  We present a Chandra and XMM-Newton study of X-ray emission from the lobes of
33 classical double radio galaxies and quasars. We report new detections of
lobe-related X-ray emission in 11 sources. Together with previous detections we
find that X-ray emission is detected from at least one radio lobe in ~75
percent of the sample. For all of the lobe detections, we find that the
measured X-ray flux can be attributed to inverse-Compton scattering of the
cosmic microwave background radiation, with magnetic field strengths in the
lobes between (0.3 - 1.3) B_eq, where the value B_eq corresponds to
equipartition between the electrons and magnetic field assuming a filling
factor of unity. There is a strong peak in the magnetic field strength
distribution at B ~ 0.7 B_eq. We find that > 70 percent of the radio lobes are
either at equipartition or electron dominated by a small factor. The
distribution of measured magnetic field strengths differs for narrow-line and
broad-line objects, in the sense that broad-line radio galaxies and quasars
appear to be further from equipartition; however, this is likely to be due to a
combination of projection effects and worse systematic uncertainty in the X-ray
analysis for those objects. Our results suggest that the lobes of classical
double radio sources do not contain an energetically dominant proton
population, because this would require the magnetic field energy density to be
similar to the electron energy density rather than the overall energy density
in relativistic particles.
