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Diffusive shock acceleration (DSA) at relativistic shocks is widely thoughtto be an important acceleration mechanism in various astrophysical jet sources,including radio-loud active galactic nuclei such as blazars. Such accelerationcan produce the non-thermal particles that emit the broadband continuumradiation that is detected from extragalactic jets. An important recentdevelopment for blazar science is the ability of Fermi-LAT spectroscopy to pindown the shape of the distribution of the underlying non-thermal particlepopulation. This paper highlights how multi-wavelength spectra spanning opticalto X-ray to gamma-ray bands can be used to probe diffusive acceleration inrelativistic, oblique, magnetohydrodynamic (MHD) shocks in blazar jets.Diagnostics on the MHD turbulence near such shocks are obtained using thermaland non-thermal particle distributions resulting from detailed Monte Carlosimulations of DSA. These probes are afforded by the characteristic propertythat the synchrotron $\nu F_{\nu}$ peak energy does not appear in the gamma-rayband above 100 MeV. We investigate self-consistently the radiative synchrotronand inverse Compton signatures of the simulated particle distributions.Important constraints on the diffusive mean free paths of electrons, and thelevel of electromagnetic field turbulence are identified for three differentcase study blazars, Mrk 501, BL Lacertae and AO 0235+164. The X-ray excess ofAO 0235+164 in a flare state can be modelled as the signature of bulk Comptonscattering of external radiation fields, thereby tightly constraining theenergy-dependence of the diffusion coefficient for electrons. The concomitantinterpretations that turbulence levels decline with remoteness from jet shocks,and the probable significant role for non-gyroresonant diffusion, are posited.

Probing Acceleration and Turbulence at Relativistic Shocks in Blazar Jets