  The application of large magnetic fields ($B \sim B_{c2}$) to layered
cuprates suppresses their high temperature superconducting behaviour and
reveals competing ground states. In the widely-studied material
YBa$_2$Cu$_3$O$_{6+x}$ (YBCO), underdoped ($p \sim 1/8$) samples show
signatures of field-induced electronic and structural changes at low
temperatures. However, the microscopic nature of the field-induced
reconstruction and the high-field state are unclear. Here we report an x-ray
study of the high-field charge density wave (CDW) in YBCO, for doping, $0.1
\lesssim p \lesssim 0.13$. For $p \sim 0.123$, we find that a field ($B \sim
10$~T) induces new CDW correlations along the CuO chain ($b$) direction only,
leading to a 3-D ordered state along this direction at $B \sim 15$~T. The CDW
signal along the $a$-direction is also enhanced by field, but does not develop
a new pattern of correlations. We find that field modifies the coupling between
the CuO$_2$ bilayers in the YBCO structure, and causes the sudden appearance of
3D CDW order. The mirror symmetry of individual bilayers is broken by the CDW
at low and high fields, allowing recently suggested Fermi surface
reconstruction.
