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The self‐organization of a magnetized multi‐ion plasma, composed of inertialess electrons and inertial H+, He+, and O+ ions, leads to the formation of quadruple Beltrami (QB) field structures. The QB self‐organized state is a linear combination of four single Beltrami fields, and it is a non‐force‐free state that shows strong magnetofluid coupling. Moreover, the QB state is characterized by four relaxed state structures of different length scales. The investigation reveals that the generalized helicities of plasma species and the densities of ion species have a significant impact on the characteristics of the self‐organized vortices in the QB state. The study also highlights the potential consequences of QB field structures on earth's inner magnetosphere, including diamagnetic and paramagnetic trends as well as heating effects resulting from disparate length scales. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The relaxation of relativistic hot electron–positron plasma is investigated by incorporating the effect of non-zero photon mass, and a quadruple Beltrami (QB) relaxed state for the magnetic vector potential is derived. The QB state is a linear superposition of four single force-free fields and is characterized by four self-organized structures of different length scales. The analysis of QB states shows that for certain values of generalized helicities at lower relativistic temperatures, plasma shows diamagnetic behaviour. It is also noteworthy that the inclusion of non-zero photon mass naturally provides the possibility of multiscale structure formation in the relaxed state. In this scenario, one of the field structures is significantly larger than the Compton wavelength of photons, while the other three structures are on the scale of the electron skin depth. The potential implications of this QB state for astrophysical environments are also discussed. [ABSTRACT FROM AUTHOR]

In sample surveys, the problem of outliers is one of the most frequent and widest, whose solution is required to be obtained using statistical techniques. To overcome this problem, various robust regression methods are being developed such as LTS, LMS, LAD, Huber-M, Hample-M, Tukey-M and Huber-MM methods. This article presents the modified Hartley–Ross type ratio estimators to estimate the population mean in sample surveys. The proposed design is taken into account under the two suppositions one is that the study variable is a non-sensitive variable, which means that measurements on it do not embarrass participants in personal interviews and other is the sensitive variable, which means that measurement errors are introduced as a result of a few dishonest responses. The use of scrambling response models helps to reduce these measurement errors to some extent. The proposed estimator is found to be more efficient than the existing classical estimators. A Numerical illustration was performed on a real data set in R-Program Software to support of our findings. [ABSTRACT FROM AUTHOR]

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 O 2 − 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. [ABSTRACT FROM AUTHOR]

The relaxed state of a magnetized four-component partially ionized dusty (PID) plasma is explored. PID plasma is composed of inertial electrons, positive ions, neutrals, and static negatively charged dust particles. When the neutrals are dragged along with the ions, the steady-state solution of vortex dynamic equations for inertial electron and ion species yields a triple Beltrami relaxed state, which is a linear combination of three single force-free fields and is characterized by three self-organized structures. The impact of plasma parameters such as Beltrami parameters and neutral (degree of ionization) and dust species densities on the nature of the relaxed state is investigated. Furthermore, the role of scale separation and its implication in space plasma are also presented. The present research will aid in elucidating the role of neutral and dust species in space, astrophysical, and laboratory plasmas. [ABSTRACT FROM AUTHOR]