  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.
