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

We examine the radiation spectra from relativistic electrons moving in a Langmuir turbulence expected to exist in high energy astrophysical objects by using numerical method. The spectral shape is characterized by the spatial scale λ, field strength σ, and frequency of the Langmuir waves, and in term of frequency they are represented by ω_0 = 2πc/λ, ω_st = eσ/mc, and ω_p, respectively. We normalize ω_st and ω_p by ω_0 as \a \equiv ω_st/ω_0 and \b \equivω_p/ω_0, and examine the spectral shape in the a-b plane. An earlier study based on Diffusive Radiation in Langmuir turbulence (DRL) theory by Fleishman and Toptygin showed that the typical frequency is γ^2ω_p and that the low frequency spectrum behaves as F_ω pronto 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,inject monoenergetic electrons, solve the equation of motion, and calculate the radiation spectra using Lienard-Wiechert potential. We find different features from the DRL theory for a>b>1. The peak frequency turns out to be γ^2ω_st which is higher than γ^2ω_p predicted in the DRL theory, and the spectral index of low frequency region is not 1 but 1/3. It is because the typical deflection angle of electrons is larger than the angle of the beaming cone sim 1/γ. We call the radiation for this case "Wiggler Radiation in Langmuir turbulence" (WRL).