Saba Majeed Gondal

EDUCATION

Ph.D. (Specialization in Theoretical and Mathematical Physics)
Title of Thesis: Beltrami States in Three Component Plasmas
MPhil (Specialization in Material Processing)
Title of Thesis: Characteristics of Gold Nanoparticles Embedded in Silicon by PLA

RESEARCH INTERESTS

• Theoretical Plasma Physics • Beltrami States • Plasma Astrophysics • Dusty Plasmas • Magneto-Fluid Coupling Theory • Solar Physics • Dynamo Theory • Stellar Atmospheres Physics • Coronal Mass Ejection • Magnetic Field and Flow structures • Fluid Dynamics.

Scopus Publications

Self-Organization of Relaxed Structures in the Lunar Atmosphere
Laiba Yaqoob, S. M. Gondal, Maha Tahir, Asma Batool, Amna Nazir
Contributions to Plasma Physics, 2025
The 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.
Application of quadruple Beltrami state on Saturnian dusty plasma
S.M. Gondal
Journal of Plasma Physics, 2025
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
Physics of Plasmas, 2024
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.
Relaxation of multi-ion plasmas in an internal conductor
S. M. Gondal
Aip Advances, 2022
The possibility of the formation and characteristics of the relaxed structures in the multi-ion magnetized plasmas consisting of heavy ions, light ions, and inertia-less electrons have been explored. Using the vortex dynamic equations with the current density, the system is relaxed to triple Beltrami states. Solutions of the relaxed states are determined in two different cases: (i) simple slab geometry and (ii) slab geometry with an internal conductor. The impact of Beltrami parameters and density ratios of the plasma components on the formation of equilibrium structures in both geometries has been studied. Moreover, we also highlight the equivalences of both geometries (simple slab geometry and a slab geometry with an internal conductor). This investigation will be useful for studying and understanding the relaxed structures in different astrophysical objects such as solar wind, Earth’s ionosphere, near-Earth plasmasheet, upper ionosphere, and Saturn and in the laboratory plasmas having two positively charged ions of different masses. Moreover, this work will be helpful in describing the underlying physics of the relaxed structures. These structures are developed in different astrophysical bodies that revolve around the planet such as Jupiter magnetosphere.
Formation of self-organized structures in internal conductor plasma
S M Gondal, M Iqbal
Physica Scripta, 2021
Abstract A possibility of the confinement of two-fluid (electrons and ions) magnetized plasma in a simple cylindrical configuration as well as in a cylindrical geometry with an internal conductor is analyzed. By controlling the characteristics roots of Triple Beltrami state the formation of diamagnetic and paramagnetic structures is investigated for a simple cylindrical geometry. For an internal conductor system, the nature of relaxed structures is only paramagnetic. These paramagnetic structures are independent of the type of the characteristics roots. The results of the present investigation will be helpful to explain the equilibrium structure in the astrophysical objects such as Jupiter magnetosphere which is co-rotated with the planet and in the laboratory.
Multiscale self-organized triple Beltrami states in four-component dusty plasmas
S.M. Gondal, M. Iqbal
Planetary and Space Science, 2021
The possibility of relaxation in Quadruple Beltrami states in a four-component magneto dusty plasma
S M Gondal, M Iqbal
Physica Scripta, 2021
Abstract The possibility of relaxation in Quadruple Beltrami states for a system of dusty plasma of opposite polarity dust particles, electrons, and ions has been investigated. The macroscopic magnetic field structures are investigated in alliance with the differential flows of electrons, ions, positively and negatively charged dust grains. For a certain set of Beltrami parameters, it is observed that the system self-organized to Quadruple Beltrami state which is characterized by four eigenvalues. To derive Quadruple Beltrami equation, two different cases are assumed. The system allows a fully diamagnetic structure by considering all the inertial forces. The development of paramagnetic and diamagnetic structures has been observed by just ignoring the inertial effects of electrons. It has been shown that the features (paramagnetic or diamagnetic) of the relaxed structures are significantly modified by the eigenvalues and masses of the oppositely charged dust particles.
Beltrami states in Earth's dusty mesosphere
S. M. Gondal
Physics of Plasmas, 2020
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, M. Iqbal
Physics of Plasmas, 2020
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, A. Shuaib
Contributions to Plasma Physics, 2019
Abstract A possibility of self‐organization of magnetized four‐component dusty plasmas to double Beltrami (DB) state is explored. It is found that for a specific set of Beltrami parameters, the four‐component dusty plasma self‐organizes to DB state. The DB state characterized by two scale parameters may represent a paramagnetic or diamagnetic field structure. The impact of Beltrami parameters, charge and densities of dust grains on formation of self‐organized structures has also been investigated. This study has potential relevance to the formation of large‐scale structures in astrophysical plasmas.
Quadruple Beltrami fields in three component plasmas
S. M. Gondal, M. Iqbal, Ashfaq H. Khosa, G. Murtaza
Physics of Plasmas, 2017
Self-organized field structures in electron-depleted multi-ion dusty plasma
M. Iqbal, S. M. Gondal, A. Shuaib, Qurat-ul-ain
Journal of Plasma Physics, 2015

Publications

1. Title: Beltrami states in Earth’s dusty mesosphere
Authors: S. M. Gondal
Journal: Physics of Plasmas 27, 113703 (2020).
2. Title: The possibility of relaxation in Quadruple Beltrami states in a four-component magneto dusty plasma Author: S. M. Gondal and M. Iqbal
Journal: Physica Scripta 96, 015602 (2020).
3. Title: Quadruple Beltrami fields in electron-depleted multi-ion dusty plasma
Authors: S. M. Gondal, and M. Iqbal
Journal: Physics of Plasmas 27, 083702 (2020).
4. Title: Double Beltrami states and loss of equilibrium in electron, positron and ion Plasmas. Authors: S. M. Gondal, M. Iqbal, Shafa Ullah, M. Asghar and Ashfaq H. Khosa
Journal: Journal of Plasma Physics 85, 905850306 (2019).
5. Title: Formation of large-scale structures in four-component dusty plasmas.
Authors: S. M. Gondal, M. Iqbal, F. Saleem, and A. Shuaib
Journal: Contribution to Plasma Physics (2019). DOI: 10.1002/
6. Title: Quadruple Beltrami field in three component plasmas.
Authors: S. M. Gondal, M. Iqbal, Journal: Physics of Plasmas 24, 062903