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In this paper, the interaction between the low energy proton ring-beam with an initial velocity perpendicular to the background magnetic field, and the background plasma is studied by one-dimensional (1D) hybrid simulations. In the initial stage, the excited plasma waves experience a fast growth exponentially, which is consistent with the linear theory. After that, three non-linear stages, including the saturation process, the fast damping process and the relatively stable stage, follow in sequence. In the linear stage, the mode-resonance damps with the pitch angle scattering of the injected protons, and the plasma oscillation reaches the peak quickly. The continuing pitch angle scattering makes the velocity distributions of the proton beam and the background ions uniformly distributed. Meanwhile, the initially excited right-handed resonant instability decreased, with only the Alfven waves left in the stable stage. The results also show that the effective heating of the background plasma is achieved after the linear stage, instead from the very beginning of the injection of the protons. This demonstrates that the excited plasma waves lead to the energy transferring from the injected proton beams to the background plasma.
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Keywords:
- low-energy proton ring-beam /
- plasma fluctuation /
- plasma heating /
- one-dimensional hybrid simulation
[1] Wu C S, Davidson R C 1972 J. Geophys. Res. 77 5399
[2] Akimoto k, Winske D, Gary S P, Thomsen M F 1993 J. Geophys. Res. 98 1419
[3] Winske D, Gary S P 1986 J. Geophys. Res. 91 6825
[4] Winske D, Wu C S, Li Y Y, Zhou G C 1984 J. Geophys. Res. 89 7327
[5] Winske D, Wu C S, Li Y Y, Mou Z Z, Guo S Y 1985 J. Geophys. Res. 90 2713
[6] Blum P W, Fahr H J 1970 Astro. Astrophys. 4 280
[7] Holzer T E 1972 Astro. Astrophys. 77 5407
[8] Wu C S, Winske D, Gaffey J D 1986 Geophy. Res. Lett. 13 865
[9] Gary S P, Hinata S, Madland C D, Winske D 1986 Geophy. Res. Lett. 13 1364
[10] Zhou G C, Li Y, Cao J B, Wang X Y 1998 Chin. Phys. Lett. 15 895
[11] Wang X Y, Wu C S, Wang S, Chao J K, Lin Y, Yoon P H 2001 Astrophys. J. 547 1159
[12] Eastman T E, Anderson R R, Frank L A, Parks G K 1981 J. Geophys. Res. 86 4379
[13] Gurgiolo C, Parks G K, Mauk B H, Lin C S, Anderson K A, Lin R P, Reme H 1981 J. Geophys. Res. 86 4415
[14] Cairns I H 1990 J. Geophys. Res. 95 15167
[15] Coates A J, Johnstone A D, Wilken B, Neubauer F M 1993 J. Geophys. Res. 98 20985
[16] Hardy D A, Hastings D E, Rivas D R, Burke W J, Cooke D L, Gentile L C 1996 J. Geophys. Res. 101 19629
[17] McComas D J, Dayeh M A, Allegrini F, Bzowski M 2012 Astrophys. J. Suppl. S 203 1
[18] McComas D J, Lewis W S, Schwadron N A 2014 Rev. Geophys. 52 118
[19] McComas D J, Allegrini F, Bochsler P, Bzowski M, Christian E R 2009 Science 326 959
[20] Fuselier S A, Allegrini F, Funsten H O, Ghielmetti A G 2009 Science 326 962
[21] Heerikhuisen J, Pogorelov N V, Zank G P 2010 Astrophys. J. Lett. 710 L172
[22] Florinski V, Zank G P, Heerikhuisen J, Hu Q, Khazanov I 2010 Astrophys. J. 719 1097
[23] Liu K J, Eberhard M, Peter G S, Dan W 2012 J. Geophys. Res. A 117 10102
[24] Cao J B, Wang X Y 1998 Chin. Phys. Lett. 15 38
[25] Gary S P, Madland C D 1988 J. Geophys. Res. 93 235
[26] Cao J B, Zhou G C, Wang X Y 1998 Geophy. Res. Lett. 25 9
[27] Cao J B, Zhou G C, Wang X Y, Wu J S 1999 Chin. J. Space Sci. 19 28 (in Chinese) [曹晋滨, 周国成, 汪学毅, 吴京生 1999 空间科学学报 19 28]
[28] Li Y, Yoon P H, Wu C S, Weatherwax A T 1997 Phys. Plasmas 4 4103
[29] Wang X Y, Lin Y 2003 Phys. Plasmas 10 3528
[30] Gary S P, Christian D M, Omidi N, Winske D 1988 J. Geophys. Res. 93 9584
[31] Fu Z F, Hu Y Q 1995 Numerical Simulation of Space Plasma (Hefei: Anhui Science and Technology Publishing House) p527 (in Chinese) [傅竹风,胡友秋 1995 空间等离子体数值模拟 (合肥: 安徽科技出版社) 第527页]
[32] Swift D W, Lee L C 1983 J. Geophys. Res. 88 111
[33] Lin Y, Wang X Y 2005 J. Geophys. Res. A 110 12216
[34] Pang Y, Lin Y, Deng X H, Wang X Y, Tan B 2010 J. Geophys. Res. 115 A0320
[35] Tan B, Lin Y, Perez J D, Wang X Y 2012 J. Geophys. Res. A 117 03217
[36] Gary S P, Smith C W, Lee M A, Goldstein M L 1984 Phys. Fluids 27 1852
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[1] Wu C S, Davidson R C 1972 J. Geophys. Res. 77 5399
[2] Akimoto k, Winske D, Gary S P, Thomsen M F 1993 J. Geophys. Res. 98 1419
[3] Winske D, Gary S P 1986 J. Geophys. Res. 91 6825
[4] Winske D, Wu C S, Li Y Y, Zhou G C 1984 J. Geophys. Res. 89 7327
[5] Winske D, Wu C S, Li Y Y, Mou Z Z, Guo S Y 1985 J. Geophys. Res. 90 2713
[6] Blum P W, Fahr H J 1970 Astro. Astrophys. 4 280
[7] Holzer T E 1972 Astro. Astrophys. 77 5407
[8] Wu C S, Winske D, Gaffey J D 1986 Geophy. Res. Lett. 13 865
[9] Gary S P, Hinata S, Madland C D, Winske D 1986 Geophy. Res. Lett. 13 1364
[10] Zhou G C, Li Y, Cao J B, Wang X Y 1998 Chin. Phys. Lett. 15 895
[11] Wang X Y, Wu C S, Wang S, Chao J K, Lin Y, Yoon P H 2001 Astrophys. J. 547 1159
[12] Eastman T E, Anderson R R, Frank L A, Parks G K 1981 J. Geophys. Res. 86 4379
[13] Gurgiolo C, Parks G K, Mauk B H, Lin C S, Anderson K A, Lin R P, Reme H 1981 J. Geophys. Res. 86 4415
[14] Cairns I H 1990 J. Geophys. Res. 95 15167
[15] Coates A J, Johnstone A D, Wilken B, Neubauer F M 1993 J. Geophys. Res. 98 20985
[16] Hardy D A, Hastings D E, Rivas D R, Burke W J, Cooke D L, Gentile L C 1996 J. Geophys. Res. 101 19629
[17] McComas D J, Dayeh M A, Allegrini F, Bzowski M 2012 Astrophys. J. Suppl. S 203 1
[18] McComas D J, Lewis W S, Schwadron N A 2014 Rev. Geophys. 52 118
[19] McComas D J, Allegrini F, Bochsler P, Bzowski M, Christian E R 2009 Science 326 959
[20] Fuselier S A, Allegrini F, Funsten H O, Ghielmetti A G 2009 Science 326 962
[21] Heerikhuisen J, Pogorelov N V, Zank G P 2010 Astrophys. J. Lett. 710 L172
[22] Florinski V, Zank G P, Heerikhuisen J, Hu Q, Khazanov I 2010 Astrophys. J. 719 1097
[23] Liu K J, Eberhard M, Peter G S, Dan W 2012 J. Geophys. Res. A 117 10102
[24] Cao J B, Wang X Y 1998 Chin. Phys. Lett. 15 38
[25] Gary S P, Madland C D 1988 J. Geophys. Res. 93 235
[26] Cao J B, Zhou G C, Wang X Y 1998 Geophy. Res. Lett. 25 9
[27] Cao J B, Zhou G C, Wang X Y, Wu J S 1999 Chin. J. Space Sci. 19 28 (in Chinese) [曹晋滨, 周国成, 汪学毅, 吴京生 1999 空间科学学报 19 28]
[28] Li Y, Yoon P H, Wu C S, Weatherwax A T 1997 Phys. Plasmas 4 4103
[29] Wang X Y, Lin Y 2003 Phys. Plasmas 10 3528
[30] Gary S P, Christian D M, Omidi N, Winske D 1988 J. Geophys. Res. 93 9584
[31] Fu Z F, Hu Y Q 1995 Numerical Simulation of Space Plasma (Hefei: Anhui Science and Technology Publishing House) p527 (in Chinese) [傅竹风,胡友秋 1995 空间等离子体数值模拟 (合肥: 安徽科技出版社) 第527页]
[32] Swift D W, Lee L C 1983 J. Geophys. Res. 88 111
[33] Lin Y, Wang X Y 2005 J. Geophys. Res. A 110 12216
[34] Pang Y, Lin Y, Deng X H, Wang X Y, Tan B 2010 J. Geophys. Res. 115 A0320
[35] Tan B, Lin Y, Perez J D, Wang X Y 2012 J. Geophys. Res. A 117 03217
[36] Gary S P, Smith C W, Lee M A, Goldstein M L 1984 Phys. Fluids 27 1852
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