Synchrotron aging in filamented magnetic fields

Magnetic fields in synchrotron sources are almost certainly inhomogeneous, mixing high-field and low-held regions. This inhomogeneity affects the evolution of a relativistic electron distribution function due to the rate of energy loss of the electrons changing as they move between the two regions. We present two models for the evolution of the distribution function, and discuss the results of these models in terms of the critical energies, or synchrotron frequencies, where the particle and photon spectra steepen. We find these critical frequencies are higher than would be the case if the electrons were confined to a homogeneous high-held region. We apply our results to the interpretation of extragalactic radio sources whose dynamical ages are known to be significantly greater than the ages inferred from their high-frequency spectral breaks.