Quantum hydrodynamics approach to the research of quantum effects and vorticity evolution in spin quantum plasmas

In this paper, we explain a magneto quantum hydrodynamics (MQHD) method for the study of the quantum evolution of a system of spinning fermions in an external electromagnetic field. The fundamental equations of microscopic quantum hydrodynamics (the momentum balance equation and the magnetic moment density equation) are derived from the many-particle microscopic Schrodinger equation with a spin-spin and Coulomb modified Hamiltonian. Using the developed approach, an extended vorticity evolution equation for the quantum spinning plasma is derived. The effects of the new spin forces and spin-spin interaction contributions on the motion of fermions, the evolution of the magnetic moment density, and vorticity generation are predicted. The influence of the intrinsic spin of electrons on whistler mode turbulence is investigated. The results can be used for theoretical studies of spinning many-particle systems, especially dense quantum plasmas in compact astrophysical objects, plasmas in semiconductors, and micro-mechanical systems, in quantum X-ray free-electron lasers.