
3067:
3066:
3057:
3056:
3055:
3046:
3045:
3035:
3020:
3018:
3017:
3012:
3010:
3009:
3004:
3003:
2995:
2988:
2987:
2979:
2963:
2961:
2960:
2955:
2953:
2951:
2947:
2942:
2941:
2925:
2924:
2923:
2914:
2908:
2903:
2893:
2882:
2880:
2879:
2870:
2869:
2868:
2859:
2858:
2848:
2836:right circ. pol.
2833:
2831:
2830:
2825:
2823:
2822:
2817:
2816:
2808:
2801:
2800:
2792:
2776:
2774:
2773:
2768:
2766:
2764:
2762:
2757:
2745:
2744:
2734:
2732:
2727:
2715:
2714:
2704:
2701:
2699:
2698:
2688:
2683:
2674:
2663:
2661:
2660:
2651:
2650:
2649:
2640:
2639:
2629:
2619:
2617:
2616:
2611:
2609:
2608:
2603:
2602:
2594:
2587:
2586:
2581:
2580:
2572:
2566:
2562:
2561:
2556:
2555:
2547:
2540:
2539:
2531:
2515:
2513:
2512:
2507:
2505:
2503:
2502:
2492:
2487:
2478:
2467:
2465:
2464:
2455:
2454:
2453:
2444:
2443:
2433:
2423:
2421:
2420:
2415:
2413:
2412:
2407:
2406:
2398:
2391:
2390:
2385:
2384:
2376:
2370:
2366:
2365:
2360:
2359:
2351:
2344:
2343:
2335:
2319:
2317:
2316:
2311:
2309:
2308:
2299:
2298:
2285:
2280:
2268:
2267:
2250:
2248:
2247:
2242:
2234:
2233:
2228:
2227:
2219:
2196:
2192:
2134:
2132:
2131:
2126:
2102:
2100:
2099:
2094:
2091:
2086:
2070:
2065:
2049:
2044:
2026:
2024:
2023:
2018:
2016:
2013:
2008:
1995:
1990:
1975:
1974:
1969:
1965:
1960:
1958:
1953:
1940:
1935:
1925:
1918:
1913:
1908:
1906:
1901:
1888:
1883:
1873:
1868:
1867:
1845:plasma frequency
1843:is the electron
1842:
1840:
1839:
1834:
1832:
1831:
1811:
1809:
1808:
1803:
1801:
1800:
1781:
1779:
1778:
1773:
1771:
1767:
1763:
1762:
1761:
1753:
1751:
1747:
1745:
1740:
1724:
1719:
1701:
1700:
1683:
1675:
1666:
1665:
1652:
1648:
1647:
1646:
1638:
1636:
1632:
1630:
1625:
1609:
1604:
1586:
1585:
1571:
1563:
1554:
1553:
1530:
1528:
1527:
1522:
1520:
1519:
1503:
1501:
1500:
1495:
1492:
1487:
1474:
1469:
1456:
1451:
1435:
1433:
1432:
1427:
1425:
1424:
1401:
1399:
1398:
1393:
1373:
1371:
1370:
1365:
1354:
1353:
1344:
1336:
1325:
1324:
1286:
1284:
1283:
1278:
1275:
1270:
1254:
1249:
1233:
1228:
1210:
1208:
1207:
1202:
1200:
1198:
1194:
1193:
1181:
1180:
1168:
1167:
1151:
1146:
1130:
1125:
1110:
1109:
1093:
1088:
1073:
1072:
1059:
1054:
1049:
1034:
1033:
1009:
1008:
980:
975:
960:
959:
935:
934:
909:
904:
903:
872:plasma frequency
849:
847:
846:
841:
838:
833:
818:
817:
808:
807:
795:
794:
776:
774:
773:
764:
763:
762:
753:
752:
742:
737:
735:
734:
724:
719:
707:
659:
657:
656:
651:
649:
648:
638:
636:
635:
626:
625:
624:
614:
613:
603:
598:
597:
573:critical density
547:plasma frequency
540:
538:
537:
532:
530:
529:
519:
513:
512:
503:
502:
493:
492:
480:
479:
463:
461:
460:
455:
453:
452:
448:
435:
434:
425:
424:
415:
410:
409:
400:
399:
384:
383:
356:
354:
353:
348:
345:
340:
325:
324:
315:
314:
302:
301:
283:
281:
280:
271:
270:
269:
260:
259:
249:
244:
242:
241:
231:
226:
214:
178:
176:
175:
170:
168:
167:
157:
152:
136:
131:
116:
115:
21:
3343:
3342:
3338:
3337:
3336:
3334:
3333:
3332:
3318:
3317:
3316:
3315:
3308:
3294:
3290:
3283:
3269:
3265:
3256:
3252:
3247:
3243:
3236:
3222:
3218:
3202:
3201:
3197:
3183:
3179:
3174:
3162:
3130:
3124:
3120:
3113:
3106:
3102:
3097:
3091:
3086:
3081:
3079:
3062:
3058:
3051:
3047:
3041:
3037:
3036:
3034:
3032:
3029:
3028:
3023:left circ. pol.
3005:
2994:
2993:
2992:
2978:
2977:
2975:
2972:
2971:
2943:
2937:
2933:
2926:
2919:
2915:
2910:
2904:
2899:
2894:
2892:
2875:
2871:
2864:
2860:
2854:
2850:
2849:
2847:
2845:
2842:
2841:
2818:
2807:
2806:
2805:
2791:
2790:
2788:
2785:
2784:
2758:
2753:
2740:
2736:
2735:
2728:
2723:
2710:
2706:
2705:
2703:
2694:
2690:
2684:
2679:
2673:
2656:
2652:
2645:
2641:
2635:
2631:
2630:
2628:
2626:
2623:
2622:
2604:
2593:
2592:
2591:
2582:
2571:
2570:
2569:
2557:
2546:
2545:
2544:
2530:
2529:
2527:
2524:
2523:
2498:
2494:
2488:
2483:
2477:
2460:
2456:
2449:
2445:
2439:
2435:
2434:
2432:
2430:
2427:
2426:
2408:
2397:
2396:
2395:
2386:
2375:
2374:
2373:
2361:
2350:
2349:
2348:
2334:
2333:
2331:
2328:
2327:
2304:
2300:
2294:
2290:
2281:
2276:
2263:
2259:
2257:
2254:
2253:
2229:
2218:
2217:
2216:
2214:
2211:
2210:
2177:
2166:
2162:
2158:
2154:
2141:
2108:
2105:
2104:
2087:
2079:
2066:
2058:
2045:
2040:
2034:
2031:
2030:
2009:
2001:
1991:
1983:
1970:
1954:
1949:
1936:
1931:
1926:
1924:
1920:
1919:
1917:
1902:
1897:
1884:
1879:
1874:
1872:
1863:
1859:
1857:
1854:
1853:
1827:
1823:
1821:
1818:
1817:
1816:frequency, and
1796:
1792:
1790:
1787:
1786:
1769:
1768:
1752:
1741:
1736:
1720:
1715:
1710:
1706:
1705:
1696:
1692:
1688:
1684:
1674:
1667:
1661:
1657:
1654:
1653:
1637:
1626:
1621:
1605:
1600:
1595:
1591:
1590:
1581:
1577:
1576:
1572:
1562:
1555:
1549:
1545:
1541:
1539:
1536:
1535:
1515:
1511:
1509:
1506:
1505:
1488:
1483:
1470:
1465:
1452:
1447:
1441:
1438:
1437:
1420:
1416:
1414:
1411:
1410:
1381:
1378:
1377:
1349:
1345:
1335:
1320:
1316:
1311:
1308:
1307:
1303:
1296:
1271:
1263:
1250:
1242:
1229:
1224:
1218:
1215:
1214:
1189:
1185:
1173:
1169:
1160:
1156:
1147:
1142:
1126:
1118:
1105:
1101:
1089:
1081:
1068:
1064:
1060:
1050:
1045:
1026:
1022:
1001:
997:
976:
971:
952:
948:
927:
923:
910:
908:
899:
895:
893:
890:
889:
880:
869:
862:
854:plane polarized
834:
826:
813:
809:
803:
799:
790:
786:
769:
765:
758:
754:
748:
744:
743:
741:
730:
726:
720:
712:
706:
698:
695:
694:
681:
644:
640:
631:
627:
620:
616:
609:
605:
604:
602:
593:
589:
587:
584:
583:
570:
544:
525:
521:
515:
508:
504:
498:
494:
488:
484:
475:
471:
469:
466:
465:
444:
440:
436:
430:
426:
420:
416:
411:
405:
401:
395:
391:
376:
372:
364:
361:
360:
341:
333:
320:
316:
310:
306:
297:
293:
276:
272:
265:
261:
255:
251:
250:
248:
237:
233:
227:
219:
213:
205:
202:
201:
196:
185:
163:
159:
153:
148:
132:
124:
111:
107:
105:
102:
101:
96:
89:
76:
71:
32:
23:
22:
15:
12:
11:
5:
3341:
3331:
3330:
3314:
3313:
3306:
3288:
3281:
3263:
3250:
3241:
3234:
3216:
3195:
3176:
3175:
3173:
3170:
3169:
3168:
3161:
3158:
3155:
3154:
3151:
3137:
3133:
3127:
3123:
3119:
3116:
3109:
3105:
3100:
3094:
3089:
3085:
3078:
3075:
3072:
3065:
3061:
3054:
3050:
3044:
3040:
3026:
3008:
3001:
2998:
2991:
2985:
2982:
2968:
2967:
2964:
2950:
2946:
2940:
2936:
2932:
2929:
2922:
2918:
2913:
2907:
2902:
2898:
2891:
2888:
2885:
2878:
2874:
2867:
2863:
2857:
2853:
2839:
2821:
2814:
2811:
2804:
2798:
2795:
2781:
2780:
2777:
2761:
2756:
2752:
2748:
2743:
2739:
2731:
2726:
2722:
2718:
2713:
2709:
2697:
2693:
2687:
2682:
2678:
2672:
2669:
2666:
2659:
2655:
2648:
2644:
2638:
2634:
2620:
2607:
2600:
2597:
2590:
2585:
2578:
2575:
2565:
2560:
2553:
2550:
2543:
2537:
2534:
2520:
2519:
2516:
2501:
2497:
2491:
2486:
2482:
2476:
2473:
2470:
2463:
2459:
2452:
2448:
2442:
2438:
2424:
2411:
2404:
2401:
2394:
2389:
2382:
2379:
2369:
2364:
2357:
2354:
2347:
2341:
2338:
2324:
2323:
2320:
2307:
2303:
2297:
2293:
2289:
2284:
2279:
2275:
2271:
2266:
2262:
2251:
2240:
2237:
2232:
2225:
2222:
2207:
2206:
2203:
2200:
2190:/ω (squared).
2176:
2173:
2169:whistler modes
2164:
2160:
2156:
2152:
2140:
2137:
2124:
2121:
2118:
2115:
2112:
2090:
2085:
2082:
2078:
2074:
2069:
2064:
2061:
2057:
2053:
2048:
2043:
2039:
2012:
2007:
2004:
2000:
1994:
1989:
1986:
1982:
1978:
1973:
1968:
1963:
1957:
1952:
1948:
1944:
1939:
1934:
1930:
1923:
1916:
1911:
1905:
1900:
1896:
1892:
1887:
1882:
1878:
1871:
1866:
1862:
1830:
1826:
1799:
1795:
1783:
1782:
1766:
1759:
1756:
1750:
1744:
1739:
1735:
1731:
1728:
1723:
1718:
1714:
1709:
1704:
1699:
1695:
1691:
1687:
1681:
1678:
1673:
1670:
1668:
1664:
1660:
1656:
1655:
1651:
1644:
1641:
1635:
1629:
1624:
1620:
1616:
1613:
1608:
1603:
1599:
1594:
1589:
1584:
1580:
1575:
1569:
1566:
1561:
1558:
1556:
1552:
1548:
1544:
1543:
1518:
1514:
1491:
1486:
1482:
1478:
1473:
1468:
1464:
1460:
1455:
1450:
1446:
1423:
1419:
1391:
1388:
1385:
1363:
1360:
1357:
1352:
1348:
1342:
1339:
1334:
1331:
1328:
1323:
1319:
1315:
1301:
1294:
1274:
1269:
1266:
1262:
1258:
1253:
1248:
1245:
1241:
1237:
1232:
1227:
1223:
1197:
1192:
1188:
1184:
1179:
1176:
1172:
1166:
1163:
1159:
1155:
1150:
1145:
1141:
1137:
1134:
1129:
1124:
1121:
1117:
1113:
1108:
1104:
1100:
1097:
1092:
1087:
1084:
1080:
1076:
1071:
1067:
1063:
1058:
1053:
1048:
1044:
1040:
1037:
1032:
1029:
1025:
1021:
1018:
1015:
1012:
1007:
1004:
1000:
996:
993:
990:
987:
984:
979:
974:
970:
966:
963:
958:
955:
951:
947:
944:
941:
938:
933:
930:
926:
922:
919:
916:
913:
907:
902:
898:
879:
876:
867:
860:
837:
832:
829:
825:
821:
816:
812:
806:
802:
798:
793:
789:
785:
782:
779:
772:
768:
761:
757:
751:
747:
740:
733:
729:
723:
718:
715:
711:
705:
702:
680:
677:
666:
665:
647:
643:
634:
630:
623:
619:
612:
608:
601:
596:
592:
568:
559:group velocity
555:phase velocity
551:speed of light
542:
528:
524:
518:
511:
507:
501:
497:
491:
487:
483:
478:
474:
451:
447:
443:
439:
433:
429:
423:
419:
414:
408:
404:
398:
394:
390:
387:
382:
379:
375:
371:
368:
344:
339:
336:
332:
328:
323:
319:
313:
309:
305:
300:
296:
292:
289:
286:
279:
275:
268:
264:
258:
254:
247:
240:
236:
230:
225:
222:
218:
212:
209:
195:
192:
183:
166:
162:
156:
151:
147:
143:
140:
135:
130:
127:
123:
119:
114:
110:
94:
87:
75:
72:
70:
67:
52:magnetic field
36:plasma physics
9:
6:
4:
3:
2:
3340:
3329:
3326:
3325:
3323:
3309:
3303:
3299:
3292:
3284:
3278:
3274:
3267:
3260:
3259:Plasma Waves
3254:
3245:
3237:
3231:
3227:
3220:
3212:
3206:
3198:
3196:9781107027374
3192:
3188:
3181:
3177:
3167:
3164:
3163:
3152:
3135:
3131:
3125:
3121:
3117:
3114:
3107:
3103:
3098:
3092:
3087:
3083:
3076:
3073:
3070:
3063:
3059:
3052:
3048:
3042:
3038:
3027:
3024:
3006:
2996:
2980:
2970:
2969:
2965:
2948:
2944:
2938:
2934:
2930:
2927:
2920:
2916:
2911:
2905:
2900:
2896:
2889:
2886:
2883:
2876:
2872:
2865:
2861:
2855:
2851:
2840:
2837:
2819:
2809:
2793:
2783:
2782:
2778:
2759:
2754:
2750:
2746:
2741:
2737:
2729:
2724:
2720:
2716:
2711:
2707:
2695:
2691:
2685:
2680:
2676:
2670:
2667:
2664:
2657:
2653:
2646:
2642:
2636:
2632:
2621:
2605:
2595:
2588:
2583:
2573:
2563:
2558:
2548:
2541:
2532:
2522:
2521:
2517:
2499:
2495:
2489:
2484:
2480:
2474:
2471:
2468:
2461:
2457:
2450:
2446:
2440:
2436:
2425:
2409:
2399:
2387:
2377:
2367:
2362:
2352:
2345:
2336:
2326:
2325:
2321:
2305:
2301:
2295:
2291:
2287:
2282:
2277:
2273:
2269:
2264:
2260:
2252:
2238:
2235:
2230:
2220:
2209:
2208:
2204:
2201:
2198:
2197:
2191:
2189:
2186:
2182:
2172:
2170:
2150:
2146:
2136:
2122:
2119:
2116:
2113:
2110:
2088:
2083:
2080:
2076:
2072:
2067:
2062:
2059:
2055:
2051:
2046:
2041:
2037:
2027:
2010:
2005:
2002:
1998:
1992:
1987:
1984:
1980:
1976:
1971:
1966:
1961:
1955:
1950:
1946:
1942:
1937:
1932:
1928:
1921:
1914:
1909:
1903:
1898:
1894:
1890:
1885:
1880:
1876:
1869:
1864:
1860:
1851:
1848:
1846:
1828:
1824:
1815:
1797:
1793:
1764:
1757:
1754:
1748:
1742:
1737:
1733:
1729:
1726:
1721:
1716:
1712:
1707:
1702:
1697:
1693:
1689:
1685:
1679:
1676:
1671:
1669:
1662:
1658:
1649:
1642:
1639:
1633:
1627:
1622:
1618:
1614:
1611:
1606:
1601:
1597:
1592:
1587:
1582:
1578:
1573:
1567:
1564:
1559:
1557:
1550:
1546:
1534:
1533:
1532:
1516:
1512:
1489:
1484:
1480:
1476:
1471:
1466:
1462:
1458:
1453:
1448:
1444:
1421:
1417:
1408:
1403:
1389:
1386:
1383:
1374:
1358:
1355:
1350:
1346:
1340:
1337:
1332:
1329:
1326:
1321:
1317:
1305:
1300:
1293:
1288:
1272:
1267:
1264:
1260:
1256:
1251:
1246:
1243:
1239:
1235:
1230:
1225:
1221:
1211:
1190:
1186:
1182:
1177:
1174:
1170:
1164:
1161:
1157:
1148:
1143:
1139:
1135:
1127:
1122:
1119:
1115:
1111:
1106:
1102:
1090:
1085:
1082:
1078:
1074:
1069:
1065:
1051:
1046:
1042:
1038:
1030:
1027:
1023:
1019:
1016:
1005:
1002:
998:
994:
991:
977:
972:
968:
964:
956:
953:
949:
945:
942:
931:
928:
924:
920:
917:
905:
900:
896:
887:
885:
875:
873:
866:
859:
855:
850:
835:
830:
827:
823:
819:
814:
810:
804:
800:
796:
791:
787:
780:
777:
770:
766:
759:
755:
749:
745:
738:
731:
727:
721:
716:
713:
709:
703:
700:
692:
690:
686:
676:
673:
671:
663:
645:
641:
632:
628:
621:
617:
610:
606:
599:
594:
590:
582:
581:
580:
578:
574:
566:
565:
560:
556:
552:
548:
526:
522:
516:
509:
505:
499:
495:
489:
485:
481:
476:
472:
449:
445:
441:
431:
427:
421:
417:
412:
406:
402:
396:
392:
385:
380:
377:
373:
369:
366:
357:
342:
337:
334:
330:
326:
321:
317:
311:
307:
303:
298:
294:
287:
284:
277:
273:
266:
262:
256:
252:
245:
238:
234:
228:
223:
220:
216:
210:
207:
199:
191:
189:
179:
164:
160:
154:
149:
145:
141:
138:
133:
128:
125:
121:
117:
112:
108:
99:
91:
83:
81:
80:Langmuir wave
74:Langmuir Wave
66:
64:
59:
57:
53:
49:
45:
41:
37:
30:
29:Electron wave
19:
3297:
3291:
3272:
3266:
3258:
3253:
3244:
3225:
3219:
3186:
3180:
2187:
2178:
2168:
2148:
2144:
2142:
2028:
1852:
1849:
1784:
1406:
1404:
1375:
1306:
1298:
1291:
1289:
1212:
888:
883:
881:
864:
857:
851:
693:
684:
682:
674:
669:
667:
572:
562:
358:
200:
197:
180:
100:
92:
84:
77:
60:
50:which has a
39:
33:
2322:Light wave
188:wave vector
58:oscillate.
3172:References
2199:Conditions
670:over-dense
3205:cite book
3136:ω
3122:ω
3104:ω
3084:ω
3077:−
3060:ω
3000:→
2990:‖
2984:→
2949:ω
2935:ω
2931:−
2917:ω
2897:ω
2890:−
2873:ω
2813:→
2803:‖
2797:→
2751:ω
2747:−
2738:ω
2721:ω
2717:−
2708:ω
2692:ω
2677:ω
2671:−
2654:ω
2599:→
2589:⊥
2577:→
2552:→
2542:⊥
2536:→
2496:ω
2481:ω
2475:−
2458:ω
2403:→
2393:‖
2381:→
2356:→
2346:⊥
2340:→
2274:ω
2261:ω
2224:→
2077:ω
2056:ω
2038:ω
1999:ω
1981:ω
1947:ω
1943:−
1929:ω
1915:±
1895:ω
1877:ω
1861:ω
1825:ω
1794:ω
1734:ω
1713:ω
1694:ω
1690:−
1659:ω
1619:ω
1598:ω
1579:ω
1547:ω
1513:ω
1481:ω
1463:ω
1445:ω
1418:ω
1330:−
1261:ω
1240:ω
1222:ω
1187:ω
1183:−
1171:ω
1158:ω
1140:ω
1116:ω
1112:−
1103:ω
1079:ω
1075:−
1066:ω
1043:ω
1039:−
1024:ω
1017:ω
999:ω
995:−
992:ω
969:ω
965:−
950:ω
946:−
943:ω
925:ω
918:ω
824:ω
788:ω
784:→
767:ω
739:−
728:ω
710:ω
704:−
642:ω
607:ε
506:ϵ
496:ω
482:≪
428:ϵ
374:ω
370:≫
367:ω
331:ω
295:ω
291:→
274:ω
246:−
235:ω
217:ω
211:−
122:ω
109:ω
56:electrons
3322:Category
3160:See also
2147:and the
852:. It is
662:SI units
575:for the
3153:L wave
2779:X wave
2518:O wave
1812:is the
545:is the
541:where ω
3304:
3279:
3232:
3193:
2567:
2371:
2149:L wave
2145:R wave
2029:where
1785:where
1376:Where
1213:Where
884:X wave
878:X wave
685:O wave
679:O wave
48:plasma
2205:Name
856:with
63:light
46:in a
42:is a
38:, an
3302:ISBN
3277:ISBN
3230:ISBN
3211:link
3191:ISBN
2179:The
2143:The
2103:and
882:The
683:The
78:The
44:wave
863:||
464:or
34:In
3324::
3207:}}
3203:{{
2188:ck
2171:.
2135:.
1847:.
1287:.
874:.
672:.
569:pe
543:pe
190:.
95:pe
88:pe
3310:.
3285:.
3238:.
3213:)
3199:.
3132:/
3126:c
3118:+
3115:1
3108:2
3099:/
3093:2
3088:p
3074:1
3071:=
3064:2
3053:2
3049:k
3043:2
3039:c
3025:)
3021:(
3007:0
2997:B
2981:k
2945:/
2939:c
2928:1
2921:2
2912:/
2906:2
2901:p
2887:1
2884:=
2877:2
2866:2
2862:k
2856:2
2852:c
2838:)
2834:(
2820:0
2810:B
2794:k
2760:2
2755:h
2742:2
2730:2
2725:p
2712:2
2696:2
2686:2
2681:p
2668:1
2665:=
2658:2
2647:2
2643:k
2637:2
2633:c
2606:0
2596:B
2584:1
2574:E
2564:,
2559:0
2549:B
2533:k
2500:2
2490:2
2485:p
2472:1
2469:=
2462:2
2451:2
2447:k
2441:2
2437:c
2410:0
2400:B
2388:1
2378:E
2368:,
2363:0
2353:B
2337:k
2306:2
2302:c
2296:2
2292:k
2288:+
2283:2
2278:p
2270:=
2265:2
2239:0
2236:=
2231:0
2221:B
2165:c
2161:L
2157:c
2153:R
2123:i
2120:,
2117:e
2114:=
2111:a
2089:2
2084:a
2081:c
2073:+
2068:2
2063:a
2060:p
2052:=
2047:2
2042:a
2011:2
2006:i
2003:p
1993:2
1988:e
1985:p
1977:+
1972:2
1967:)
1962:2
1956:2
1951:i
1938:2
1933:e
1922:(
1910:2
1904:2
1899:i
1891:+
1886:2
1881:e
1870:=
1865:2
1829:p
1798:c
1765:]
1758:2
1755:1
1749:)
1743:2
1738:p
1730:4
1727:+
1722:2
1717:c
1708:(
1703:+
1698:c
1686:[
1680:2
1677:1
1672:=
1663:L
1650:]
1643:2
1640:1
1634:)
1628:2
1623:p
1615:4
1612:+
1607:2
1602:c
1593:(
1588:+
1583:c
1574:[
1568:2
1565:1
1560:=
1551:R
1517:L
1490:2
1485:c
1477:+
1472:2
1467:p
1459:=
1454:2
1449:h
1422:R
1407:c
1390:D
1387:,
1384:S
1362:)
1359:0
1356:,
1351:x
1347:E
1341:D
1338:S
1333:j
1327:,
1322:x
1318:E
1314:(
1302:0
1299:B
1297:⊥
1295:1
1292:E
1273:2
1268:i
1265:p
1257:+
1252:2
1247:e
1244:p
1236:=
1231:2
1226:p
1196:)
1191:2
1178:i
1175:c
1165:e
1162:c
1154:(
1149:2
1144:p
1136:+
1133:)
1128:2
1123:e
1120:c
1107:2
1099:(
1096:)
1091:2
1086:i
1083:c
1070:2
1062:(
1057:]
1052:2
1047:p
1036:)
1031:e
1028:c
1020:+
1014:(
1011:)
1006:i
1003:c
989:(
986:[
983:]
978:2
973:p
962:)
957:e
954:c
940:(
937:)
932:i
929:c
921:+
915:(
912:[
906:=
901:2
897:n
868:0
865:B
861:1
858:E
836:2
831:e
828:p
820:+
815:2
811:k
805:2
801:c
797:=
792:2
781:0
778:=
771:2
760:2
756:c
750:2
746:k
732:2
722:2
717:e
714:p
701:1
664:)
660:(
646:2
633:2
629:e
622:e
618:m
611:o
600:=
595:c
591:n
527:2
523:e
517:/
510:0
500:2
490:e
486:m
477:e
473:n
450:2
446:/
442:1
438:)
432:0
422:e
418:m
413:/
407:2
403:e
397:e
393:n
389:(
386:=
381:e
378:p
343:2
338:e
335:p
327:+
322:2
318:k
312:2
308:c
304:=
299:2
288:0
285:=
278:2
267:2
263:c
257:2
253:k
239:2
229:2
224:e
221:p
208:1
184:e
182:C
165:2
161:k
155:2
150:e
146:C
142:3
139:+
134:2
129:e
126:p
118:=
113:2
31:.
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.