Excitation of Langmuir waves by the lower energy cutoff behavior of power-law electrons

TL;DR

This study investigates how power-law electrons with a lower energy cutoff can effectively excite Langmuir waves, revealing dependencies of growth rate and wave number on electron distribution parameters, which enhances understanding of plasma emissions.

Contribution

The paper demonstrates that power-law electrons with a steepness cutoff efficiently excite Langmuir waves, highlighting the influence of cutoff behavior on wave growth and characteristics.

Findings

Growth rate increases with steepness index ($\

decreases with power-law index ($\

Wave number decreases with characteristic velocity ($v_{c}$) and increases with thermal velocity ($v_T$).

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 ($\delta$) and decreases with the power-law index ($\alpha$). The wave number of the fastest growing LWs ($k\lambda_D$), 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.