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The self-organization of a thermally relativistic magnetized plasma comprising of electrons, positrons and static ions is investigated. The self-organized state is found to be the superposition of three distinct Beltrami fields known as triple Beltrami (TB) state. In general, the eigenvalues associated with the multiscale self-organized vortices may be a pair of complex conjugate and real one. It is shown that all the eigenvalues become real when thermal energy increases or the positron density decreases. The impact of relativistic temperature and positron density on the formation of self-organized structures is investigated. The self-organized field and flow vortices may vary simultaneously on vastly different length scales. The disparate variation of self-organized vortices is important in the context of dynamo theory. The present work is useful to study the formation of multiscale vortices and dynamo mechanisms in multi-species thermally relativistic plasmas.

The self-organization in a multi-ion plasma composed of electrons and two species of positively charged ions is investigated. It is shown that when canonical vorticities and velocities of all the plasma fluids are aligned, the magnetic field self-organizes to Quadruple Beltrami state (superposition of four Beltrami fields). The self-organized magnetic and velocity fields strongly depend on the relative strengths of the generalized vorticities, flows, inertia and densities of the plasma species. Thus, it is possible to generate a wide variety of multiscale magnetic field and flow structures. It is also shown that relaxed magnetic fields and velocities can vary on vastly different length scales simultaneously and are coupled together through singular perturbation generated by Hall effect. In this multi Beltrami self-organized states, then, the dynamo mechanism emerges naturally. The scale separation also suggests the heating of the plasma through a dissipative process. The work could be useful to study the dynamics and morphology of the multiscale magnetic field configurations in laboratory and astrophysical plasmas.

A thermally relativistic electron-positron-ion (EPI) plasma self-organizes into a quadruple Beltrami (QB) field. The QB field, which is the combination of four Beltrami fields, is described by four scale parameters. These scale parameters are often either real or both real and complex in nature. The values of the scale parameters are determined by Beltrami parameters, relativistic temperatures, and the densities of plasma species. It is demonstrated that all the scale parameters become real at higher relativistic temperatures and ion densities, which naturally lead to paramagnetic structures. It is also shown that the scale separation in the QB state provides the possibility of field and flow generation in such thermally relativistic plasmas. The present study may have implications for space, astrophysical and laboratory plasmas.