  Vela X is a pulsar wind nebula (PWN) associated with the active pulsar
B0833-45 and contained within the Vela supernova remnant (SNR). A collimated
X-ray filament ("cocoon") extends south-southwest from the pulsar to the center
of Vela X. VLA observations uncovered radio emission coincident with the
eastern edge of the cocoon and H.E.S.S. has detected TeV $\gamma$-ray emission
from this region as well. Using XMM-\textit{Newton} archival data, covering the
southern portion of this feature, we analyze the X-ray properties of the
cocoon. The X-ray data are best fit by an absorbed nonequilibrium plasma model
with a powerlaw component. Our analysis of the thermal emission shows enhanced
abundances of O, Ne, and Mg within the cocoon, indicating the presence of
ejecta-rich material from the propagation of the SNR reverse shock, consistent
with Vela X being a disrupted PWN. We investigate the physical processes that
excite the electrons in the PWN to emit in the radio, X-ray and $\gamma$-ray
bands. The radio and non-thermal X-ray emission can be explained by synchrotron
emission. We model the $\gamma$-ray emission by Inverse Compton scattering of
electrons off of cosmic microwave background (CMB) photons. We use a
3-component broken power law to model the synchrotron emission, finding an
intrinsic break in the electron spectrum at $\sim5 \times 10^{6}$ keV and a
cooling break at $\sim$ 5.5 $\times 10^{10}$ keV. This cooling break along with
a magnetic field strength of 5 $\times 10^{-6}$ G indicate that the synchrotron
break occurs at $\sim$1 keV.
