Magnetospheric chorus wave instability induced by relativistic Kappa-type distributions
Abstract We study the field-aligned propagating magnetospheric chorus wave instability using a fully relativistic wave growth formula, the previously developed relativistic Kappa-type (KT) distribution and the regular Kappa distribution of energetic electrons. We demonstrate that the peak growth rat...
Ausführliche Beschreibung
Autor*in: |
Yang, QiWu [verfasserIn] Yang, Chang [verfasserIn] He, YiHua [verfasserIn] Liu, Si [verfasserIn] Zhou, QingHua [verfasserIn] Xiao, FuLiang [verfasserIn] |
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Sprache: |
Englisch |
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2016 |
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Übergeordnetes Werk: |
Enthalten in: Science in China - Heidelberg : Springer, 1997, 59(2016), 11 vom: 25. Aug., Seite 1739-1745 |
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Übergeordnetes Werk: |
volume:59 ; year:2016 ; number:11 ; day:25 ; month:08 ; pages:1739-1745 |
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DOI / URN: |
10.1007/s11431-016-0161-2 |
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Katalog-ID: |
SPR019287690 |
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520 | |a Abstract We study the field-aligned propagating magnetospheric chorus wave instability using a fully relativistic wave growth formula, the previously developed relativistic Kappa-type (KT) distribution and the regular Kappa distribution of energetic electrons. We demonstrate that the peak growth rate using the nonrelativistic Kappa simulation is higher than that using either the relativistic KT or the Kappa simulation at/above 100 keV, because the significant relativistic effect yields a reduction in the relativistic anisotropy. The relativistic anisotropy Arel basically decreases as the thermal parameter $ θ^{2} $ increases, allowing the peak growth by relativistic KT or Kappa distribution to stay at the lower frequency region. The growth rates tend to increase with the loss-cone parameter l because the overall anisotropy increases. Moreover, at high energy ~1.0 MeV, both the growth rate and the upper cutoff frequency become smaller as l increases for the relativistic KT calculation because the significant relativistic effect reduces both the resonant anisotropy and the number of the hot electrons, which is in contrast to the relativistic and nonrelativistic Kappa distribution calculations because the less relativistic or non-relativistic effect enhances the resonant anisotropy as l increases. The above results can be applied to the whistler-mode wave instability in the outer radiation belts of the Earth, the Jovian inner magnetosphere and other astrophysical plasmas where relativistic electrons often exist. | ||
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650 | 4 | |a wave-particle interaction |7 (dpeaa)DE-He213 | |
650 | 4 | |a chorus wave instability |7 (dpeaa)DE-He213 | |
700 | 1 | |a Yang, Chang |e verfasserin |4 aut | |
700 | 1 | |a He, YiHua |e verfasserin |4 aut | |
700 | 1 | |a Liu, Si |e verfasserin |4 aut | |
700 | 1 | |a Zhou, QingHua |e verfasserin |4 aut | |
700 | 1 | |a Xiao, FuLiang |e verfasserin |4 aut | |
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10.1007/s11431-016-0161-2 doi (DE-627)SPR019287690 (SPR)s11431-016-0161-2-e DE-627 ger DE-627 rakwb eng 600 ASE 600 ASE 50.00 bkl Yang, QiWu verfasserin aut Magnetospheric chorus wave instability induced by relativistic Kappa-type distributions 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract We study the field-aligned propagating magnetospheric chorus wave instability using a fully relativistic wave growth formula, the previously developed relativistic Kappa-type (KT) distribution and the regular Kappa distribution of energetic electrons. We demonstrate that the peak growth rate using the nonrelativistic Kappa simulation is higher than that using either the relativistic KT or the Kappa simulation at/above 100 keV, because the significant relativistic effect yields a reduction in the relativistic anisotropy. The relativistic anisotropy Arel basically decreases as the thermal parameter $ θ^{2} $ increases, allowing the peak growth by relativistic KT or Kappa distribution to stay at the lower frequency region. The growth rates tend to increase with the loss-cone parameter l because the overall anisotropy increases. Moreover, at high energy ~1.0 MeV, both the growth rate and the upper cutoff frequency become smaller as l increases for the relativistic KT calculation because the significant relativistic effect reduces both the resonant anisotropy and the number of the hot electrons, which is in contrast to the relativistic and nonrelativistic Kappa distribution calculations because the less relativistic or non-relativistic effect enhances the resonant anisotropy as l increases. The above results can be applied to the whistler-mode wave instability in the outer radiation belts of the Earth, the Jovian inner magnetosphere and other astrophysical plasmas where relativistic electrons often exist. Kappa-type distribution (dpeaa)DE-He213 energetic electrons (dpeaa)DE-He213 wave-particle interaction (dpeaa)DE-He213 chorus wave instability (dpeaa)DE-He213 Yang, Chang verfasserin aut He, YiHua verfasserin aut Liu, Si verfasserin aut Zhou, QingHua verfasserin aut Xiao, FuLiang verfasserin aut Enthalten in Science in China Heidelberg : Springer, 1997 59(2016), 11 vom: 25. Aug., Seite 1739-1745 (DE-627)385614756 (DE-600)2142897-9 1862-281X nnns volume:59 year:2016 number:11 day:25 month:08 pages:1739-1745 https://dx.doi.org/10.1007/s11431-016-0161-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_152 GBV_ILN_161 GBV_ILN_171 GBV_ILN_187 GBV_ILN_224 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 50.00 ASE AR 59 2016 11 25 08 1739-1745 |
spelling |
10.1007/s11431-016-0161-2 doi (DE-627)SPR019287690 (SPR)s11431-016-0161-2-e DE-627 ger DE-627 rakwb eng 600 ASE 600 ASE 50.00 bkl Yang, QiWu verfasserin aut Magnetospheric chorus wave instability induced by relativistic Kappa-type distributions 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract We study the field-aligned propagating magnetospheric chorus wave instability using a fully relativistic wave growth formula, the previously developed relativistic Kappa-type (KT) distribution and the regular Kappa distribution of energetic electrons. We demonstrate that the peak growth rate using the nonrelativistic Kappa simulation is higher than that using either the relativistic KT or the Kappa simulation at/above 100 keV, because the significant relativistic effect yields a reduction in the relativistic anisotropy. The relativistic anisotropy Arel basically decreases as the thermal parameter $ θ^{2} $ increases, allowing the peak growth by relativistic KT or Kappa distribution to stay at the lower frequency region. The growth rates tend to increase with the loss-cone parameter l because the overall anisotropy increases. Moreover, at high energy ~1.0 MeV, both the growth rate and the upper cutoff frequency become smaller as l increases for the relativistic KT calculation because the significant relativistic effect reduces both the resonant anisotropy and the number of the hot electrons, which is in contrast to the relativistic and nonrelativistic Kappa distribution calculations because the less relativistic or non-relativistic effect enhances the resonant anisotropy as l increases. The above results can be applied to the whistler-mode wave instability in the outer radiation belts of the Earth, the Jovian inner magnetosphere and other astrophysical plasmas where relativistic electrons often exist. Kappa-type distribution (dpeaa)DE-He213 energetic electrons (dpeaa)DE-He213 wave-particle interaction (dpeaa)DE-He213 chorus wave instability (dpeaa)DE-He213 Yang, Chang verfasserin aut He, YiHua verfasserin aut Liu, Si verfasserin aut Zhou, QingHua verfasserin aut Xiao, FuLiang verfasserin aut Enthalten in Science in China Heidelberg : Springer, 1997 59(2016), 11 vom: 25. Aug., Seite 1739-1745 (DE-627)385614756 (DE-600)2142897-9 1862-281X nnns volume:59 year:2016 number:11 day:25 month:08 pages:1739-1745 https://dx.doi.org/10.1007/s11431-016-0161-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_152 GBV_ILN_161 GBV_ILN_171 GBV_ILN_187 GBV_ILN_224 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 50.00 ASE AR 59 2016 11 25 08 1739-1745 |
allfields_unstemmed |
10.1007/s11431-016-0161-2 doi (DE-627)SPR019287690 (SPR)s11431-016-0161-2-e DE-627 ger DE-627 rakwb eng 600 ASE 600 ASE 50.00 bkl Yang, QiWu verfasserin aut Magnetospheric chorus wave instability induced by relativistic Kappa-type distributions 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract We study the field-aligned propagating magnetospheric chorus wave instability using a fully relativistic wave growth formula, the previously developed relativistic Kappa-type (KT) distribution and the regular Kappa distribution of energetic electrons. We demonstrate that the peak growth rate using the nonrelativistic Kappa simulation is higher than that using either the relativistic KT or the Kappa simulation at/above 100 keV, because the significant relativistic effect yields a reduction in the relativistic anisotropy. The relativistic anisotropy Arel basically decreases as the thermal parameter $ θ^{2} $ increases, allowing the peak growth by relativistic KT or Kappa distribution to stay at the lower frequency region. The growth rates tend to increase with the loss-cone parameter l because the overall anisotropy increases. Moreover, at high energy ~1.0 MeV, both the growth rate and the upper cutoff frequency become smaller as l increases for the relativistic KT calculation because the significant relativistic effect reduces both the resonant anisotropy and the number of the hot electrons, which is in contrast to the relativistic and nonrelativistic Kappa distribution calculations because the less relativistic or non-relativistic effect enhances the resonant anisotropy as l increases. The above results can be applied to the whistler-mode wave instability in the outer radiation belts of the Earth, the Jovian inner magnetosphere and other astrophysical plasmas where relativistic electrons often exist. Kappa-type distribution (dpeaa)DE-He213 energetic electrons (dpeaa)DE-He213 wave-particle interaction (dpeaa)DE-He213 chorus wave instability (dpeaa)DE-He213 Yang, Chang verfasserin aut He, YiHua verfasserin aut Liu, Si verfasserin aut Zhou, QingHua verfasserin aut Xiao, FuLiang verfasserin aut Enthalten in Science in China Heidelberg : Springer, 1997 59(2016), 11 vom: 25. Aug., Seite 1739-1745 (DE-627)385614756 (DE-600)2142897-9 1862-281X nnns volume:59 year:2016 number:11 day:25 month:08 pages:1739-1745 https://dx.doi.org/10.1007/s11431-016-0161-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_152 GBV_ILN_161 GBV_ILN_171 GBV_ILN_187 GBV_ILN_224 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 50.00 ASE AR 59 2016 11 25 08 1739-1745 |
allfieldsGer |
10.1007/s11431-016-0161-2 doi (DE-627)SPR019287690 (SPR)s11431-016-0161-2-e DE-627 ger DE-627 rakwb eng 600 ASE 600 ASE 50.00 bkl Yang, QiWu verfasserin aut Magnetospheric chorus wave instability induced by relativistic Kappa-type distributions 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract We study the field-aligned propagating magnetospheric chorus wave instability using a fully relativistic wave growth formula, the previously developed relativistic Kappa-type (KT) distribution and the regular Kappa distribution of energetic electrons. We demonstrate that the peak growth rate using the nonrelativistic Kappa simulation is higher than that using either the relativistic KT or the Kappa simulation at/above 100 keV, because the significant relativistic effect yields a reduction in the relativistic anisotropy. The relativistic anisotropy Arel basically decreases as the thermal parameter $ θ^{2} $ increases, allowing the peak growth by relativistic KT or Kappa distribution to stay at the lower frequency region. The growth rates tend to increase with the loss-cone parameter l because the overall anisotropy increases. Moreover, at high energy ~1.0 MeV, both the growth rate and the upper cutoff frequency become smaller as l increases for the relativistic KT calculation because the significant relativistic effect reduces both the resonant anisotropy and the number of the hot electrons, which is in contrast to the relativistic and nonrelativistic Kappa distribution calculations because the less relativistic or non-relativistic effect enhances the resonant anisotropy as l increases. The above results can be applied to the whistler-mode wave instability in the outer radiation belts of the Earth, the Jovian inner magnetosphere and other astrophysical plasmas where relativistic electrons often exist. Kappa-type distribution (dpeaa)DE-He213 energetic electrons (dpeaa)DE-He213 wave-particle interaction (dpeaa)DE-He213 chorus wave instability (dpeaa)DE-He213 Yang, Chang verfasserin aut He, YiHua verfasserin aut Liu, Si verfasserin aut Zhou, QingHua verfasserin aut Xiao, FuLiang verfasserin aut Enthalten in Science in China Heidelberg : Springer, 1997 59(2016), 11 vom: 25. Aug., Seite 1739-1745 (DE-627)385614756 (DE-600)2142897-9 1862-281X nnns volume:59 year:2016 number:11 day:25 month:08 pages:1739-1745 https://dx.doi.org/10.1007/s11431-016-0161-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_152 GBV_ILN_161 GBV_ILN_171 GBV_ILN_187 GBV_ILN_224 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 50.00 ASE AR 59 2016 11 25 08 1739-1745 |
allfieldsSound |
10.1007/s11431-016-0161-2 doi (DE-627)SPR019287690 (SPR)s11431-016-0161-2-e DE-627 ger DE-627 rakwb eng 600 ASE 600 ASE 50.00 bkl Yang, QiWu verfasserin aut Magnetospheric chorus wave instability induced by relativistic Kappa-type distributions 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract We study the field-aligned propagating magnetospheric chorus wave instability using a fully relativistic wave growth formula, the previously developed relativistic Kappa-type (KT) distribution and the regular Kappa distribution of energetic electrons. We demonstrate that the peak growth rate using the nonrelativistic Kappa simulation is higher than that using either the relativistic KT or the Kappa simulation at/above 100 keV, because the significant relativistic effect yields a reduction in the relativistic anisotropy. The relativistic anisotropy Arel basically decreases as the thermal parameter $ θ^{2} $ increases, allowing the peak growth by relativistic KT or Kappa distribution to stay at the lower frequency region. The growth rates tend to increase with the loss-cone parameter l because the overall anisotropy increases. Moreover, at high energy ~1.0 MeV, both the growth rate and the upper cutoff frequency become smaller as l increases for the relativistic KT calculation because the significant relativistic effect reduces both the resonant anisotropy and the number of the hot electrons, which is in contrast to the relativistic and nonrelativistic Kappa distribution calculations because the less relativistic or non-relativistic effect enhances the resonant anisotropy as l increases. The above results can be applied to the whistler-mode wave instability in the outer radiation belts of the Earth, the Jovian inner magnetosphere and other astrophysical plasmas where relativistic electrons often exist. Kappa-type distribution (dpeaa)DE-He213 energetic electrons (dpeaa)DE-He213 wave-particle interaction (dpeaa)DE-He213 chorus wave instability (dpeaa)DE-He213 Yang, Chang verfasserin aut He, YiHua verfasserin aut Liu, Si verfasserin aut Zhou, QingHua verfasserin aut Xiao, FuLiang verfasserin aut Enthalten in Science in China Heidelberg : Springer, 1997 59(2016), 11 vom: 25. Aug., Seite 1739-1745 (DE-627)385614756 (DE-600)2142897-9 1862-281X nnns volume:59 year:2016 number:11 day:25 month:08 pages:1739-1745 https://dx.doi.org/10.1007/s11431-016-0161-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_152 GBV_ILN_161 GBV_ILN_171 GBV_ILN_187 GBV_ILN_224 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 50.00 ASE AR 59 2016 11 25 08 1739-1745 |
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Yang, QiWu @@aut@@ Yang, Chang @@aut@@ He, YiHua @@aut@@ Liu, Si @@aut@@ Zhou, QingHua @@aut@@ Xiao, FuLiang @@aut@@ |
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We demonstrate that the peak growth rate using the nonrelativistic Kappa simulation is higher than that using either the relativistic KT or the Kappa simulation at/above 100 keV, because the significant relativistic effect yields a reduction in the relativistic anisotropy. The relativistic anisotropy Arel basically decreases as the thermal parameter $ θ^{2} $ increases, allowing the peak growth by relativistic KT or Kappa distribution to stay at the lower frequency region. The growth rates tend to increase with the loss-cone parameter l because the overall anisotropy increases. Moreover, at high energy ~1.0 MeV, both the growth rate and the upper cutoff frequency become smaller as l increases for the relativistic KT calculation because the significant relativistic effect reduces both the resonant anisotropy and the number of the hot electrons, which is in contrast to the relativistic and nonrelativistic Kappa distribution calculations because the less relativistic or non-relativistic effect enhances the resonant anisotropy as l increases. 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magnetospheric chorus wave instability induced by relativistic kappa-type distributions |
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Magnetospheric chorus wave instability induced by relativistic Kappa-type distributions |
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Abstract We study the field-aligned propagating magnetospheric chorus wave instability using a fully relativistic wave growth formula, the previously developed relativistic Kappa-type (KT) distribution and the regular Kappa distribution of energetic electrons. We demonstrate that the peak growth rate using the nonrelativistic Kappa simulation is higher than that using either the relativistic KT or the Kappa simulation at/above 100 keV, because the significant relativistic effect yields a reduction in the relativistic anisotropy. The relativistic anisotropy Arel basically decreases as the thermal parameter $ θ^{2} $ increases, allowing the peak growth by relativistic KT or Kappa distribution to stay at the lower frequency region. The growth rates tend to increase with the loss-cone parameter l because the overall anisotropy increases. Moreover, at high energy ~1.0 MeV, both the growth rate and the upper cutoff frequency become smaller as l increases for the relativistic KT calculation because the significant relativistic effect reduces both the resonant anisotropy and the number of the hot electrons, which is in contrast to the relativistic and nonrelativistic Kappa distribution calculations because the less relativistic or non-relativistic effect enhances the resonant anisotropy as l increases. The above results can be applied to the whistler-mode wave instability in the outer radiation belts of the Earth, the Jovian inner magnetosphere and other astrophysical plasmas where relativistic electrons often exist. |
abstractGer |
Abstract We study the field-aligned propagating magnetospheric chorus wave instability using a fully relativistic wave growth formula, the previously developed relativistic Kappa-type (KT) distribution and the regular Kappa distribution of energetic electrons. We demonstrate that the peak growth rate using the nonrelativistic Kappa simulation is higher than that using either the relativistic KT or the Kappa simulation at/above 100 keV, because the significant relativistic effect yields a reduction in the relativistic anisotropy. The relativistic anisotropy Arel basically decreases as the thermal parameter $ θ^{2} $ increases, allowing the peak growth by relativistic KT or Kappa distribution to stay at the lower frequency region. The growth rates tend to increase with the loss-cone parameter l because the overall anisotropy increases. Moreover, at high energy ~1.0 MeV, both the growth rate and the upper cutoff frequency become smaller as l increases for the relativistic KT calculation because the significant relativistic effect reduces both the resonant anisotropy and the number of the hot electrons, which is in contrast to the relativistic and nonrelativistic Kappa distribution calculations because the less relativistic or non-relativistic effect enhances the resonant anisotropy as l increases. The above results can be applied to the whistler-mode wave instability in the outer radiation belts of the Earth, the Jovian inner magnetosphere and other astrophysical plasmas where relativistic electrons often exist. |
abstract_unstemmed |
Abstract We study the field-aligned propagating magnetospheric chorus wave instability using a fully relativistic wave growth formula, the previously developed relativistic Kappa-type (KT) distribution and the regular Kappa distribution of energetic electrons. We demonstrate that the peak growth rate using the nonrelativistic Kappa simulation is higher than that using either the relativistic KT or the Kappa simulation at/above 100 keV, because the significant relativistic effect yields a reduction in the relativistic anisotropy. The relativistic anisotropy Arel basically decreases as the thermal parameter $ θ^{2} $ increases, allowing the peak growth by relativistic KT or Kappa distribution to stay at the lower frequency region. The growth rates tend to increase with the loss-cone parameter l because the overall anisotropy increases. Moreover, at high energy ~1.0 MeV, both the growth rate and the upper cutoff frequency become smaller as l increases for the relativistic KT calculation because the significant relativistic effect reduces both the resonant anisotropy and the number of the hot electrons, which is in contrast to the relativistic and nonrelativistic Kappa distribution calculations because the less relativistic or non-relativistic effect enhances the resonant anisotropy as l increases. The above results can be applied to the whistler-mode wave instability in the outer radiation belts of the Earth, the Jovian inner magnetosphere and other astrophysical plasmas where relativistic electrons often exist. |
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Magnetospheric chorus wave instability induced by relativistic Kappa-type distributions |
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Moreover, at high energy ~1.0 MeV, both the growth rate and the upper cutoff frequency become smaller as l increases for the relativistic KT calculation because the significant relativistic effect reduces both the resonant anisotropy and the number of the hot electrons, which is in contrast to the relativistic and nonrelativistic Kappa distribution calculations because the less relativistic or non-relativistic effect enhances the resonant anisotropy as l increases. 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