Vortex formation in Kelvin–Helmholtz driven instability in dense quantum magnetoplasma

In this work, we investigate nonlinear vortex formation in dense magnetized quantum plasma using a quantum hydrodynamic framework inspired by linear models in Ref. [A. Rasheed, M. Jamil, and G. Murtaza, “Kelvin–Helmholtz instability in a dense quantum magnetoplasma with exchange correlations,” Z. Naturforsch. A , vol. 78, pp. 1123–1130, 2023]. While the linear dispersion relation remains unchanged from previous studies [A. Rasheed, M. Jamil, and G. Murtaza, “Kelvin–Helmholtz instability in a dense quantum magnetoplasma with exchange correlations,” Z. Naturforsch. A , vol. 78, pp. 1123–1130, 2023], the present work extends the analysis to the nonlinear regime by incorporating convective and mode-coupling effects. We derive and solve fluid equations incorporating Fermi pressure, Bohm potential, and exchange-correlation effects, focusing on the nonlinear development of Kelvin–Helmholtz (KH) instability. Our analytical solutions reveal the presence of stationary dipolar vortex structures. Conditions for their formation, as well as the influence of quantum parameters, are discussed. The results have relevance for both astrophysical and laboratory plasma environments.