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

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 ω{sub 0} = 2πc/λ, ω{sub st} = eσ/mc, and ω{sub p}, respectively. We normalize ω{sub st} and ω {sub p} by ω{sub 0} as a ≡ ω{sub st}/ω{sub 0} and b ≡ ω{sub p}/ω{sub 0}, 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 and Toptygin showed that the typical frequency is γ{sup 2}ω{sub p} and that the low frequency spectrum behaves as F {sub ω}∝ω{sup 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 peakmore » frequency turns out to be γ{sup 2}ω{sub st}, which is higher than the γ{sup 2}ω{sub p} 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'.« less