arXiv subjects

Abeer A. Mahmoud

Publications and source records attributed to Abeer A. Mahmoud.

5 recordsLinked to original sources

arXiv2026

Structural Requirements for Ion-Acoustic Double Layers: A Parametric Perturbation Analysis of the Maxwellian Limit

Standard Maxwellian plasmas exhibit a mathematical \textit{rigidity}, possessing insufficient degrees of freedom to support electrostatic double layers (DLs) and yielding only soliton solutions. This study investigates the hypothesis that the formation of DLs is a generic consequence of breaking this structural rigidity through parametric perturbation. By introducing two independent continuous control parameters, $δ_1$ and $δ_2$, into the electron distribution, we demonstrate that DLs are a structural property of any plasma model that relaxes the strict Maxwellian constraint. Through a Gardner small-amplitude expansion, we analytically prove that a perturbation must modify both the quadratic and cubic density coefficients to decouple the nonlinear structure and generate physical, supersonic double layers, deriving small-amplitude acoustic-limit threshold conditions of $δ_1 > 1$ and $δ_2 > 7/3$. We show that these theoretical boundaries broaden for large-amplitude, nonlinear structures. By mapping the exact existence regions of DLs in phase space, we demonstrate how higher-order terms relax the weak-amplitude limits, confirming that the Maxwellian state represents a singular point where the DL solution collapses.

physics.plasm-ph↗

arXiv2026

Incompressible Extended Magnetohydrodynamics Waves: Implications of Electron Inertia

This paper explores plasma wave modes using the extended magnetohydrodynamics (XMHD) model, incorporating Hall drift and electron inertia effects. We utilize the geometric optics ansatz to study perturbed quantities, with a focus on incompressible systems. Our research concludes with the derivation of the dispersion relation for incompressible XMHD and the associated eigenvector solutions, offering new perspectives on plasma wave behavior under these extended scenarios. The dispersion relation shows distinct ion cyclotron and whistler wave branches, with characteristic saturation at the ion and electron gyrofrequencies, respectively. Comparisons between Hall MHD and XMHD demonstrate that XMHD provides a more accurate representation of plasma dynamics, especially at higher wave numbers, bridging the gap between simplified models and comprehensive two-fluid descriptions and smoothing out singularities present in Hall MHD solutions and capturing more physics of the full two-fluid model.

physics.plasm-ph↗

arXiv2010

Ion-Acoustic Waves in Unmagnitized Collisionless Weakly Relativistic Plasma using Time-Fractional KdV Equation

The reductive perturbation method has been employed to derive the Korteweg-de Vries (KdV) equation for small but finite amplitude electrostatic ion-acoustic waves in unmagnitized collisionless weakly relativistic warm plasma. The Lagrangian of the time fractional KdV equation is used in similar form to the Lagrangian of the regular KdV equation. The variation of the functional of this Lagrangian leads to the Euler-Lagrange equation that leads to the time fractional KdV equation. The Riemann-Liouvulle definition of the fractional derivative is used to describe the time fractional operator in the fractional KdV equation. The variational-iteration method given by He is used to solve the derived time fractional KdV equation. The calculations of the solution with initial condition A0*sech(cx)^2 are carried out. The result of the present investigation may be applicable to some plasma environments, such as ionosphere.

physics.plasm-ph↗

arXiv2010

Time-Fractional KdV Equation Describing the Propagation of Electron-Acoustic Waves in plasma

The reductive perturbation method has been employed to derive the Korteweg-de Vries (KdV) equation for small but finite amplitude electron-acoustic waves. The Lagrangian of the time fractional KdV equation is used in similar form to the Lagrangian of the regular KdV equation. The variation of the functional of this Lagrangian leads to the Euler-Lagrange equation that leads to the time fractional KdV equation. The Riemann-Liouvulle definition of the fractional derivative is used to describe the time fractional operator in the fractional KdV equation. The variational-iteration method given by He is used to solve the derived time fractional KdV equation. The calculations of the solution with initial condition A0*sech(cx)^2 are carried out. The result of the present investigation may be applicable to some plasma environments, such as the Earth's magnetotail region.

physics.plasm-ph↗

arXiv2010

Solution of Time-Fractional Korteweg-de Vries Equation in warm Plasma

The reductive perturbation method has been employed to derive the Korteweg-de Vries (KdV) equation for small but finite amplitude ion-acoustic waves. The Lagrangian of the time fractional KdV equation is used in similar form to the Lagrangian of the regular KdV equation. The variation of the functional of this Lagrangian leads to the Euler-Lagrange equation that leads to the time fractional KdV equation. The Riemann-Liouvulle definition of the fractional derivative is used to describe the time fractional operator in the fractional KdV equation. The variational-iteration method given by He is used to solve the derived time fractional KdV equation. The calculations of the solution with initial condition A0*sech(cx)^2 are carried out. The result of the present investigation may be applicable to some plasma environments, such as ionosphere.

physics.plasm-ph↗