  Using Chandra images of cluster cores with clear radio bubbles, we have
determined k, which is the ratio of the total particle energy to that of the
electrons radiating between 10 MHz and 10 GHz. Radiative and dynamical
constraints on the bubbles indicate that the ratio of the energy factor, k, to
the volume filling factor, f, lies within the range 1 < k/f < 1000. Assuming
pressure equilibrium between the radio-emitting plasma and the surrounding
X-ray gas, none of the lobes have equipartition between relativistic particles
and magnetic field. There is no evidence for any dependence of the upper limit
of the k/f ratio on any physical parameter of the cluster or the radio source.
The distribution of the upper limit on k/f appears to be bimodal, the value for
some clusters being ~3 and for the others ~300. We show that this is may due to
the composition of the jet which forms the bubbles, the variation in the volume
filling fraction or variation in the amount of re-acceleration occurring in the
bubble.
