An extended model of quantum magnetohydrodynamics (QMHD) is developed from the formulation of Haas Phys. Plasmas 12, 062117 (2005), incorporating thermal transport effects and clarifying key modeling assumptions. The present work introduces the systematic emergence of nonlinear coherent vortex structures arising from the coupling among the plasma flow, magnetic field, and quantum diffraction at MHD equilibrium. Threefold improvements are achieved: (i) relaxation of the adiabatic closure through the explicit inclusion of heat-flux transport; (ii) replacement of Haas' assumed relation ρ∝A, where ρ is the plasma mass density and A is the magnetic flux function, with a self-consistent equilibrium relation compatible with an electron Boltzmann response; and (iii) correction of the axial magnetic energy density Bz2 to properly reflect its equilibrium dependence on the boundary conditions. The resulting equilibrium equations preserve the Liouville-type structure characteristic of the original QMHD model, while admitting analytic equilibrium solutions in which the temperature profile naturally generates cat-eye vortex structures in the flow, analogous to those found in classical MHD flows. These structures emerge only when the condition β0H2≥12 is satisfied, where β0 denotes the plasma beta at infinity, and H=kλeth/2π is the dimensionless quantum diffraction parameter (k and λeth are the inverse characteristic length scale and the electron thermal de Broglie wavelength, respectively). The results provide a more physically consistent QMHD equilibrium description for quantum plasmas and contribute to recent developments in nonlinear dynamics and structures in extended plasma models.
Zhen G. Ma (Fri,) studied this question.