arXiv subjects

Hamdi M. Abdelhamid

Publications and source records attributed to Hamdi M. Abdelhamid.

8 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↗

arXiv2024

Hamiltonian formulation of X-point collapse in an extended magnetohydrodynamics framework

The study of X-point collapse in magnetic reconnection has witnessed extensive research in the context of space and laboratory plasmas. In this paper, a recently derived mathematical formulation of X-point collapse applicable in the regime of extended magnetohydrodynamics (XMHD) is shown to possess a noncanonical Hamiltonian structure composed of five dynamical variables inherited from its parent model. The Hamiltonian and the noncanonical Poisson bracket are both derived, and the latter is shown to obey the requisite properties of antisymmetry and the Jacobi identity (an explicit proof of the latter is provided). In addition, the governing equations for the Casimir invariants are presented, and one such solution is furnished. The above features can be harnessed and expanded in future work, such as developing structure-preserving integrators for this dynamical system.

physics.plasm-ph↗

arXiv2016

Nonlinear Helicons ---an analytical solution elucidating multi-scale structure

The helicon waves exhibit varying characters depending on plasma parameters, geometry, and wave numbers. Here we elucidate an intrinsic multi-scale property embodied by the combination of dispersive effect and nonlinearity. The extended magnetohydrodynamics model (exMHD) is capable of describing wide range of parameter space. By using the underlying Hamiltonian structure of exMHD, we construct an exact nonlinear solution which turns out to be a combination of two distinct modes, the helicon and Trivelpiece-Gould (TG) waves. In the regime of relatively low frequency or high density, however, the combination is made of the TG mode and an ion cyclotron wave (slow wave). The energy partition between these modes is determined by the helicities carried by the wave fields.

physics.plasm-ph↗

arXiv2016

Extended MHD turbulence and its applications to the solar wind

Extended MHD is a one-fluid model that incorporates two-fluid effects such as electron inertia and the Hall drift. This model is used to construct fully nonlinear Alfvénic wave solutions, and thereby derive the kinetic and magnetic spectra by resorting to a Kolmogorov-like hypothesis based on the constant cascading rates of the energy and generalized helicities of this model. The magnetic and kinetic spectra are derived in the ideal $\left(k < 1/λ_i\right)$, Hall $\left(1/λ_i < k < 1/λ_e \right)$, and electron inertia $\left(k > 1/λ_e\right)$ regimes; $k$ is the wavenumber and $λ_s = c/ω_{p s}$ is the skin depth of species `$s$'. In the Hall regime, it is shown that the emergent results are fully consistent with previous numerical and analytical studies, especially in the context of the solar wind. The focus is primarily on the electron inertia regime, where magnetic energy spectra with power-law indexes of $-11/3$ and $-13/3$ are always recovered. The latter, in particular, is quite close to recent observational evidence from the solar wind with a potential slope of approximately $-4$ in this regime. It is thus plausible that these spectra may constitute a part of the (extended) inertial range, as opposed to the standard `dissipation' range paradigm.

physics.plasm-ph↗

arXiv2016

Multi-region relaxed Hall magnetohydrodynamics with flow

The recent formulations of multi-region relaxed magnetohydrodynamics (MRxMHD) have generalized the famous Woltjer-Taylor states by incorporating a collection of "ideal barriers" that prevent global relaxation, and flow. In this paper, we generalize MRxMHD with flow to include Hall effects (MRxHMHD), and thereby obtain the partially relaxed counterparts of the famous double Beltrami states as a special subset. The physical and mathematical consequences arising from the introduction of the Hall term are also presented. We demonstrate that our results (in the ideal MHD limit) constitute an important subset of ideal MHD equilibria, and we compare our approach against other variational principles proposed for deriving the partially relaxed states.

physics.plasm-ph↗

arXiv2015

Nonlinear Alfvén waves in extended magnetohydrodynamics

Large-amplitude Alfvén waves are observed in various systems in space and laboratories, demonstrating an interesting property that the wave shapes are stable even in the nonlinear regime. The ideal magnetohydrodynamics (MHD) model predicts that an Alfvén wave keeps an arbitrary shape constant when it propagates on a homogeneous ambient magnetic field. However, such arbitrariness is an artifact of the idealized model that omits the dispersive effects. Only special wave forms, consisting of two component sinusoidal functions, can maintain the shape; we derive fully nonlinear Alfvén waves by an extended MHD model that includes both the Hall and electron inertia effects. Interestingly, these \small-scale effects" change the picture completely; the large-scale component of the wave cannot be independent of the small scale component, and the coexistence of them forbids the large scale component to have a free wave form. This is a manifestation of the nonlinearity-dispersion interplay, which is somewhat different from that of solitons.

physics.plasm-ph↗

arXiv2015

Hamiltonian Formalism of Extended Magnetohydrodynamics

The extended magnetohydrodynamics (MHD) system, including the Hall effect and the electron inertia effect, has a Hamiltonian structure embodied by a noncanonical Poisson algebra on an infinite-dimensional phase space. A nontrivial part of the formulation is the proof of Jacobi's identity for the Poisson bracket. We unearth a basic Lie algebra that generates the Poisson bracket. A class of similar Poisson algebra may be generated by the same Lie algebra, which encompasses the Hall MHD system and inertial MHD system.

physics.plasm-ph↗