Influence of wave normal angle on gyroresonance between chorus waves and outer radiation belt electrons

Abstract In this paper, using a Gaussian distribution of wave normal angle X=tanθ, and considering contributions of harmonic resonances n up to ±5, we analyze the effect of normal angle on diffusion coefficients induced by gyroresonance between chorus waves and electrons with energies 0.1 and 1.0 Me...
Ausführliche Beschreibung

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Autor*in:	Ding, YuanHui [verfasserIn] He, ZhaoGuo [verfasserIn] Zhang, ZeLong [verfasserIn] Xiao, FuLiang [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2013

Schlagwörter:	diffusion coefficients wave normal angle resonant interaction

Übergeordnetes Werk:	Enthalten in: Science in China - Heidelberg : Springer, 1997, 56(2013), 11 vom: 26. Sept., Seite 2681-2689
Übergeordnetes Werk:	volume:56 ; year:2013 ; number:11 ; day:26 ; month:09 ; pages:2681-2689

Links:	Volltext

DOI / URN:	10.1007/s11431-013-5363-6

Katalog-ID:	SPR01927825X

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520			\|a Abstract In this paper, using a Gaussian distribution of wave normal angle X=tanθ, and considering contributions of harmonic resonances n up to ±5, we analyze the effect of normal angle on diffusion coefficients induced by gyroresonance between chorus waves and electrons with energies 0.1 and 1.0 MeV on the dayside and nightside at L=4.5. When pitch angle αe>10°, for 0.1 and 1.0 MeV electrons on the dayside and nightside, diffusion coefficients of five orders (−2,−1, 0, 1, 2) decrease with increasing normal angle peak, leading to the total diffusion coefficients decreasing with increasing peak. When αe<10°, for 1.0 MeV electrons on the dayside and 0.1 MeV electrons on the dayside and nightside, the positive order diffusion coefficients are generally smaller than the same negative order ones; in the meanwhile, diffusion coefficients of orders (−2, 1, 2) are very small, the dominant order n=−1 diffusion coefficients change very little, hence the total diffusion coefficients almost remain unchanged. However, for 1.0 MeV electrons on the nightside, diffusion coefficients of orders (−2, 1, 2) which are larger than those of the order (−1) resonance increase with increasing peak, hence the total diffusion coefficients increase with increasing peak. The current results show that the wave normal angle plays an important role in the quantitative analysis of gyroresonance between chorus waves and electrons in the outer radiation belt.
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allfields	10.1007/s11431-013-5363-6 doi (DE-627)SPR01927825X (SPR)s11431-013-5363-6-e DE-627 ger DE-627 rakwb eng 600 ASE 600 ASE 50.00 bkl Ding, YuanHui verfasserin aut Influence of wave normal angle on gyroresonance between chorus waves and outer radiation belt electrons 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this paper, using a Gaussian distribution of wave normal angle X=tanθ, and considering contributions of harmonic resonances n up to ±5, we analyze the effect of normal angle on diffusion coefficients induced by gyroresonance between chorus waves and electrons with energies 0.1 and 1.0 MeV on the dayside and nightside at L=4.5. When pitch angle αe>10°, for 0.1 and 1.0 MeV electrons on the dayside and nightside, diffusion coefficients of five orders (−2,−1, 0, 1, 2) decrease with increasing normal angle peak, leading to the total diffusion coefficients decreasing with increasing peak. When αe<10°, for 1.0 MeV electrons on the dayside and 0.1 MeV electrons on the dayside and nightside, the positive order diffusion coefficients are generally smaller than the same negative order ones; in the meanwhile, diffusion coefficients of orders (−2, 1, 2) are very small, the dominant order n=−1 diffusion coefficients change very little, hence the total diffusion coefficients almost remain unchanged. However, for 1.0 MeV electrons on the nightside, diffusion coefficients of orders (−2, 1, 2) which are larger than those of the order (−1) resonance increase with increasing peak, hence the total diffusion coefficients increase with increasing peak. The current results show that the wave normal angle plays an important role in the quantitative analysis of gyroresonance between chorus waves and electrons in the outer radiation belt. diffusion coefficients (dpeaa)DE-He213 wave normal angle (dpeaa)DE-He213 resonant interaction (dpeaa)DE-He213 He, ZhaoGuo verfasserin aut Zhang, ZeLong verfasserin aut Xiao, FuLiang verfasserin aut Enthalten in Science in China Heidelberg : Springer, 1997 56(2013), 11 vom: 26. Sept., Seite 2681-2689 (DE-627)385614756 (DE-600)2142897-9 1862-281X nnns volume:56 year:2013 number:11 day:26 month:09 pages:2681-2689 https://dx.doi.org/10.1007/s11431-013-5363-6 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 56 2013 11 26 09 2681-2689
spelling	10.1007/s11431-013-5363-6 doi (DE-627)SPR01927825X (SPR)s11431-013-5363-6-e DE-627 ger DE-627 rakwb eng 600 ASE 600 ASE 50.00 bkl Ding, YuanHui verfasserin aut Influence of wave normal angle on gyroresonance between chorus waves and outer radiation belt electrons 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this paper, using a Gaussian distribution of wave normal angle X=tanθ, and considering contributions of harmonic resonances n up to ±5, we analyze the effect of normal angle on diffusion coefficients induced by gyroresonance between chorus waves and electrons with energies 0.1 and 1.0 MeV on the dayside and nightside at L=4.5. When pitch angle αe>10°, for 0.1 and 1.0 MeV electrons on the dayside and nightside, diffusion coefficients of five orders (−2,−1, 0, 1, 2) decrease with increasing normal angle peak, leading to the total diffusion coefficients decreasing with increasing peak. When αe<10°, for 1.0 MeV electrons on the dayside and 0.1 MeV electrons on the dayside and nightside, the positive order diffusion coefficients are generally smaller than the same negative order ones; in the meanwhile, diffusion coefficients of orders (−2, 1, 2) are very small, the dominant order n=−1 diffusion coefficients change very little, hence the total diffusion coefficients almost remain unchanged. However, for 1.0 MeV electrons on the nightside, diffusion coefficients of orders (−2, 1, 2) which are larger than those of the order (−1) resonance increase with increasing peak, hence the total diffusion coefficients increase with increasing peak. The current results show that the wave normal angle plays an important role in the quantitative analysis of gyroresonance between chorus waves and electrons in the outer radiation belt. diffusion coefficients (dpeaa)DE-He213 wave normal angle (dpeaa)DE-He213 resonant interaction (dpeaa)DE-He213 He, ZhaoGuo verfasserin aut Zhang, ZeLong verfasserin aut Xiao, FuLiang verfasserin aut Enthalten in Science in China Heidelberg : Springer, 1997 56(2013), 11 vom: 26. Sept., Seite 2681-2689 (DE-627)385614756 (DE-600)2142897-9 1862-281X nnns volume:56 year:2013 number:11 day:26 month:09 pages:2681-2689 https://dx.doi.org/10.1007/s11431-013-5363-6 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 56 2013 11 26 09 2681-2689
allfields_unstemmed	10.1007/s11431-013-5363-6 doi (DE-627)SPR01927825X (SPR)s11431-013-5363-6-e DE-627 ger DE-627 rakwb eng 600 ASE 600 ASE 50.00 bkl Ding, YuanHui verfasserin aut Influence of wave normal angle on gyroresonance between chorus waves and outer radiation belt electrons 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this paper, using a Gaussian distribution of wave normal angle X=tanθ, and considering contributions of harmonic resonances n up to ±5, we analyze the effect of normal angle on diffusion coefficients induced by gyroresonance between chorus waves and electrons with energies 0.1 and 1.0 MeV on the dayside and nightside at L=4.5. When pitch angle αe>10°, for 0.1 and 1.0 MeV electrons on the dayside and nightside, diffusion coefficients of five orders (−2,−1, 0, 1, 2) decrease with increasing normal angle peak, leading to the total diffusion coefficients decreasing with increasing peak. When αe<10°, for 1.0 MeV electrons on the dayside and 0.1 MeV electrons on the dayside and nightside, the positive order diffusion coefficients are generally smaller than the same negative order ones; in the meanwhile, diffusion coefficients of orders (−2, 1, 2) are very small, the dominant order n=−1 diffusion coefficients change very little, hence the total diffusion coefficients almost remain unchanged. However, for 1.0 MeV electrons on the nightside, diffusion coefficients of orders (−2, 1, 2) which are larger than those of the order (−1) resonance increase with increasing peak, hence the total diffusion coefficients increase with increasing peak. The current results show that the wave normal angle plays an important role in the quantitative analysis of gyroresonance between chorus waves and electrons in the outer radiation belt. diffusion coefficients (dpeaa)DE-He213 wave normal angle (dpeaa)DE-He213 resonant interaction (dpeaa)DE-He213 He, ZhaoGuo verfasserin aut Zhang, ZeLong verfasserin aut Xiao, FuLiang verfasserin aut Enthalten in Science in China Heidelberg : Springer, 1997 56(2013), 11 vom: 26. Sept., Seite 2681-2689 (DE-627)385614756 (DE-600)2142897-9 1862-281X nnns volume:56 year:2013 number:11 day:26 month:09 pages:2681-2689 https://dx.doi.org/10.1007/s11431-013-5363-6 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 56 2013 11 26 09 2681-2689
allfieldsGer	10.1007/s11431-013-5363-6 doi (DE-627)SPR01927825X (SPR)s11431-013-5363-6-e DE-627 ger DE-627 rakwb eng 600 ASE 600 ASE 50.00 bkl Ding, YuanHui verfasserin aut Influence of wave normal angle on gyroresonance between chorus waves and outer radiation belt electrons 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this paper, using a Gaussian distribution of wave normal angle X=tanθ, and considering contributions of harmonic resonances n up to ±5, we analyze the effect of normal angle on diffusion coefficients induced by gyroresonance between chorus waves and electrons with energies 0.1 and 1.0 MeV on the dayside and nightside at L=4.5. When pitch angle αe>10°, for 0.1 and 1.0 MeV electrons on the dayside and nightside, diffusion coefficients of five orders (−2,−1, 0, 1, 2) decrease with increasing normal angle peak, leading to the total diffusion coefficients decreasing with increasing peak. When αe<10°, for 1.0 MeV electrons on the dayside and 0.1 MeV electrons on the dayside and nightside, the positive order diffusion coefficients are generally smaller than the same negative order ones; in the meanwhile, diffusion coefficients of orders (−2, 1, 2) are very small, the dominant order n=−1 diffusion coefficients change very little, hence the total diffusion coefficients almost remain unchanged. However, for 1.0 MeV electrons on the nightside, diffusion coefficients of orders (−2, 1, 2) which are larger than those of the order (−1) resonance increase with increasing peak, hence the total diffusion coefficients increase with increasing peak. The current results show that the wave normal angle plays an important role in the quantitative analysis of gyroresonance between chorus waves and electrons in the outer radiation belt. diffusion coefficients (dpeaa)DE-He213 wave normal angle (dpeaa)DE-He213 resonant interaction (dpeaa)DE-He213 He, ZhaoGuo verfasserin aut Zhang, ZeLong verfasserin aut Xiao, FuLiang verfasserin aut Enthalten in Science in China Heidelberg : Springer, 1997 56(2013), 11 vom: 26. Sept., Seite 2681-2689 (DE-627)385614756 (DE-600)2142897-9 1862-281X nnns volume:56 year:2013 number:11 day:26 month:09 pages:2681-2689 https://dx.doi.org/10.1007/s11431-013-5363-6 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 56 2013 11 26 09 2681-2689
allfieldsSound	10.1007/s11431-013-5363-6 doi (DE-627)SPR01927825X (SPR)s11431-013-5363-6-e DE-627 ger DE-627 rakwb eng 600 ASE 600 ASE 50.00 bkl Ding, YuanHui verfasserin aut Influence of wave normal angle on gyroresonance between chorus waves and outer radiation belt electrons 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this paper, using a Gaussian distribution of wave normal angle X=tanθ, and considering contributions of harmonic resonances n up to ±5, we analyze the effect of normal angle on diffusion coefficients induced by gyroresonance between chorus waves and electrons with energies 0.1 and 1.0 MeV on the dayside and nightside at L=4.5. When pitch angle αe>10°, for 0.1 and 1.0 MeV electrons on the dayside and nightside, diffusion coefficients of five orders (−2,−1, 0, 1, 2) decrease with increasing normal angle peak, leading to the total diffusion coefficients decreasing with increasing peak. When αe<10°, for 1.0 MeV electrons on the dayside and 0.1 MeV electrons on the dayside and nightside, the positive order diffusion coefficients are generally smaller than the same negative order ones; in the meanwhile, diffusion coefficients of orders (−2, 1, 2) are very small, the dominant order n=−1 diffusion coefficients change very little, hence the total diffusion coefficients almost remain unchanged. However, for 1.0 MeV electrons on the nightside, diffusion coefficients of orders (−2, 1, 2) which are larger than those of the order (−1) resonance increase with increasing peak, hence the total diffusion coefficients increase with increasing peak. The current results show that the wave normal angle plays an important role in the quantitative analysis of gyroresonance between chorus waves and electrons in the outer radiation belt. diffusion coefficients (dpeaa)DE-He213 wave normal angle (dpeaa)DE-He213 resonant interaction (dpeaa)DE-He213 He, ZhaoGuo verfasserin aut Zhang, ZeLong verfasserin aut Xiao, FuLiang verfasserin aut Enthalten in Science in China Heidelberg : Springer, 1997 56(2013), 11 vom: 26. Sept., Seite 2681-2689 (DE-627)385614756 (DE-600)2142897-9 1862-281X nnns volume:56 year:2013 number:11 day:26 month:09 pages:2681-2689 https://dx.doi.org/10.1007/s11431-013-5363-6 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 56 2013 11 26 09 2681-2689
language	English
source	Enthalten in Science in China 56(2013), 11 vom: 26. Sept., Seite 2681-2689 volume:56 year:2013 number:11 day:26 month:09 pages:2681-2689
sourceStr	Enthalten in Science in China 56(2013), 11 vom: 26. Sept., Seite 2681-2689 volume:56 year:2013 number:11 day:26 month:09 pages:2681-2689
format_phy_str_mv	Article
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topic_facet	diffusion coefficients wave normal angle resonant interaction
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container_title	Science in China
authorswithroles_txt_mv	Ding, YuanHui @@aut@@ He, ZhaoGuo @@aut@@ Zhang, ZeLong @@aut@@ Xiao, FuLiang @@aut@@
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author	Ding, YuanHui
spellingShingle	Ding, YuanHui ddc 600 bkl 50.00 misc diffusion coefficients misc wave normal angle misc resonant interaction Influence of wave normal angle on gyroresonance between chorus waves and outer radiation belt electrons
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topic_title	600 ASE 50.00 bkl Influence of wave normal angle on gyroresonance between chorus waves and outer radiation belt electrons diffusion coefficients (dpeaa)DE-He213 wave normal angle (dpeaa)DE-He213 resonant interaction (dpeaa)DE-He213
topic	ddc 600 bkl 50.00 misc diffusion coefficients misc wave normal angle misc resonant interaction
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title	Influence of wave normal angle on gyroresonance between chorus waves and outer radiation belt electrons
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title_full	Influence of wave normal angle on gyroresonance between chorus waves and outer radiation belt electrons
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author_browse	Ding, YuanHui He, ZhaoGuo Zhang, ZeLong Xiao, FuLiang
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title_sort	influence of wave normal angle on gyroresonance between chorus waves and outer radiation belt electrons
title_auth	Influence of wave normal angle on gyroresonance between chorus waves and outer radiation belt electrons
abstract	Abstract In this paper, using a Gaussian distribution of wave normal angle X=tanθ, and considering contributions of harmonic resonances n up to ±5, we analyze the effect of normal angle on diffusion coefficients induced by gyroresonance between chorus waves and electrons with energies 0.1 and 1.0 MeV on the dayside and nightside at L=4.5. When pitch angle αe>10°, for 0.1 and 1.0 MeV electrons on the dayside and nightside, diffusion coefficients of five orders (−2,−1, 0, 1, 2) decrease with increasing normal angle peak, leading to the total diffusion coefficients decreasing with increasing peak. When αe<10°, for 1.0 MeV electrons on the dayside and 0.1 MeV electrons on the dayside and nightside, the positive order diffusion coefficients are generally smaller than the same negative order ones; in the meanwhile, diffusion coefficients of orders (−2, 1, 2) are very small, the dominant order n=−1 diffusion coefficients change very little, hence the total diffusion coefficients almost remain unchanged. However, for 1.0 MeV electrons on the nightside, diffusion coefficients of orders (−2, 1, 2) which are larger than those of the order (−1) resonance increase with increasing peak, hence the total diffusion coefficients increase with increasing peak. The current results show that the wave normal angle plays an important role in the quantitative analysis of gyroresonance between chorus waves and electrons in the outer radiation belt.
abstractGer	Abstract In this paper, using a Gaussian distribution of wave normal angle X=tanθ, and considering contributions of harmonic resonances n up to ±5, we analyze the effect of normal angle on diffusion coefficients induced by gyroresonance between chorus waves and electrons with energies 0.1 and 1.0 MeV on the dayside and nightside at L=4.5. When pitch angle αe>10°, for 0.1 and 1.0 MeV electrons on the dayside and nightside, diffusion coefficients of five orders (−2,−1, 0, 1, 2) decrease with increasing normal angle peak, leading to the total diffusion coefficients decreasing with increasing peak. When αe<10°, for 1.0 MeV electrons on the dayside and 0.1 MeV electrons on the dayside and nightside, the positive order diffusion coefficients are generally smaller than the same negative order ones; in the meanwhile, diffusion coefficients of orders (−2, 1, 2) are very small, the dominant order n=−1 diffusion coefficients change very little, hence the total diffusion coefficients almost remain unchanged. However, for 1.0 MeV electrons on the nightside, diffusion coefficients of orders (−2, 1, 2) which are larger than those of the order (−1) resonance increase with increasing peak, hence the total diffusion coefficients increase with increasing peak. The current results show that the wave normal angle plays an important role in the quantitative analysis of gyroresonance between chorus waves and electrons in the outer radiation belt.
abstract_unstemmed	Abstract In this paper, using a Gaussian distribution of wave normal angle X=tanθ, and considering contributions of harmonic resonances n up to ±5, we analyze the effect of normal angle on diffusion coefficients induced by gyroresonance between chorus waves and electrons with energies 0.1 and 1.0 MeV on the dayside and nightside at L=4.5. When pitch angle αe>10°, for 0.1 and 1.0 MeV electrons on the dayside and nightside, diffusion coefficients of five orders (−2,−1, 0, 1, 2) decrease with increasing normal angle peak, leading to the total diffusion coefficients decreasing with increasing peak. When αe<10°, for 1.0 MeV electrons on the dayside and 0.1 MeV electrons on the dayside and nightside, the positive order diffusion coefficients are generally smaller than the same negative order ones; in the meanwhile, diffusion coefficients of orders (−2, 1, 2) are very small, the dominant order n=−1 diffusion coefficients change very little, hence the total diffusion coefficients almost remain unchanged. However, for 1.0 MeV electrons on the nightside, diffusion coefficients of orders (−2, 1, 2) which are larger than those of the order (−1) resonance increase with increasing peak, hence the total diffusion coefficients increase with increasing peak. The current results show that the wave normal angle plays an important role in the quantitative analysis of gyroresonance between chorus waves and electrons in the outer radiation belt.
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title_short	Influence of wave normal angle on gyroresonance between chorus waves and outer radiation belt electrons
url	https://dx.doi.org/10.1007/s11431-013-5363-6
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up_date	2024-07-04T00:56:07.891Z
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