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Magnetized plasmas are well known to exhibit a rich spectrum of collectivemodes. Here, we focus on the density modes in dense or cold plasmas, wherestrong coupling effects alter the mode spectrum known from traditional weaklycoupled plasmas. In particular, we study the dynamic structure factor (DSF) ofthe magnetized one-component plasma with molecular dynamics simulations.Extending our previous results [H.~K\"ahlert and M.~Bonitz, Phys. Rev. Research\textbf{2022}, 4, 013197], it is shown that Bernstein modes can be observed inthe weakly magnetized regime, where they are found below the upper hybridfrequency, provided the coupling strength is sufficiently low. We investigatethe DSF for a variety of different wave numbers and plasma parameters and showthat even small magnetization can give rise to a strong zero-frequency modeperpendicular to the magnetic field and change the dispersion as well as thedamping of the upper hybrid mode.

Dynamic structure factor and excitation spectrum of the one-component plasma: the case of weak to moderate magnetization