  Radiative emissions from electrons and positrons generated by dark matter
(DM) annihilation or decay are one of the most investigated signals in indirect
searches of WIMPs. Ideal targets must have large ratio of DM to baryonic
matter. However, such ``dark'' systems have a poorly known level of magnetic
turbulence, which determines the residence time of the electrons and positrons
and therefore also the strength of the expected signal. This typically leads to
significant uncertainties in the derived DM bounds. In a novel approach, we
compute the self-confinement of the DM-induced electrons and positrons. Indeed,
they themselves generate irregularities in the magnetic field, thus setting a
lower limit on the presence of the magnetic turbulence. We specifically apply
this approach to dwarf spheroidal galaxies. Finally, by comparing the expected
synchrotron emission with radio data from the direction of the Draco galaxy
collected at the Giant Metre Radio Telescope, we show that the proposed
approach can be used to set robust and competitive bounds on WIMP DM.
