  We study the two-component repulsive Fermi gas with imbalanced populations in
one dimension. Starting from the Bethe Ansatz solution we calculate
analytically the phase diagram for the homogeneous system. We show that three
phases appear: the balanced phase, the fully polarised phase and the partially
polarised phase. By means of the local density approximation and the equation
of state for the homogeneous system we calculate the density profile for the
harmonically confined case. We show that a two-shell structure appears: at the
center of the cloud we find the partially polarised phase and at the edges the
fully polarised one. The radii of the inner and outer shells are calculated for
different values of the polarisation and the coupling strength. We calculate
the dependence of the magnetisation on the polarisation for different values of
the coupling strength and we show that the susceptibility is always finite.
