  It is shown that the nonlinear kinetic theory of cosmic ray (CR) acceleration
in supernova remnants (SNRs) describes the shell-type nonthermal X-ray
morphology of Cas A, obtained in Chandra observations, in a satisfactory way.
The set of empirical parameters, like distance, source size and total energy
release, is the same which reproduces the dynamical properties of the SNR and
the spectral characteristics of the emission produced by CRs. The extremely
small spatial scales in the observed morphological structures at hard X-ray
energies are due to a large effective magnetic field $B_d \sim 500$ $\mu$G in
the interior which is at the same time not only required but also sufficient to
achieve the excellent agreement between the spatially integrated radio and
X-ray synchrotron spectra and their calculated form. The only reasonably
thinkable condition for the production of such a large effective field strength
is a very efficiently accelerated nuclear CR component. Therefore the Chandra
data confirm first of all the inference that Cas A indeed accelerates nuclear
CRs with the high efficiency required for Cas A to be considered as a member of
the main class of Galactic CR sources and, secondly, that the nonlinear kinetic
theory of CR acceleration in SNRs is a reliable method to determine the
magnetic field value in SNRs.
