Astrophysical chaotic gun effect

We propose a kinetic equation for a special kind of acceleration: chaotic gun effect. Then we infer a distribution function which can depict the instability condition. With this distribution function we derive the power spectrum of the synchrotron emission and we prove the power law form of the power spectrum. We show that the spectral index of the emission spectrum is related to the spectral index of the number of the charged particles in the beam. Our numeric simulations show that the spectrum has a break at a frequency threshold where the chaotic acceleration becomes efficient. Assuming this threshold to the set on of the efficient chaotic gun effect we estimate the magnetic strength .Our paper advocates an electromagnetic process able to accelerate charged particles to high energies starting from low energies. Assuming the high-energy particles spectra of Mkn 501 to be produced by the synchrotron emission during chaotic gun effect we estimate some parameters of the source.