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A quadruple Beltrami (QB) equilibrium state for a four-component plasma that consists of inertial electrons, positrons, lighter positive (H+) ions and heavier negative ions O2−$\left({\mathrm{O}}_{2}^{-}\right)$is derived and investigated. The QB relaxed state is a linear superposition of four distinct single Beltrami fields and provides the possibility of the formation of four self-organized vortices of different length scales. In addition, robust magnetofluid coupling characterizes this non-force-free state. The analysis of the QB state also shows that by adjusting the generalized helicities and densities of plasma species, the formation of multiscale structures as well as the paramagnetic and diamagnetic behavior of the relaxed state can be controlled.

The relaxed state of a magnetized relativistic hot plasma composed of inertial electrons and positrons having different relativistic temperatures and a fraction of static positive ions is studied. From the steady-state solutions of vortex dynamics equations and the relation for current density, a non-force-free triple Beltrami (TB) relaxed state equation is derived. The TB state is characterized by three scale parameters that consequently provide three different self-organized structures. The analysis of the relaxed state shows that for specific values of generalized helicities, the disparity in relativistic temperature and the existence of a small fraction of static positive ions in pair plasma can transform the nature of scale parameters. Moreover, an analytical solution of the TB state for an axisymmetric cylindrical geometry with an internal conductor configuration demonstrates that due to asymmetries of temperature and density of plasma species, diamagnetic structures can transform into paramagnetic ones and vice versa. The present study will improve our understanding of pair plasmas in trap-based plasma confinement experiments and astrophysical environments.

The relaxation of a relativistic hot electrons-positron plasma with a small fraction of cold electrons and ion species is investigated, and a quadruple Beltrami (QB) relaxed state is derived. The QB state is a non-force-free state that is a linear combination of four single force-free states and is therefore comprised of four self-organized structures. Additionally, triple as well as double Beltrami states can be obtained by adjusting the generalized helicities of plasma species. The analysis of the relaxed states demonstrates that, for specific values of the generalized helicities, cold species density and relativistic temperature can transform paramagnetic structures into diamagnetic structures and vice versa. Also, when the flow vortices of plasma species are aligned with the magnetic field, it leads to a classically perfect diamagnetic relaxed state, and the strength of the magnetic field increases with a decrease in relativistic temperature and an increase in cold species density. The current investigation aims to enhance comprehension of energy transformation mechanisms and the formation of multiscale structures in astrophysical and laboratory plasmas.