  We present NuSTAR observations of the powerful radio galaxy Cygnus A,
focusing on the central absorbed active galactic nucleus (AGN). Cygnus A is
embedded in a cool-core galaxy cluster, and hence we also examine archival
XMM-Newton data to facilitate the decomposition of the spectrum into the AGN
and intracluster medium (ICM) components. NuSTAR gives a source-dominated
spectrum of the AGN out to >70keV. In gross terms, the NuSTAR spectrum of the
AGN has the form of a power law (Gamma~1.6-1.7) absorbed by a neutral column
density of N_H~1.6x10^23 cm^-2. However, we also detect curvature in the hard
(>10keV) spectrum resulting from reflection by Compton-thick matter out of our
line-of-sight to the X-ray source. Compton reflection, possibly from the outer
accretion disk or obscuring torus, is required even permitting a high-energy
cutoff in the continuum source; the limit on the cutoff energy is E_cut>111keV
(90% confidence). Interestingly, the absorbed power-law plus reflection model
leaves residuals suggesting the absorption/emission from a fast
(15,000-26,000km/s), high column-density (N_W>3x10^23 cm^-2), highly ionized
(xi~2,500 erg cm/s) wind. A second, even faster ionized wind component is also
suggested by these data. We show that the ionized wind likely carries a
significant mass and momentum flux, and may carry sufficient kinetic energy to
exercise feedback on the host galaxy. If confirmed, the simultaneous presence
of a strong wind and powerful jets in Cygnus A demonstrates that feedback from
radio-jets and sub-relativistic winds are not mutually exclusive phases of AGN
activity but can occur simultaneously.
