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 geome
tric 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.
There are still some important unanswered questions about the detailed particle acceleration and escape occurring during the quiescent epoches. As a result, the particle distribution that is adopted in the blazar quiescent spectral model have numerou
s unconstrained shapes. To help remedy this problem, we introduce a analytical particle transport model to reproduce quiescent broadband spectral energy distribution of blazar. In this model, the exact electron distribution is solved from a generalized transport equation that contains the terms describing first-order and secondary-order emph{Fermi} acceleration, escape of particle due to both the advection and spatial diffusion, energy losses due to synchrotron emission and inverse-Compton scattering of an assumed soft photon field. We suggest that the advection is a significant escape mechanism in blazar jet. We find that in our model the advection process tends to harden the particle distribution, which enhances the high energy components of resulting synchrotron and synchrotron self-Comptom spectrum from jet. Our model is able to roughly reproduce the observed spectra of extreme BL Lac object 1ES 0414+009 with reasonable assumptions about the physical parameters.
