  In this paper we explicate a method of magneto quantum hydrodynamics (MQHD)
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) were derived from the many-particle microscopic Schroodinger
equation with $Spin-Spin and Coulomb modified Hamiltonian. Using the developed
approach the extended vorticity evolution equation for the quantum spinning
plasma were derived. The effects of new spin forces and spin-spin interaction
contributions on the motion of fermions, evolution of the magnetic moment
density and vorticity generation were predicted. The influence of the intrinsic
spin of electrons in the nonlinear whistler mode turbulence was investigated.
This results can be used for the 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.
