  A recent high-field magnetization experiment found a phase transition of
unknown character in the layered, frustrated antiferromagnet RbCuCl_3, in a
transverse field (in the layers). Motivated by these results, we have examined
the magnetic structures predicted by a model of RbCuCl_3, using the classical
approximation. At small fields, we obtain the structure already known to be
optimal, an incommensurate (IC) spiral with wave vector q in the layers. At
higher fields, we find a staircase of long-period commensurate (C) phases
(separated initially by the low-field IC phase), then two narrow IC phases,
then a fourth IC phase (also with intermediate C phases), and finally the
ferromagnetically aligned phase at the saturation field H_S. The
three-sublattice C states familiar from the theory of the triangular
antiferromagnet are never optimal. The C phases and the two intermediate IC
phases were previously unknown in this context. The magnetization is
discontinuous at a field \approx 0.4H_S, in qualitative agreement with
experiment, though we find much fine structure not reported.
