Swift observations of Mrk 421. I. 2005-2008

The best fits of the 0.3-10keV spectra were mainly obtained using the log-parabolic model, yielding low spectral curvatures expected in the case of the efficient stochastic acceleration of particles. During strong X-ray flares, the position of the synchrotron spectral energy distribution peak E_p_ was beyond 8keV for 41 spectra, while it sometimes was situated at the UV frequencies in quiescent states.

The photon index at 1 keV exhibited a broad range, and the values a<1.70 were observed during the strong flares, hinting at the possible presence of a jet hadronic component. The spectral parameters were correlated in some periods, expected in the framework of the first- and second-order Fermi accelerations of X-ray emitting particles, as well as in the case of turbulence spectrum. The 0.3-10keV flux and spectral parameters sometimes showed very fast variability down to the fluctuations by 6-20% in 180-960s, possibly related to the small-scale turbulent areas containing strongest magnetic fields.