The Relation between Magnetic-field Intensity and Size of the Emission Region in the High-synchrotron-peaked BL Lacertae Object Mrk 421

Magnetic effects are thought to dominate the formation of BL Lac object jets, but the role and influence of large-scale magnetic fields within the jets remains incompletely understood. We utilize a one-zone synchrotron-self-Compton (SSC) model with broken-power-law electron injection to reproduce multiwavelength spectral energy distributions (SEDs) of the high-synchrotron-peaked BL Lac object Mrk 421 for 73 activity states, constraining six key physical parameters. We investigate the correlation between magnetic-field strength B and emission-region size R and estimate the powers of relativistic electrons, cold protons, magnetic fields, and total jet power. We find a significant anticorrelation log B = ( − 0.93 ± 0.05 ) log R + ( 14.22 ± 0.83 ) . The derived slope close to −1 is compatible with theoretical expectations for a toroidal magnetic geometry, though parameter couplings inherent to the leptonic model cannot be fully excluded. Markov Chain Monte Carlo (MCMC) posterior analyses demonstrate that this B – R scaling is not merely an artefact of intra-epoch parameter degeneracy. On emission-region scales the jet is particle-kinetic-energy dominated; distinct electron-acceleration mechanisms (shocks, magnetic reconnection) operate across different activity states, and the conventional Poynting-flux-dominated scenario cannot account for the observed radiative power.