  The magnetically ordered ground state of CeRhIn$_{5}$ at ambient pressure and
zero magnetic field is an incomensurate helicoidal phase with the propagation
vector $\bf{k}$=(1/2, 1/2, 0.298) and the magnetic moment in the basal plane of
the tetragonal structure. We determined by neutron diffraction the two
different magnetically ordered phases of CeRhIn$_{5}$ evidenced by bulk
measurements under applied magnetic field in its basal plane. The low
temperature high magnetic phase corresponds to a sine-wave structure of the
magnetization being commensurate with $\bf{k}$=(1/2, 1/2, 1/4). At high
temperature, the phase is incommensurate with $\bf{k}$=(1/2, 1/2, 0.298) and a
possible small ellipticity. The propagation vector of this phase is the same as
the one of the zero-field structure.
