Unveiling the X-ray/TeV engine in Mkn 421

Aims. Our goal was to find important clues concerning particle acceleration in relativistic jets through the analysis of multi-wavelength observations of TeV blazars. Methods. Simultaneous observations of Mkn 421 were taken in very high energy gamma-rays (> 200 GeV, CAT experiment), X-rays (RXTE), and optical (KVA). Multi-day RXTE observations are also presented, allowing for detailed modelling of the spectral variability. Results. Short timescale (approximate to 30 mn) variations in VHE gamma-rays are found, correlated with X-rays, but not with the optical. The X-ray spectrum hardens with flux until the photon indices saturate above a threshold flux approximate to 10(-9) erg s(-1) cm(-2). The fractional variability decreases from X-rays to optical as a power law with F-var proportional to E-0.24 +/- 0.01. The full spectral energy distribution is well-fitted by synchrotron self-Compton emission from cooling electrons injected with a Maxwellian distribution of characteristic energy gamma(b). Fluctuations in the injected power with P-inj proportional to gamma(4)(b) explain the observed variability. Conclusions. The spectral saturation and the power-law dependence of the fractional variability are novel results that may extend to other TeV blazars. The ability of Maxwellian injections to reproduce the observed features suggest second-order Fermi acceleration or magnetic reconnection may play the dominant role in particle acceleration.