Mrk 421 was repeatedly observed with BeppoSAX in 1997 and 1998. This is the
first of two papers where we present the results of a thorough temporal an
d spectral analysis of all the data available to us, focusing in particular
on the flare of 1998 April, which was simultaneously observed also at TeV
energies. Here we focus on the time analysis, while the spectral analysis a
nd physical interpretation are presented in the companion paper. The detail
ed study of the flare in different energy bands reveals very important new
results: (1) hard photons lag the soft ones by 2-3 ks-a behavior opposite t
o what is normally found in high-energy peak BL Lac X-ray spectra; (2) the
hare light curve is symmetric in the softest X-ray band, while it becomes i
ncreasingly asymmetric at higher energies, with the decay being progressive
ly slower than the rise; and (3) the flux decay of the flare can be intrins
ically achromatic if a stationary underlying emission component is present.
The temporal and spectral information obtained challenge the simplest mode
ls currently adopted for the (synchrotron) emission and most importantly pr
ovide clues on the particle acceleration process.