General properties of the radiation spectra from relativistic electrons moving in langmuir turbulence

Abstract

Using a numerical method, we examine the radiation spectra from relativistic electrons moving in Langmuir turbulence, which are expected to exist in high energy astrophysical objects. The spectral shape is characterized by the spatial scale λ, field strength σ, and frequency of the Langmuir waves, and in terms of frequency they are represented by ω0 = 2πc/λ, ωst = eσ/mc, and ωp, respectively. We normalize ωst and ωp by ω0 as a ≡ ωst/ ω0 and b ≡ ωp/ω0, and examine the spectral shape in the a-b plane. An earlier study based on the diffusive radiation in Langmuir turbulence (DRL) theory by Fleishman & Toptygin showed that the typical frequency is γ2ωp and that the low frequency spectrum behaves as F ω∝ω 1 for b > 1 irrespective of a. Here, we adopt the first principle numerical approach to obtain the radiation spectra in more detail. We generate Langmuir turbulence by superposing Fourier modes, injecting monoenergetic electrons, solving the equation of motion, and calculating the radiation spectra using a Lienard-Wiechert potential. We find different features from the DRL theory for a > b > 1. The peak frequency turns out to be γ2ωst, which is higher than the γ2ωp predicted by the DRL theory, and the spectral index of the low frequency region is not 1 but 1/3. This is because the typical deflection angle of electrons is larger than the angle of the beaming cone ̃1/γ. We call the radiation for this case "wiggler radiation in Langmuir turbulence." © 2014. The American Astronomical Society. All rights reserved.