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 \lambda , field strength \sigma , and frequency of the Langmuir waves , and in term of frequency they are represented by \omega _ { 0 } = 2 \pi c / \lambda , \omega _ { \mathrm { st } } = e \sigma / mc , and \omega _ { \mathrm { p } } , respectively .
We normalize \omega _ { \mathrm { st } } and \omega _ { p } by \omega _ { 0 } as a \equiv \omega _ { \mathrm { st } } / \omega _ { 0 } and b \equiv \omega _ { \mathrm { p } } / \omega _ { 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 & Toptygin showed that the typical frequency is \gamma ^ { 2 } \omega _ { \mathrm { p } } and that the low frequency spectrum behaves as F _ { \omega } \propto \omega ^ { 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 \gamma ^ { 2 } \omega _ { \mathrm { st } } which is higher than \gamma ^ { 2 } \omega _ { \mathrm { 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 / \gamma .
We call the radiation for this case ” Wiggler Radiation in Langmuir turbulence ” ( WRL ) .