Motivated by recent reports of strongly correlated radio and X-ray variability in 3C 279 (Grandi et al.), we have computed the relative amplitudes of variations in the synchrotron flux at ν and the self-Compton X-ray flux at 1 keV [R(ν)] for a homogeneous sphere of relativistic electrons orbiting in a tangled magnetic field. We consider three cases: the Thomson depth of the sphere (τT) varying at fixed magnetic field strength (B), B varying at fixed τT, and equal fractional changes in τT and B. Relative to synchrotron self-Compton scattering without induced Compton scattering, stimulated scattering reduces the amplitude of R(ν) by as much as an order of magnitude when τT 1. When τT varies in a fixed magnetic field, Rτ increases monotonically from 0.01 at ν0, the self-absorption turnover frequency, to 0.5 at 100ν0. Variations in B reduce R at all ν, up to a factor of 2 if τT is constant, and introduce local extrema in R. The relative amplitudes of the correlated fluctuations in the radio-millimeter and X-ray fluxes from 3C 279 are consistent with the synchrotron self-Compton model if τT varies in a fixed magnetic field and induced Compton scattering is the dominant source of radio opacity. The variation amplitudes are too small to be produced by the passage of a shock through the synchrotron emission region unless the magnetic field is perpendicular to the shock front.
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