Strongly disordered pseudogapped superconductors are expected to display arbitrarily high values of kinetic inductance close to the superconductor-insulator transition (SIT), which make them attractive for the implementation of large dissipationless inductance. We develop the theory of the collective modes in these superconductors and discuss associated dissipation at microwave frequencies. We obtain the collective mode spectra dependence on the disorder level and conclude that collective modes become a relevant source of dissipation and noise in the outer proximity of the SIT.
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