Abstract
A set of self-consistent equations of weak turbulence theory that describe the time evolution of the electron velocity distribution and of the spectra of Langmuir and ion sound waves is solved numerically, considering the presence of a core electron population and a ring-beam electron distribution. The results obtained show that the finite pitch angle of the beam relative to the direction of the ambient magnetic field leads to a spectrum of Langmuir waves which is more complex than the spectrum obtained in the case of beams with zero pitch angle, to an enlarged plateau in the beam region of the electron velocity distribution and to the generation of a prominent high-velocity population in the electron velocity distribution.
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References
Z.-J. Tong, C.-B. Wang, P.-J. Zhang, J. Liu, Phys. Plasmas 24, 052902 (2017). https://doi.org/10.1063/1.4982213
M. Horky, Y. Omura, O. Santolik, Phys. Plasmas 25, 042905 (2018). https://doi.org/10.1063/1.5025912
M. Horky, Y. Omura, Phys. Plasmas 26, 022904 (2019). https://doi.org/10.1063/1.5077094
X. Zhou, P.A. Munoz, J. Buechner, S. Liu, Astrophys. J. 891, 92 (2020). https://doi.org/10.3847/1538-4357/ab6a0d
C.S. Wu, J. Geophys. Res. 89, 8857 (1984). https://doi.org/10.1029/JA089iA10p08857
I.H. Cairns, S.A. Knock, P.A. Robinson, Z. Kuncic, in Advances in Space Environment Research, chapter Type II solar radio bursts: Theory and space weather implications, ed. by A.C.-L. Chian et al (Springer, Dordrecht, 2003)
I.H. Cairns, J. Geophys, Res. 93, 858 (1988). https://doi.org/10.1029/JAo93iA02p00858
M. Karlický, M. Vandas, Planet. Space Sci. 55, 2336 (2007). https://doi.org/10.1016/j.pss.2007.05.015
L.F. Ziebell, Astrophys. Space Sci. 366, 60 (2021). https://doi.org/10.1007/s10509-021-03966-y
P.H. Yoon, L.F. Ziebell, R. Gaelzer, J. Pavan, Phys. Plasmas 19, 102303, 9pp (2012). https://doi.org/10.1063/1.4757224
L.F. Ziebell, P.H. Yoon, R. Gaelzer, J. Pavan, Phys. Plasmas 21, 012306 (2014). https://doi.org/10.1063/1.4863453
L.F. Ziebell, P.H. Yoon, L.T. Petruzzellis, R. Gaelzer, J. Pavan, Astrophys. J. 806, 237 (2015). https://doi.org/10.1088/0004-637X/806/2/237
R. Gaelzer, L.F. Ziebell, A. Figueroa-Viñas, P.H. Yoon, C.-M. Ryu, Astrophys. J. 677, 676 (2008). https://doi.org/10.1086/527430
P.H. Yoon, J. Geophys. Res. 119, 7074 (2014). https://doi.org/10.1002/2014JA020353
Funding
LFZ acknowledges support from CNPq (Brazil), Grant No. 302708/2018-9, and partial support by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 001. PHY acknowledges NASA Grant No. NNH18ZDA001N-HSR and NSF Grants No. 1842643 and 2203321 to the University of Maryland.
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Ziebell, L.F., Yoon, P.H. Electron Acceleration by Quasilinear Processes in the Presence of a Ring-beam Electron Population. Braz J Phys 52, 87 (2022). https://doi.org/10.1007/s13538-022-01085-9
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DOI: https://doi.org/10.1007/s13538-022-01085-9