  We analyze the magnetic field evolution in dense quark matter with unbroken
chiral symmetry, which can be found inside quark and hybrid stars. The magnetic
field evolves owing to the chiral magnetic effect in the presence of the
electroweak interaction between quarks. In our study, we also take into account
the magnetohydrodynamic turbulence effects in dense quark matter. We derive the
kinetic equations for the spectra of the magnetic helicity density and the
magnetic energy density as well as for the chiral imbalances. On the basis of
the numerical solution of these equations, we find that turbulence effects are
important for the behavior of small scale magnetic fields. It is revealed that,
under certain initial conditions, these magnetic fields behave similarly to the
electromagnetic flashes of some magnetars. We suggest that fluctuations of
magnetic fields, described in frames of our model, which are created in the
central regions of a magnetized compact star, can initiate magnetar bursts.
