A new class of vortices has been observed in the stratosphere after several extreme wildfires (Canada 2017, Australia 2020) and volcanic eruptions (Raikoke 2019). They are long-lived coherent plumes of aerosols and combustion/volcanic compounds confined within mesoscale (100s to 1000 km diameter) anticyclones. Due to their anomalous composition, these ascending anticyclonically-trapped plumes (ATPs) generate significant radiative forcing and diabatically-driven vertical motions. The present paper investigates the fundamental processes shaping the dynamics of ATPs from two complementary approaches: analytically in a potential vorticity (PV) perspective and using idealized but more complete numerical simulations with the Weather Research and Forecast (WRF) model. We adapt the axisymmetric Eliassen balanced vortex model, introduced as a prototype for tropical cyclones, to the case of a vortical flow forced by a diabatically-active Lagrangian tracer. Invoking an extended PV impermeability theorem, it is first clarified that ATP formation is consubstantial to the large injection of mass into the stratified flow at extratropical latitude. We also prove that vertically self-translating, strictly zero-PV ellipsoidal anticyclonic plumes with uniform tracer constitute an exact solution of the governing equations, thus accommodating the joint ascent of tracer and PV in ATPs. The numerical simulations reveal that finite-PV plumes with distributed tracer evolve into a vertically asymmetrical structure featuring a tracer and anticyclonic PV front followed by a tracer tail where cyclonic PV develops. Switching to potential radius-potential temperature coordinate, the dynamics reduces to that of a comb of 1-dimensional Burgers’equation for the tracer, supplemented by a slave equation for PV. By virtue of the symmetry of the problem when neglecting the background density gradient, cooled vortices undergo a similar evolution during their early subsidence, a situation which may apply to the 2022 Hunga Tonga-Hunga-Ha’apai volcanic plume. Finally, the impact of the initial conditions are discussed.