Current and future measurements of the Lund jet plane density in pp and Pb-Pb collisions with ALICE

Jets are excellent probes of the quark-gluon plasma (QGP) produced in heavy-ion collisions because the partons inside jets interact with the medium, leading to jet energy loss and substructure modification - a phenomenon called jet quenching. In particular, observables that focus on the hard parton splittings inside the jet can be used to isolate different jet-medium interactions and answer questions about the microscopic structure of the QGP. The primary Lund jet plane density is a two-dimensional visual representation of the parton splittings within the jet that can be used to isolate different regions of the QCD phase space. In heavy-ion collisions it provides a map of the space-time structure of the QGP. This talk will highlight recent measurements from ALICE that probe specific regions of the Lund plane. Some regions remain inaccessible due to current experimental constraints such as the heavy-ion background and precision. This talk will discuss how the ALICE Run 3 upgrades and the future ALICE 3 detector design will allow us to overcome some of these challenges and provide access to some of the previously inaccessible regions of the Lund plane.