Abstract
Langmuir waves (LWs), which are believed to play a crucial role in the plasma emission of solar radio bursts, can be excited by streaming instability of energetic electron beams. However, solar hard X-ray observations imply that the energetic flare electrons usually have a power-law energy distribution with a lower energy cutoff. In this paper, we investigate LWs driven by the power-law electrons. The results show that power-law electrons with the steepness cutoff behavior can excite LWs effectively because of the population inversion distribution below the cutoff energy (E c ). The growth rate of LWs increases with the steepness index (δ) and decreases with the power-law index (α). The wave number of the fastest growing LWs (kλ D ), decreases with the characteristic velocity of the power-law electrons (\(v_{c}=\sqrt{2E_{c}/m_{e}}\)) and increases with the thermal velocity of ambient electrons (v T ). This can be helpful for us to understand better the physics of LWs and the dynamics of energetic electron beams in space and astrophysical plasmas.
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Acknowledgements
This work is supported by the National Natural Science Foundation of China (Grant Nos. 11303082, 11373070, 41074107, 41304136, 11103044), by West Light Foundation of CAS (No. XBBS201223), and by Key Laboratory of Solar Activity at National Astronomical Observatories, CAS.
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Tang, J., Wu, D., Zhao, G. et al. Excitation of Langmuir waves by the lower energy cutoff behavior of power-law electrons. Astrophys Space Sci 353, 131–135 (2014). https://doi.org/10.1007/s10509-014-1998-4
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DOI: https://doi.org/10.1007/s10509-014-1998-4