Kinetic Description of Rotating Gases in External Magnetic Fields in the Framework of the Thomas-Fermi-Dirac Approach

Aim of this work is to extend the results obtained in a previous study on the magnetic confinement and stability of a rotating quantum degenerate fermion gas. This extension consists in the inclusion in the previously set up model of the effects of the exchange forces, and generalises the Thomas-Fermi (TF) approach used in the referenced work towards a Thomas-Fermi-Dirac (TFD) statistical description. The TF model has not only been used extensively and with success in these years to study atomic, nuclear, and molecular properties, or to evaluate features of matter in extreme conditions such as low temperatures and/or high densities typical of astrophysics and inertial confinement fusion experiments, but also to found hydrodynamic theories for the diffusion and stability of fermion plasmas (Rozsnyai, B. F. (1972). Relativistic Hartree-Fock-Slater calculations for arbitrary temperature and matter density. Phys. Rev. A 5(3):1137-1149), one component nonneutral degenerate fluids, plasmas etc. In this article an equation for density profiles in cylindrical symmetry is found, from the semiclassical kinetic theory of quantum uses (Pathria, R. K. (1996). Statistical Mechanics. 2nd ed. Oxford: Butterworth & Heinemann). which takes into account the effects of temperature, average velocity, external magnetic field and quantum exchange. Numerical and approximate analytical solutions of this equation for the case of complete quantum degeneracy are given and comparisons with the previous results are carried out.