Critical behavior and inversion curves of magnetic-AdS black holes surrounded by quintessence field

This study investigates the thermodynamic characteristics, specifically the Joule-Thomson expansion, of non-linear magnetically charged AdS black holes filled with a quintessence field, thereby explaining the role of dark energy and non-linear electrodynamics in their structure and phase transition behavior. Having built the geometry of black holes with mass, magnetic charge, cosmological constant and quintessence parameters, we get explicit analytical results in the form of critical temperature, pressure and horizon radius in the extended phase space. Within this context, the mass is considered to be the enthalpy, and the cosmological constant is associated with the thermodynamic pressure. We have shown that the existence of quintessence distorts the background spacetime and has a large effect upon the phase transitions; the critical behavior and horizon properties are governed mainly by the magnetic charge. The higher the magnetic charge, the larger the cooling domain, and the quintessence changes the inversion curve and increases the separation of thermal domains. These factors are sensitive to the cooling and heating regimes, as can be observed in a detailed analysis of the Joule-Thomson expansion. The interaction of mass, charge, and quintessence in the thermodynamics of black holes can be expressed graphically by plots of the isenthalic and inversion curves on the pressure-temperature plane.