  We study the ground-state magnetic phase diagram of a spin S=1/2
antiferromagnetic two-leg ladder in the presence of period two lattice units
modulated, Dzyaloshinskii-Moriya (DM) interaction along the legs. We consider
the case of collinear DM vectors and strong rung exchange and magnetic field.
In this limit we map the initial ladder model onto the effective spin
$\sigma=1/2$ XXZ chain and study the latter using the continuum-limit
bosonization approach. We identified four quantum phase transitions and
corresponding critical magnetic fields, which mark transitions from the spin
gapped regimes into the gapless quantum spin-liquid regimes. In the gapped
phases the magnetization curve of the system shows plateaus at magnetisation
M=0 and to its saturation value per rung M=1. We have shown that the very
presence of alternating DM interaction leads to opening of a gap in the
excitation spectrum at magnetization M=0.5. The width of the magnetization
plateau at M=0.5, is determined by the associated with the dynamical generation
of a gap in the spectrum is calculated and is shown that its length scales as
$(D_{0}D_{1}/J^{2})^{\alpha}$ where $D_{0},D_{1}$ are uniform and staggered
components of the DM term, $J$ is the intraleg exchange and $\alpha \leq 3/4$
and weakly depends on the DM couplings.
