arXiv subjects

Yves Elskens

Publications and source records attributed to Yves Elskens.

At least 19 recordsLinked to original sources

arXiv2025

Isochronous bifurcations dependence on the driving mode phase shift in two-harmonic standard maps

Some dynamical properties of nonlinear coupled systems can be described by the two-harmonic standard map, a two-dimensional area-preserving system with two parameters, where two distinct arbitrary resonant modes compete. Usually, the initial phase of the resonant modes is considered to be null. In this paper, we consider a non-null phase shift between the two competing isochronous modes that form the system. We observe that a non-zero phase shift alters the phase space, changing the stability and positions of the fixed points. Furthermore, the phase shift can change the dominant mode and create intermediate modes between the main ones. Lastly, we analyze the effect of the phase shift on the onset of secondary shearless curves in the phase space. Thus, different phase shifts result in various scenarios in which secondary shearless curves emerge in the phase space.

nlin.CD↗

arXiv2025

Hamiltonian chaos for one particle with two waves: Self-consistent dynamics

A simple model of wave-particle interaction is studied in its self-consistent form, that is, where the particles are allowed to feedback on the waves dynamics. We focus on the configurations of locked solutions (equilibria) and how the energy-momentum exchange mechanism induces chaos in the model. As we explore the system, we analyse the mathematical structure that gives rise to locked states and how the model's non-linearity enables multiple equilibrium amplitudes for waves. We also explain the predominance of regularity as we vary the control parameters and the mechanism behind the emergence of chaos under limited parameter choices.

nlin.CD↗

arXiv2025

Non-autonomous standard nontwist map

Area-preserving nontwist maps locally violate the twist condition, giving rise to shearless curves. Nontwist systems appear in different physical contexts, such as plasma physics, climate physics, classical mechanics, etc. Generic properties of nontwist maps are captured by the standard nontwist map, which depends on a convection parameter $a$ and a modulation coefficient $b$. In the spirit of non-autonomous systems, we consider the standard nontwist map (SNM) with a linearly increasing modulation coefficient, and we investigate the evolution of an ensemble of points on the phase space that initially lies on the shearless invariant curve in the initial state, called shearless snapshot torus. Differently from the SNM with constant parameters -- where we can see different scenarios of collision/annihilation of periodic orbits leading to global transport, depending on the region in the parameter space -- for the SNM with time-dependent parameters, the route to chaos is not only related to the path in the $(a, b)$ parameter space, but also to the scenario of the evolution of parameter $b_n$. In this work, we identify power-law relationships between key parameters for the chaotic transition and the iteration time. Additionally, we analyze system reversibility during the chaotic transition and demonstrate an extra transport, where parameter variation modifies the diffusion coefficient.

physics.comp-ph↗

arXiv2024

Identifying ballistic modes via Poincar\'e sections

Exploring chaotic systems via Poincar\'e sections has proven essential in dynamical systems, yet measuring their characteristics poses challenges to identify the various dynamical regimes considered. In this paper, we propose a new approach that uses image processing to distinguish chaotic and regular regions of area-preserving dynamics, and then classify the transport regime. We characterize different transport regimes in the standard map with the proposed method based on image reconstruction techniques, identifying the superdiffusion much faster than the usual mean square displacement method. The procedure is also applied to a two-wave, time-dependent Hamiltonian to investigate superdiffusion in function of two parameters.

nlin.CD↗

arXiv2024

Benchmark: Tao's symplectic integration method

A benchmark test was conducted for a new symplectic integration method originally developed by Molei Tao. The method raises interest due to its explicit evolution equation, with applicability to both separable and non-separable Hamiltonian systems, and an easy-to-implement, easily generalizable algorithm. In order to compare the method with other, more well-known methods, namely St\"{o}rmer-Verlet and Runge-Kutta, we conducted a series of benchmark tests comparing their performance in terms of CPU time, system invariants functions conservation, and numerical symplectic area conservation. Overall, it was found that despite being slower than the more optimized Runge-Kutta-Cash-Karp, Tao's method presents a similar performance to St\"{o}rmer-Verlet, with the extra perk of being more generic and not requiring the use of implicit equations for the evolution of the equations of motion.

physics.comp-ph↗

arXiv2023

Island myriads in periodic potentials

A phenomenon of emergence of stability islands in phase-space is reported for two periodic potentials with tiling symmetries, one square and the other hexagonal, inspired by bidimensional Hamiltonian models of optical lattices. The structures found, here termed as island myriads, resemble web-tori with notable fractality and arise at energy levels reaching that of unstable equilibria. In general, the myriad is an arrangement of concentric island chains with properties relying on the translational and rotational symmetries of the potential functions. In the square system, orbits within the myriad come in isochronous pairs and can have different periodic closure, either returning to their initial position or jumping to identical sites in neighbor cells of the lattice, therefore impacting transport properties. As seen when compared to a more generic case, i.e. the rectangular lattice, the breaking of square symmetry disrupts the myriad even for small deviations from its equilateral configuration. For the hexagonal case, the myriad was found but in attenuated form, mostly due to extra instabilities in the potential surface that prevent the stabilization of orbits forming the chains.

nlin.PS↗

arXiv2023

Shearless curve breakup in the biquadratic nontwist map

Nontwist area-preserving maps violate the twist condition along shearless invariant curves, which act as transport barriers in phase space. Recently, some plasma models have presented multiple shearless curves in phase space and these curves can break up independently. In this paper, we describe the different shearless curve breakup scenarios of the so-called biquadratic nontwist map, a recently proposed area-preserving map derived from a plasma model, that captures the essential behavior of systems with multiple shearless curves. Three different scenarios are found and their dependence on the system parameters is analyzed. The results indicate a relation between shearless curve breakup and periodic orbit reconnection-collision sequences. In addition, even after a shearless curve breakup, the remaining curves inhibit global transport.

nlin.CD↗

arXiv2022

Fractal and Wada escape basins in the chaotic particle drift motion in tokamaks

The ${\bf E}\times{\bf B}$ drift motion of particles in tokamaks provides valuable information on the turbulence-driven anomalous transport. One of the characteristic features of the drift motion dynamics is the presence of chaotic orbits for which the guiding center can experience large-scale drifts. If one or more exits are placed within that chaotic orbit, the corresponding escape basins structure is complicated and, indeed, exhibits fractal structures. We investigate those structures through a number of numerical diagnostics, tailored to quantify the final-state uncertainty related to the fractal escape basins. We estimate the escape basin boundary dimension through the uncertainty exponent method, and quantify final-state uncertainty by the basin entropy and the basin boundary entropy. Finally, we describe the so-called Wada property, for the case of three or more escape basins. This property is verified both qualitatively and quantitatively, using a grid approach.

physics.plasm-ph↗

arXiv2022

Diffusion transitions in a 2D periodic lattice

Spatial diffusion of particles in periodic potential models has provided a good framework for studying the role of chaos in global properties of classical systems. Here a bidimensional "soft" billiard, classically modeled from an optical lattice hamiltonian system, is used to study diffusion transitions with the control parameters variation. Sudden transitions between normal and ballistic regimes are found and characterized by inspection of the topological changes in phase-space. Transitions correlated with increases in global stability area are shown to occur for energy levels where local maxima points become accessible, deviating trajectories approaching it. These instabilities promote a slowing down of the dynamics and an island myriad bifurcation phenomenon, along with the suppression of long flights within the lattice. Other diffusion regime variations occurring during small intervals of control parameters are shown to be related to the emergence of a set of orbits with long flights, thus altering the total average displacement for long integration times but without global changes in phase-space.

cond-mat.stat-mech↗

arXiv2021

Time simulation of the nonlinear wave-particle interaction in meters long traveling-wave tubes

We propose a multi-particle self-consistent Hamiltonian (derived from an N-body description) that is applicable for periodic structures such as traveling-wave tubes (TWTs), gyrotrons, free-electron lasers, or particle accelerators. We build a 1D symplectic multi-particle algorithm to simulate the nonlinear wave-particle interaction in the time domain occurring in an experimental 3-meters long helix TWT. Our algorithm is efficient thanks to a drastic reduction model. A 3D helix version of our reduction model is provided. Finally, we establish an explicit expression of the electromagnetic power in the time domain and in non-monochromatic (non-"continuous waveform") regime.

physics.plasm-ph↗

arXiv2020

Hard-core collisional dynamics in the hamiltonian mean-field model

We consider a modification of the well studied Hamiltonian Mean-Field model by introducing a hard-core point-like repulsive interaction and propose a numerical integration scheme to integrate numerically its dynamics. Our results show that the outcome of the initial violent relaxation is altered, and also that the phase-diagram is modified with a critical temperature at a higher value than in the non-collisional counterpart.

cond-mat.stat-mech↗

arXiv2020

Microscopic foundations of kinetic plasma theory: The relativistic Vlasov--Maxwell equations and their radiation-reaction-corrected generalization

It is argued that the relativistic Vlasov--Maxwell equations of the kinetic theory of plasma approximately describe a relativistic system of $N$ charged point particles interacting with the electromagnetic Maxwell fields in a Bopp--Landé--Thomas--Podolsky (BLTP) vacuum, provided the microscopic dynamics lasts long enough.The purpose of this work is not to supply an entirely rigorous vindication, but to lay down a conceptual road map for the microscopic foundations of the kinetic theory of special-relativistic plasma, and to emphasize that a rigorous derivation seems feasible. Rather than working with a BBGKY-type hierarchy of $n$-point marginal probability measures, the approach proposed in this paper works with the distributional PDE of the actual empirical 1-point measure, which involves the actual empirical 2-point measure in a convolution term.The approximation of the empirical 1-point measure by a continuum density, and of the empirical 2-point measure by a (tensor) product of this continuum density with itself, yields a finite-$N$ Vlasov-like set of kinetic equations which includes radiation-reaction and nontrivial finite-$N$ corrections to the Vlasov--Maxwell-BLTP model. The finite-$N$ corrections formally vanish in a mathematical scaling limit $N\to\infty$ in which charges $\propto 1/\surd{N}$. The radiation-reaction term vanishes in this limit, too. The subsequent formal limit sending Bopp's parameter $\varkappa\to\infty$ yields the Vlasov--Maxwell model.

physics.plasm-ph↗

arXiv2019

Critical Exponent for the Lyapunov Exponent and Phase Transitions -- The Generalized Hamiltonian Mean-Field Model

We compute semi-analytic and numerical estimates for the largest Lyapunov exponent in a many-particle system with long-range interactions, extending previous results for the Hamiltonian Mean Field model with a cosine potential. Our results evidence a critical exponent associated to a power law decay of the largest Lyapunov exponent close to second-order phase-transitions, close to the same value as for the cosine Hamiltonian Mean Field model, suggesting the possible universality of this exponent. We also show that the exponent for first-order phase transitions has a different value from both theoretical and numerical estimates.

cond-mat.stat-mech↗

arXiv2019

DIMOHA: A Time-Domain Algorithm for Traveling-Wave Tube Simulations

To simulate traveling-wave tubes (TWTs) in time domain and more generally the wave-particle interaction in vacuum devices, we developed the DIscrete MOdel with HAmiltonian approach (dimoha) as an alternative to current particle-in-cell (PIC) and frequency approaches. Indeed, it is based on a longitudinal N-body Hamiltonian approach satisfying Maxwell's equations. Advantages of dimoha comprise: (i) it allows arbitrary waveform (not just field envelope), including continuous waveform (CW), multiple carriers or digital modulations (shift keying); (ii) the algorithm is much faster than PIC codes thanks to a field discretization allowing a drastic degree-of-freedom reduction, along with a robust symplectic integrator; (iii) it supports any periodic slow-wave structure design such as helix or folded waveguides; (iv) it reproduces harmonic generation, reflection, oscillation and distortion phenomena; (v) it handles nonlinear dynamics, including intermodulations, trapping and chaos. dimoha accuracy is assessed by comparing it against measurements from a commercial Ku-band tapered helix TWT and against simulations from a sub-THz folded waveguide TWT with a staggered double-grating slow-wave structure. The algorithm is also tested for multiple-carriers simulations with success.

physics.plasm-ph↗

arXiv2019

Cross-field chaotic transport of electrons by $\vec E \times \vec B$ electron drift instability in Hall thrusters

One special interest for the industrial development of Hall thruster is characterizing the anomalous cross-field electron transport observed after the channel exit. Since the ionization efficiency is more than 90%, the neutral atom density in that domain is so low that the electron collisions cannot explain the high electron flux observed experimentally. Indeed this is 100 times higher than the collisional transport. In Hall thruster geometry, as ions are not magnetized the electric and magnetic field configuration creates a huge difference in drift velocity between electrons and ions, which generates electron cyclotron drift instability or $\vec E \times \vec B$ electron drift instability. Here we are focusing on collision-less chaotic transport of electrons by those unstable modes generated by $\vec E \times \vec B$ drift instability. We found that in presence of these electrostatic modes electron dynamics become chaotic. They gain energy from the background waves which increases electron temperature along perpendicular direction by a significant amount, $T_{\rm perp}/T_{\rm parallel}\sim 4$, and a significant amount of crossfield electron transport is observed along the axial direction.

physics.plasm-ph↗

arXiv2019

Universality of the Abraham-Minkowski dilemma for photon momenta beyond dielectric materials

The authors) Whenever light is slowed down, for any cause, two different formulas give its momentum. For dielectrics, the coexistence of those momenta was the heart of the century-old Abraham-Minkowski dilemma, recently resolved. We demonstrate that this framework extends to momentum exchange in wave-particle interaction; in particular to Langmuir waves for Landau damping and to vacuum waveguides of electron tubes (metallic slow-wave structures). Focussing on the latter, we show that the dilemma resolution is not limited to discriminating between kinematic and canonical momenta but also involves a non-negligible momentum flux from Maxwell's electromagnetic stress. The existence of two momenta in materials, plasmas, and waveguides, for which light velocity modification has entirely different origin, points to the universality of the Abraham-Minkowski dilemma.

physics.plasm-ph↗

arXiv2018

Basic microscopic plasma physics from N-body mechanics

Computing is not understanding. This is exemplified by the multiple and discordant interpretations of Landau damping still present after seventy years. For long deemed impossible, the mechanical N-body description of this damping, not only enables its rigorous and simple calculation, but makes unequivocal and intuitive its interpretation as the synchronization of almost resonant passing particles. This synchronization justifies mechanically why a single formula applies to both Landau growth and damping. As to the electrostatic potential, the phase mixing of many beam modes produces Landau damping, but it is unexpectedly essential for Landau growth too. Moreover, collisions play an essential role in collisionless plasmas. In particular, Debye shielding results from a cooperative dynamical self-organization process, where "collisional" deflections due to a given electron diminish the apparent number of charges about it. The finite value of exponentiation rates due to collisions is crucial for the equivalent of the van Kampen phase mixing to occur in the N-body system. The N-body approach incorporates spontaneous emission naturally, whose compound effect with Landau damping drives a thermalization of Langmuir waves. O'Neil's damping with trapping typical of initially large enough Langmuir waves results from a phase transition. As to collisional transport, there is a smooth connection between impact parameters where the two-body Rutherford picture is correct, and those where a collective description is mandatory. The N-body approach reveals two important features of the Vlasovian limit: it is singular and it corresponds to a renormalized description of the actual N-body dynamics.

physics.plasm-ph↗

arXiv2018

The Traveling-Wave Tube in the History of Telecommunication

The traveling-wave tube is a critical subsystem for satellite data transmission. Its role in the history of wireless communications and in the space conquest is significant, but largely ignored, even though the device remains widely used nowadays. This paper present, albeit non-exhaustively, circumstances and contexts that led to its invention, and its part in the worldwide (in particular in Europe) expansion of TV broadcasting via microwave radio-relays and satellites. We also discuss its actual contribution to space applications and its conception. The originality of this paper comes from the wide period covered (from first slow-wave structures in 1889 to present space projects) and from connection points made between this device and commercial exploitations. The appendix deals with an intuitive pedagogical description of the wave-particle interaction.

physics.hist-ph↗