  The widespread detection of synchrotron X-ray emission from the jets of
low-power, nearby radio galaxies implies the presence of electrons at and above
TeV energies. In this paper we explore the possibility that the TeV gamma-rays
detected from the radio galaxies Cen A and M87, which both have bright,
well-studied X-ray jets, are produced at least in part by inverse-Compton
scattering of various photon fields by the high-energy electrons responsible
for the synchrotron X-rays on kiloparsec scales. We describe a new numerical
code that we have developed to carry out inverse-Compton calculations taking
account of all the relevant physics and using detailed models of the jets and
the photon fields in which they are embedded, and show that existing
constraints on the very high-energy (VHE) gamma-ray fluxes of these two objects
already place significant constraints on the magnetic field strengths in the
jet in Cen A. Finally, we discuss the prospects for constraints on radio galaxy
jet physics that may be obtained from observations with the Cerenkov Telescope
Array (CTA).
