Propagation Diagnostics of Supernova Remnant Environments around Young Repeating Fast Radio Bursts. I. Hydrodynamic Evolution of the Source-local Dispersion Measure

Repeating fast radio bursts may reside in young supernova remnant (SNR) environments whose evolving plasma contributes to the observed dispersion measure (DM). We use two-dimensional axisymmetric hydrodynamic simulations to study the interaction between a continuous anisotropic wind from a young neutron star and homologously expanding supernova ejecta. We follow the evolution to approximately 160 yr and calculate the source-local DM along different viewing directions, using a passive tracer to separate wind and non-wind contributions. In the fiducial model, the strongly polar-focused wind inflates a low-density cavity, while the swept-up shell remains broadly rounded and the DM shows moderate angular variation. The DM is dominated by ejecta and swept-up non-wind material. The solid-angle-averaged ambient-subtracted excess DM declines throughout the evolution, approximately following t age-2 during the first several tens of years and becoming modestly steeper later. Variations in wind and ejecta parameters modify the normalization, early evolution, and viewing-angle dependence, but the angle-averaged DM declines in all models, while different bipolar wind profiles produce similar long-term evolution. For FRB 20190520B, the fiducial model reaches a decline rate comparable to the source-frame value inferred from observations at approximately 20 yr, when the mean excess DM is approximately 1.8 times 10 squared pc cm-3. Thus, such a young environment can retain a substantial electron column while producing a rapid secular decrease. Repeater diversity suggests that SNR-driven expansion may coexist with additional time-dependent plasma structures or ionization changes.