Saba Majeed Gondal

Scopus Publications

Application of quadruple Beltrami state on Saturnian dusty plasma
S.M. Gondal
Cambridge University Press (CUP)
This investigation explores the potential formation of a relaxed equilibrium state, specifically the quadruple Beltrami state, in a three-component dusty plasma consisting of electrons, ions and negatively charged dust particles. This equilibrium state is derived by employing momentum-balanced equations along with Ampere's law. The quadruple Beltrami state is a composite of four Beltrami states, each associated with four distinct eigenvalues. Using the variational principle, we obtained the same relaxed state based on the system's constraints, which include magnetofluid energy, and the helicity of electrons, ions and dust particles. The unified flow is also derived. Dynamo action is investigated in two configurations: a rectangular geometry and a rectangular geometry with an internal conductor. Small-scale turbulent dynamo behaviour is observed in the former, while large-scale turbulent dynamo effects are noted in the latter. The magnitude of the magnetic field is found to be greater in the configuration with an internal conductor. Additionally, flow profiles are plotted as functions of Beltrami parameters and density variations of plasma species. This study contributes to the understanding of relaxation theory and the underlying physics of systems with an internal conductor, such as Saturn (planetary rings around a magnetosphere) and Jupiter magnetosphere, Uranus, Neptune, etc.

Relaxed magnetic structures in the Saturn's ring
S. M. Gondal
AIP Publishing
A theoretical investigation is presented to explain the formation and characteristics of relaxed equilibrium structures in a three-component dusty plasma within Saturn's atmosphere, composed of negatively charged dust particles, electrons, and ions. The Quadruple Beltrami equation is derived by utilizing the vortex dynamic equations along with the current density. Solutions for the higher Beltrami states are obtained in two different modes, a simple rectangular geometry and a coplanar rectangular geometry, to explore the characteristics of relaxed structures within the Saturn magnetosphere and its rings. The solutions are depicted through some plots by varying the Beltrami parameters and the densities of the plasma species. It is observed that only paramagnetic structures are formed in the coplanar geometry, while variations in the Beltrami parameters and plasma species densities significantly affect the magnetic characteristics of the relaxed structures in a simple rectangular geometry. This paper will provide an important contribution to understand the atmospheric vortical structures developed in different astronomical bodies that have double or more than double configurations, such as Saturn's rings, Jupiter magnetosphere, Uranus, Neptune, etc.

Self-Organization of Relaxed Structures in the Lunar Atmosphere
Laiba Yaqoob, S. M. Gondal, Maha Tahir, Asma Batool, and Amna Nazir
Wiley
ABSTRACTThe study investigates the relaxation of a three‐component dusty plasma in the lunar atmosphere. By employing Ampère's law with momentum balance equation of the plasma species, which includes an electron, a positive ion, and a negatively charged dust particle, a Triple Beltrami (TB) state is obtained. This TB state is characterized by three scale parameters, which may be real or complex. The Cartesian coordinate geometry is employed to analyze the magnetic field profiles. The Beltrami parameters, mass of negative charged dust particulates and density variations at different height and angle have a significant impact on the magnetic properties of the self‐organized structures in lunar atmosphere. The study reveals that all scale parameters associated with diamagnetic structures are real and complex, while all scale parameters for paramagnetic structures are real. It has been shown that the magnetic field, along with its complex conjugate and real part, increases with height and angle, and only diamagnetic structures are formed in the lunar atmosphere. The findings of this study should help to explain relaxed structures found in other astronomical objects and in lab settings including negatively charged dust particles, ions, and electrons.

Relaxation of multi-ion plasmas in an internal conductor
S. M. Gondal
AIP Publishing

Formation of self-organized structures in internal conductor plasma
S M Gondal and M Iqbal
IOP Publishing

Multiscale self-organized triple Beltrami states in four-component dusty plasmas
S.M. Gondal and M. Iqbal
Elsevier BV

The possibility of relaxation in Quadruple Beltrami states in a four-component magneto dusty plasma
S M Gondal and M Iqbal
IOP Publishing

Beltrami states in Earth's dusty mesosphere
S. M. Gondal
AIP Publishing
The study is the description of a three fluid (electrons, ions, and negatively charged dust grains) model of dusty plasmas which is a strong coupling between the magnetic field and the fluid aspects of the plasma. The generalized vorticities and the associated flows become parallel to each other by satisfying the Beltrami condition. Having solved the steady-state solutions with the Ampere's law for the magnetic field has given rise to a quadruple Beltrami state. The self-organized state has four scale parameters. The dynamics of the magnetic field are illustrated graphically in the x–y plane. The characteristics of the self-organized structures are strongly influenced by the scale parameters and the mass of the negatively charged dust grains. The equilibria magnetic field structures for the Earth's mesosphere revealed diamagnetic behavior. A transition into a paramagnetic state from a diamagnetic state was observed by slightly decreasing the mass of the dust grains. This identification can be useful to study and understand the noctilucent cloud and polar mesospheric summer echo in the Earth's mesosphere. The current study will be suitable to study the environmental and defense science. Moreover, this work will be fruitful to understand the environment of the planet Earth in the future.

Quadruple Beltrami state in electron-depleted multi-ion dusty plasmas
S. M. Gondal and M. Iqbal
AIP Publishing
In magnetized electron-depleted multi-ion dusty plasmas, a possibility of self-organization is determined. Making use of the equation of motion of the plasma's mobile species, i.e., a positive ion and two types of negative ions with Ampere's law, we obtain a quadruple Beltrami field. This higher order Beltrami field is characterized by four scale parameters. We have investigated the generation of self-organized structures. The typical length of these structures is attributed to the skin depth λp of positive ions. The influence of Beltrami parameters and scale parameters on the structure formation has also been investigated. It is found that there is a possibility of the formation of large scale structures of the order of system size and the formation of small scale structures of the order of skin depth simultaneously in the electron depleted multi-ion dusty plasmas, which are very useful to explain the dynamo theory. This study should be useful to describe the relaxed structures in space plasmas such as the D-region of Earth's mesosphere and F-ring of Saturn and in laboratory work where the dust particles are present as impurities.

Formation of large-scale structures in four-component dusty plasmas
S.M. Gondal, M. Iqbal, F. Saleem, and A. Shuaib
Wiley

Quadruple Beltrami fields in three component plasmas
S. M. Gondal, M. Iqbal, Ashfaq H. Khosa, and G. Murtaza
AIP Publishing
A possibility of three component plasma to self-organize to Quadruple Beltrami State is explored. The Quadruple Beltrami State is characterized by four Beltarmi fields. The state emerges as a natural consequence of the contributions of all the linear and nonlinear forces present in an ideal plasma. The role of species density in the creation of relaxed structures is also investigated and found to be effective in transformation of field structures. The study will be helpful to understand formation of structures in astrophysical and laboratory plasmas.

Self-organized field structures in electron-depleted multi-ion dusty plasma
M. Iqbal, S. M. Gondal, A. Shuaib, and Qurat-ul-ain
Cambridge University Press (CUP)
It is shown that there exists a strong interaction between the magnetic and kinetic aspects of a multi-ion plasma. The interaction appears as a system of simultaneous equations which show the alignment of vortices to flows and satisfy the Beltrami condition. Solving these equations lead to a non-force-free magnetic field which can be cast as a superposition of three multiscale force-free magnetic field configurations. It is the consequence of different Beltrami parameters of positive and negative ion fluids. It is also shown that self-organized paramagnetic and diamagnetic field structures could be created by varying the vorticities and flows of ion fluids.

Saba Majeed Gondal

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