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We study the generation of strong large scale magnetic fields in compactstars containing degenerate quark matter with unbroken chiral symmetry. Themagnetic field growth is owing to the magnetic field instability driven by theelectroweak interaction of quarks. In this system we predict the enhancement ofthe seed magnetic field $10^{12}\,\text{G}$ to the strengths$(10^{14}-10^{15})\,\text{G}$. In our analysis we use the typical parameters ofthe quark matter in the core of a hybrid star or in a quark star. We also applyof the obtained results to model the generation of magnetic fields inmagnetars.

Generation of strong magnetic fields in hybrid and quark stars driven by the electroweak interaction of quarks