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 thisdistribution function we derive the power spectrum of the synchrotron emission and we provethe power law form of the power spectrum. We show that the spectral index of the emissionspectrum 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 wherethe chaotic acceleration becomes efficient. Assuming this threshold to the set on of the efficienchaotic gun effect we estimate the magnetic strength .Our paper advocates an electromagneticprocess able to accelerate charged particles to high energies starting from low energies. Assumingthe high-energy particles spectra of Mkn 501 to be produced by the synchrotron emission duringchaotic gun effect we estimate some parameters of the source.
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