  We report on deep XMM-Newton observations of the vertex filament in the
southern giant lobe of the Fanaroff-Riley class I radio galaxy Centaurus A. We
find no X-ray excess from the filament region and place a 3 sigma upper limit
on the 1 keV flux density of the filament of 9.6 nJy. This directly constrains
the electron density and magnetic field strength in the filament. For the first
time in an individual filament, we show that so long as the particle index >=2,
the excess in synchrotron emissivity cannot be produced purely by excess
electrons: the filament magnetic field strength must be higher than in the
giant lobes as a whole, and close to or above the equipartition value for the
filament. The filaments are not significantly overpressured with respect to the
surrounding lobe with a pressure provided by relativistic electrons.
