  We study the effect of a migrating planet ($10<M_p<20$ Earth mass) on the
dynamics of pebbles in a radiative disk using 2D two-fluid simulations carried
out with the RoSSBi code. The combined action of the waves induced by the
migrating planet and drag back-reaction on the gas produces a complex evolution
of the flux of pebbles. The waves excite zonal flows which act as dust traps,
and accumulate pebbles. Owing to drag back-reaction, a Kelvin-Helmholtz
instability develops, generating turbulent dust rings containing several Earth
masses of solids, where planetesimal formation is likely. The more massive the
planet, the faster the dust rings develop. In competition with planet
migration, this process triggers several dust rings, with a radial separation
scaling as $1/M_p$. We discover a transition around $13$ Earth masses. Below
that, pebbles are stopped at the inner side of the planet's orbit, but pebble
accretion on the planet is sustained. Above that, drag back-reaction in the
dust ring region flattens the pressure profile while the planet migrates, which
limits further growth by pebble accretion. This new {\it pebble isolation mass}
is about a factor of 2 lower than often reported in the literature. This
reduces the overall formation timescale of Super-Earth planets, while favoring
their survival after the disk's dissipation because further accretion is
stifled. Finally, our results support an hybrid model for the formation of
Jupiter via both pebbles and planetesimals accretion.
