  It is surprising to find a fact for migration in the peak positions of
synchrotron spectra energy distribution component during in the activity epochs
of Mrk 421, accompanying with an orphan flaring at the X-ray and GeV-TeV
$\gamma$-ray bands. A geometric interpretation and standard shock or stochastic
acceleration models of blazar emission have difficulty reproducing these
observed behaviours. The present paper introduces a linear acceleration by
integrating the reconnection electric field into the particle transport model
for the observed behaviours of Mrk 421. We note that the strong evidence for
evolution of multi-wavelength spectral energy distribution characteristic by
shifting the peak frequency, accompanying with an orphan flaring at the X-ray
and GeV-TeV $\gamma$-ray bands provides an important electrostatic acceleration
diagnostic in blazar jet. Assuming suitable model parameters, we apply the
results of the simulation to the 13-day flaring event in 2010 March of Mrk 421,
concentrating on the evolution of multi-wavelength spectral energy distribution
characteristic by shifting the peak frequency. It is clear that the ratio of
the electric field and magnetic field strength plays an important role in
temporal evolution of the peak frequency of synchrotron spectral energy
distribution component. We suggest the electrostatic acceleration responsible
for the evolution of multi-wavelength spectral energy distribution
characteristic by shifting the peak frequency is reasonable. Based on the model
results, we issue that the peak frequency of the synchrotron spectral energy
distribution component may denote a temporary characteristic of blazars, rather
than a permanent one.
