498:
1084:
is that Λ ≫ 1. When this is the case, collective electrostatic interactions dominate over binary collisions, and the plasma particles can be treated as if they only interact with a smooth background field, rather than through pairwise interactions (collisions). The
892:
380:
255:
1064:
754:
31:, denoted by capital Lambda, Λ. The plasma parameter is usually interpreted to be the argument of the Coulomb logarithm, which is the ratio of the maximum impact parameter to the classical distance of closest approach in
385:
87:
789:
673:
943:
118:
This expression is typically valid for a plasma in which ion thermal velocities are much less than electron thermal velocities. A detailed discussion of the
Coulomb logarithm is available in the
174:
954:
591:
297:
680:
292:
780:
169:
618:
38:
623:
899:
1251:
547:
1222:
J.D. Callen, University of
Wisconsin-Madison, Draft Material for Fundamentals of Plasma Physics book: Collective Plasma Phenomena
493:{\displaystyle N_{\text{D}}={\frac {(\epsilon _{0}kT_{\text{e}})^{\frac {3}{2}}}{q_{\text{e}}^{3}{n_{\text{e}}}^{\frac {1}{2}}}}}
144:). This definition of the plasma parameter is more frequently (and appropriately) called the Debye number, and is denoted
887:{\displaystyle \Gamma ={\frac {q_{\text{e}}^{2}}{4\pi \epsilon _{0}kT_{\text{e}}}}{\sqrt{\frac {4\pi n_{\text{e}}}{3}}}.}
125:
Note that the word parameter is usually used in plasma physics to refer to bulk plasma properties in general: see
375:{\displaystyle \lambda _{\text{D}}={\sqrt {\frac {\epsilon _{0}kT_{\text{e}}}{n_{\text{e}}q_{\text{e}}^{2}}}}}
1080:
One of the criteria which determine whether a collection of charged particles can rigorously be termed an
250:{\displaystyle N_{\text{D}}={\frac {4\pi }{3}}n_{\text{e}}\lambda _{\text{D}}^{3}={\frac {1}{3}}\Lambda }
1059:{\displaystyle \Gamma _{s}={\frac {q_{s}^{2}}{4\pi \epsilon _{0}kT_{s}}}{\sqrt{\frac {4\pi n_{s}}{3}}}.}
265:
259:
Since these two definitions differ only by a factor of three, they are frequently used interchangeably.
1266:
759:
509:
1235:
147:
28:
749:{\displaystyle E_{\text{C}}={\frac {q_{\text{e}}^{2}}{4\pi \epsilon _{0}\langle r\rangle }},}
603:
132:
An alternative definition of this parameter is given by the average number of electrons in a
1204:
Chen, F.F., Introduction to Plasma
Physics and Controlled Fusion, (Springer, New York, 2006)
947:
In general, for multicomponent plasmas one defines the coupling parameter for each species
1213:
Miyamoto, K., Fundamentals of Plasma
Physics and Controlled Fusion, (Iwanami, Tokyo, 1997)
8:
783:
519:
1101:
Depending on the magnitude of Λ, plasma properties can be characterized as following:
1086:
126:
32:
17:
133:
1223:
100:
1260:
1081:
141:
137:
111:
1090:
82:{\displaystyle \Lambda =4\pi n_{\text{e}}\lambda _{\text{D}}^{3}}
620:, defined as a ratio of the Coulomb energy to the thermal one:
668:{\displaystyle \Gamma ={\frac {E_{\text{C}}}{kT_{\text{e}}}}.}
544:
Confusingly, some authors define the plasma parameter as:
938:{\displaystyle \Gamma \sim \Lambda ^{-{\frac {2}{3}}}\ .}
896:
Clearly, up to a numeric factor of the order of unity,
171:. In this context, the plasma parameter is defined as
957:
902:
792:
762:
683:
626:
606:
550:
388:
300:
268:
177:
150:
41:
600:A closely related parameter is the plasma coupling
35:. In this case, the plasma parameter is given by:
1058:
937:
886:
774:
748:
667:
612:
585:
492:
374:
286:
249:
163:
81:
1089:of each species in an ideal plasma is that of an
1075:
1072:stands for either electrons or (a type of) ions.
1258:
294:is dropped. When the Debye length is given by
756:where for the typical inter-particle distance
586:{\displaystyle \epsilon _{p}=\Lambda ^{-1}\ .}
769:
763:
737:
731:
1096:
1172:Very "cold" "high pressure" arc discharge
1259:
1238:lecture notes from Richard Fitzpatrick
677:The Coulomb energy (per particle) is
595:
1170:Solid-density laser ablation plasmas
382:, the plasma parameter is given by
13:
959:
910:
903:
793:
627:
607:
565:
287:{\displaystyle {\frac {4\pi }{3}}}
244:
42:
14:
1278:
1245:
775:{\displaystyle \langle r\rangle }
1228:
1216:
1207:
1198:
1076:The ideal plasma approximation
432:
405:
1:
1252:NRL Plasma Formulary 2007 ed.
1191:
540:is the electron temperature.
164:{\displaystyle N_{\text{D}}}
7:
1174:Inertial fusion experiments
1110:Plasma parameter magnitude
10:
1283:
510:permittivity of free space
15:
1109:
1106:
1145:Electrostatic influence
140:(a sphere of radius the
16:Not to be confused with
1181:Magnetic fusion devices
1156:Typical characteristic
1126:Strongly coupled plasma
1097:Plasma properties and Λ
613:{\displaystyle \Gamma }
531:is the electron charge,
1129:Weakly coupled plasma
1060:
939:
888:
776:
750:
669:
614:
587:
494:
376:
288:
251:
165:
83:
1061:
940:
889:
782:usually is taken the
777:
751:
670:
615:
588:
495:
377:
289:
252:
166:
84:
1236:The plasma parameter
1183:Space plasma physics
955:
900:
790:
760:
681:
624:
604:
548:
386:
298:
266:
262:Often the factor of
175:
148:
120:NRL Plasma Formulary
39:
29:dimensionless number
1179:Ionospheric physics
1148:Almost continuously
987:
815:
784:Wigner-Seitz radius
713:
462:
367:
230:
136:contained within a
78:
1176:Stellar interiors
1140:Densely populated
1137:Sparsely populated
1056:
973:
935:
884:
801:
772:
746:
699:
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596:Coupling parameter
583:
520:Boltzmann constant
490:
448:
372:
353:
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247:
216:
161:
79:
64:
33:Coulomb scattering
1267:Plasma parameters
1189:
1188:
1087:equation of state
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1045:
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127:plasma parameters
71:
61:
18:Plasma parameters
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1162:Hot and diffuse
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1103:
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59:
25:plasma parameter
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1281:
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431:
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421:
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357:
347:
343:
342:
335:
331:
322:
318:
317:
314:
305:
301:
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295:
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267:
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263:
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182:
178:
176:
173:
172:
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151:
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122:, pages 34–35.
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58:
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40:
37:
36:
21:
12:
11:
5:
1280:
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1255:
1254:
1247:
1246:External links
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1206:
1196:
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1190:
1187:
1186:
1177:
1168:
1164:
1163:
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1159:Cold and dense
1157:
1153:
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1149:
1146:
1142:
1141:
1138:
1135:
1131:
1130:
1127:
1124:
1120:
1119:
1118:Λ ≫ 1 (Γ ≪ 1)
1116:
1112:
1111:
1108:
1098:
1095:
1077:
1074:
1055:
1049:
1044:
1038:
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203:
199:
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181:
154:
116:
115:
107:
104:
101:number density
96:
76:
67:
57:
53:
50:
47:
44:
9:
6:
4:
3:
2:
1279:
1268:
1265:
1264:
1262:
1253:
1250:
1249:
1237:
1231:
1225:
1219:
1210:
1201:
1197:
1178:
1169:
1166:
1165:
1161:
1158:
1155:
1154:
1150:
1147:
1144:
1143:
1139:
1136:
1134:Debye sphere
1133:
1132:
1128:
1125:
1122:
1121:
1117:
1115:Λ ≪ 1 (Γ ≫ 1)
1114:
1113:
1105:
1102:
1094:
1092:
1088:
1083:
1073:
1071:
1066:
1053:
1047:
1042:
1036:
1032:
1028:
1025:
1013:
1009:
1005:
1000:
996:
992:
989:
983:
978:
974:
968:
963:
950:
945:
932:
922:
919:
914:
906:
894:
881:
875:
870:
860:
856:
853:
837:
833:
828:
824:
820:
817:
811:
802:
796:
786:. Therefore,
785:
766:
743:
734:
726:
722:
718:
715:
709:
700:
694:
685:
675:
662:
650:
646:
636:
630:
593:
580:
572:
569:
561:
556:
552:
536:
533:
527:
524:
521:
517:
514:
511:
503:
502:
501:
481:
478:
466:
458:
449:
440:
437:
422:
418:
413:
409:
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390:
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354:
344:
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328:
323:
319:
311:
302:
279:
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260:
257:
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236:
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217:
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201:
197:
194:
188:
179:
152:
143:
139:
135:
130:
128:
123:
121:
113:
105:
103:of electrons,
102:
95:
92:
91:
90:
74:
65:
55:
51:
48:
45:
34:
30:
26:
19:
1230:
1218:
1209:
1200:
1185:Plasma ball
1107:Description
1100:
1082:ideal plasma
1079:
1069:
1067:
951:separately:
948:
946:
895:
676:
599:
543:
534:
525:
515:
261:
258:
142:Debye length
138:Debye sphere
131:
124:
119:
117:
112:Debye length
93:
24:
22:
1151:Occasional
1192:References
1167:Examples
1123:Coupling
1091:ideal gas
1029:π
997:ϵ
993:π
960:Γ
915:−
911:Λ
907:∼
904:Γ
857:π
825:ϵ
821:π
794:Γ
770:⟩
764:⟨
738:⟩
732:⟨
723:ϵ
719:π
628:Γ
608:Γ
570:−
566:Λ
553:ϵ
410:ϵ
320:ϵ
303:λ
276:π
245:Λ
218:λ
198:π
66:λ
52:π
43:Λ
1261:Category
518:is the
508:is the
110:is the
99:is the
1068:Here,
930:
578:
500:where
134:plasma
89:where
27:is a
1234:See
23:The
1224:PDF
129:.
1263::
1093:.
1070:s
1054:.
1048:3
1043:3
1037:s
1033:n
1026:4
1014:s
1010:T
1006:k
1001:0
990:4
984:2
979:s
975:q
969:=
964:s
949:s
933:.
923:3
920:2
882:.
876:3
871:3
865:e
861:n
854:4
842:e
838:T
834:k
829:0
818:4
812:2
807:e
803:q
797:=
767:r
744:,
735:r
727:0
716:4
710:2
705:e
701:q
695:=
690:C
686:E
663:.
655:e
651:T
647:k
641:C
637:E
631:=
581:.
573:1
562:=
557:p
538:e
535:T
529:e
526:q
522:,
516:k
512:,
506:0
504:ε
482:2
479:1
471:e
467:n
459:3
454:e
450:q
441:2
438:3
433:)
427:e
423:T
419:k
414:0
406:(
400:=
395:D
391:N
364:2
359:e
355:q
349:e
345:n
337:e
333:T
329:k
324:0
312:=
307:D
280:3
273:4
240:3
237:1
232:=
227:3
222:D
212:e
208:n
202:3
195:4
189:=
184:D
180:N
157:D
153:N
114:.
108:D
106:λ
97:e
94:n
75:3
70:D
60:e
56:n
49:4
46:=
20:.
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