arXiv subjects

I. L. Caldas

Publications and source records attributed to I. L. Caldas.

At least 19 recordsLinked to original sources

arXiv2026

The Role of Phase and Spatial Modes in Wave-Induced Plasma Transport

We derive a two-dimensional symplectic map for particle motion at the plasma edge by modeling the electrostatic potential as a superposition of integer spatial harmonics with relative phase shift, then reduce it to a two-wave model to study the transport dependence on the perturbation amplitudes, relative phase, and spatial-mode choice. Using particle transmissivity as a confinement criterion, identical-mode pairs exhibit phase-controlled behavior: anti-phase waves produce destructive interference and strong confinement while in-phase waves add constructively and drive chaotic transport. Mode-mismatched pairs produce richer phase-space structure with higher-order resonances and sticky regions; the transmissivity boundaries become geometrically complex. Box-counting dimensions quantify this: integer dimension smooth boundaries for identical modes versus non-integer fractal-like dimension for distinct modes, demonstrating that phase and spectral content of waves jointly determine whether interference suppresses or promotes transport.

physics.plasm-ph↗

arXiv2024

Larmor radius effect on the control of chaotic transport in tokamaks

We investigate the influence of the finite Larmor radius on the dynamics of guiding-center test particles subjected to an $\mathbf{E} \times \mathbf{B}$ drift in a large aspect-ratio tokamak. For that, we adopt the drift-wave test particle transport model presented by W. Horton [Physics of Plasmas \textbf{5}, 3910 (1998)] and introduce a second-order gyro-averaged extension, which accounts for the finite Larmor radius effect that arises from a spatially varying electric field. Using this extended model, we numerically examine the influence of the finite Larmor radius on chaotic transport and the formation of transport barriers. For non-monotonic plasma profiles, we show that the twist condition of the dynamical system, i.e.,\ KAM theorem's non-degeneracy condition for the Hamiltonian, is violated along a special curve, which, under non-equilibrium conditions, exhibits significant resilience to destruction, thereby inhibiting chaotic transport. This curve acts as a robust barrier to transport and is usually called shearless transport barrier. While varying the amplitude of the electrostatic perturbations, we analyze bifurcation diagrams of the shearless barriers and escape rates of orbits to explore the impact of the finite Larmor radius on controlling chaotic transport. Our findings show that increasing the Larmor radius enhances the robustness of transport barriers, as larger electrostatic perturbation amplitudes are required to disrupt them. Additionally, as the Larmor radius increases, even in the absence of transport barriers, we observe a reduction in the escape rates, indicating a decrease in chaotic transport.

physics.plasm-ph↗

arXiv2024

Shearless effective barriers to chaotic transport induced by even twin islands in nontwist systems

For several decades now it has been known that systems with shearless invariant tori, nontwist Hamiltonian systems, possess barriers to chaotic transport. These barriers are resilient to breakage under perturbation and therefore regions where they occur are natural places to look for barriers to transport. We describe a novel kind of effective barrier that persists after the shearless torus is broken. Because phenomena are generic, for convenience we study the Standard Nontwist Map (SNM), an area-preserving map that violates the twist condition locally in the phase space. The novel barrier occurs in nontwist systems when twin even period islands are present, which happens for a broad range of parameter values in the SNM. With a phase space composed of regular and irregular orbits, the movement of chaotic trajectories is hampered by the existence of both shearless curves, total barriers, and a network of partial barriers formed by the stable and unstable manifolds of the hyperbolic points. Being a degenerate system, the SNM has twin islands and, consequently, twin hyperbolic points. We show that the structures formed by the manifolds intrinsically depend on period parity of the twin islands. For this even scenario the novel structure, named a torus free barrier, occurs because the manifolds of different hyperbolic points form an intricate chain atop a dipole configuration and the transport of chaotic trajectories through the chain becomes a rare event. This structure impacts the emergence of transport, the escape basin for chaotic trajectories, the transport mechanism and the chaotic saddle. The case of odd periodic orbits is different: we find for this case the emergence of transport immediately after the breakup of the last invariant curve, and this leads to a scenario of higher transport, with intricate escape basin boundary and a chaotic saddle with non-uniformly distributed points.

nlin.CD↗

arXiv2024

Isochronous island bifurcations driven by resonant magnetic perturbations in Tokamaks

Recent evidences show that heteroclinic bifurcations in magnetic islands may be caused by the amplitude variation of resonant magnetic perturbations in tokamaks. To investigate the onset of these bifurcations, we consider a large aspect ratio tokamak with an ergodic limiter composed of two pairs of rings that create external primary perturbations with two sets of wave numbers. An individual pair produces hyperbolic and elliptic periodic points, and its associated islands, that are consistent with the Poincaré-Birkhoff fixed point theorem. However, for two pairs producing external perturbations resonant on the same rational surface, we show that different configurations of isochronous island chains may appear on phase space according to the amplitude of the electric currents in each pair of the ergodic limiter. When one of the electric currents increases, isochronous bifurcations take place and new islands are created with the same winding number as the preceding islands. We present examples of bifurcation sequences displaying (a) direct transitions from the island chain configuration generated by one of the pairs to the configuration produced by the other pair, and (b) transitions with intermediate configurations produced by the limiter pairs coupling. Furthermore, we identify shearless bifurcations inside some isochronous islands, originating nonmonotonic local winding number profiles with associated shearless invariant curves.

physics.plasm-ph↗

arXiv2023

Shaping the edge radial electric field to create shearless transport barriers in tokamaks

In tokamak-confined plasmas, particle transport can be reduced by modifying the radial electric field. In this paper, we investigate the influence of both a well-like and a hill-like shaped radial electric field profile on the creation of shearless transport barriers (STBs) at the plasma edge, which are a type of barrier that can prevent chaotic transport and are related to the presence of extreme values in the rotation number profile. For that, we apply an ExB drift model to describe test particle orbits in large aspect-ratio tokamaks. We show how these barriers depend on the electrostatic fluctuation amplitudes and on the width and depth (height) of the radial electric field well-like (hill-like) profile. We find that, as the depth (height) increases, the STB at the plasma edge becomes more resistant to fluctuations, enabling access to an improved confinement regime that prevents chaotic transport. We also present parameter spaces with the radial electric field parameters, indicating the STB existence for several electric field configurations at the plasma edge, for which we obtain a fractal structure at the barrier/non-barrier frontier, typical of quasi-integrable Hamiltonian systems.

physics.plasm-ph↗

arXiv2023

ExB drift particle transport in tokamaks

In tokamaks, modification of the plasma profiles can reduce plasma transport, improving particle confinement. However, this improvement is still not completely understood. In this work, we consider a drift wave test particle model to investigate the influence of the electric and magnetic field profiles on plasma transport. Test particle orbits subjected to ExB drift are numerically integrated and their transport coefficient is obtained. We conclude that sheared profiles reduce particle transport, even for high amplitude perturbations. In particular, nonmonotonic electric and magnetic fields produce shearless transport barriers, which are particularly resistant to perturbations and reduce even more the transport coefficient.

physics.plasm-ph↗

arXiv2023

Plastic neural network with transmission delays promotes equivalence between function and structure

The brain is formed by cortical regions that are associated with different cognitive functions. Neurons within the same region are more likely to connect than neurons in distinct regions, making the brain network to have characteristics of a network of subnetworks. The values of synaptic delays between neurons of different subnetworks are greater than those of the same subnetworks. This difference in communication time between neurons has consequences on the firing patterns observed in the brain, which is directly related to changes in neural connectivity, known as synaptic plasticity. In this work, we build a plastic network of Hodgkin-Huxley neurons in which the connectivity modifications follow a spike-time dependent rule. We define an internal-delay among neurons communicating within the same subnetwork, an external-delay for neurons belonging to distinct subnetworks, and study how these communicating delays affect the entire network dynamics. We observe that the neuronal network exhibits a specific connectivity configuration for each synchronised pattern. Our results show how synaptic delays and plasticity work together to promote the formation of structural coupling among the neuronal subnetworks. We conclude that plastic neuronal networks are able to promote equivalence between function and structure meaning that topology emerges from behaviour and behaviour emerges from topology, creating a complex dynamical process where topology adapts to conform with the plastic rules and firing patterns reflect the changes on the synaptic weights.

q-bio.NC↗

arXiv2022

Shearless bifurcations in particle transport for reversed shear tokamaks

Some internal transport barriers in tokamaks have been related to the vicinity of extrema of the plasma equilibrium profiles. This effect is numerically investigated by considering the guiding-center trajectories of plasma particles undergoing ExB drift motion, considering that the electric field has a stationary nonmonotonic radial profile and an electrostatic fluctuation. In addition, the equilibrium configuration has a nonmonotonic safety factor profile. The numerical integration of the equations of motion yields a symplectic map with shearless barriers. By changing the parameters of the safety factor profile, the appearance, and breakup of these shearless curves are observed. The successive shearless curves breakup and recovering is explained using concepts from bifurcation theory. We also present bifurcation sequences associated to the creation of multiple shearless curves. Physical consequences of scenarios with multiple shearless curves are discussed.

physics.plasm-ph↗

arXiv2022

Biquadratic Nontwist Map: a model for shearless bifurcations

Area-preserving nontwist maps are used to describe a broad range of physical systems. In those systems, the violation of the twist condition leads to nontwist characteristic phenomena, such as reconnection-collision sequences and shearless invariant curves that act as transport barriers in the phase space. Although reported in numerical investigations, the shearless bifurcation, i.e., the emergence scenario of multiple shearless curves, is not well understood. In this work, we derive an area-preserving map as a local approximation of a particle transport model for confined plasmas. Multiple shearless curves are found in this area-preserving map, with the same shearless bifurcation scenario numerically observed in the original model. Due to its symmetry properties and simple functional form, this map is proposed as a model to study shearless bifurcations.

nlin.CD↗

arXiv2022

Internal energy exchanges and chaotic dynamics in an intrinsically coupled system

Intrinsically coupled nonlinear systems present different oscillating components that exchange energy among themselves. A paradigmatic example is the spring pendulum, which displays spring, pendulum, and coupled oscillations. We analyze the energy exchanges among the oscillations, and obtain that it is enhanced for chaotic orbits. Moreover, the highest rates of energy exchange for the coupling occur along the homoclinic tangle of the primary hyperbolic point embedded in a chaotic sea. The results show a clear relation between internal energy exchanges and the dynamics of a coupled system.

nlin.CD↗

arXiv2021

Onset of internal transport barriers in tokamaks

Barriers have been identified in magnetically confined plasmas reducing the particle transport and improving the confinement. One of them, the primary shearless barriers are associated to extrema of non-monotonic plasma profiles. Previously, we identified these barriers in a model described by a map that allows the integration of charged particles motion in drift waves for a long time scale. In this work, we show how the existence of these robust barriers depends on the fluctuation amplitude and on the electric shear. Moreover, we also find control parameter intervals for which these primary barriers onset and break-up are recurrent. Another noticeable feature, in these transitions, is the appearance of a layer of particle trajectory stickiness after the shearless barrier break-up or before its onset. Besides the mentioned primary barriers, we also observe sequences of secondary shearless barriers, not reported before, created and destroyed by a sequence of bifurcations as the main control parameters, the fluctuation amplitude and electric shear, are varied. Furthermore, in these bifurcations, we also find hitherto unknown double and triple secondary shearless barriers which constitute a noticeable obstacle to the chaotic transport.

physics.plasm-ph↗

arXiv2021

Low-dimensional chaos in the single wave model for self-consistent wave-particle Hamiltonian

We analyze nonlinear aspects of the self-consistent wave-particle interaction using Hamiltonian dynamics in the single wave model, where the wave is modified due to the particle dynamics. This interaction plays an important role in the emergence of plasma instabilities and turbulence. The simplest case, where one particle (N = 1) is coupled with one wave (M = 1), is completely integrable, and the nonlinear effects reduce to the wave potential pulsating while the particle either remains trapped or circulates forever. On increasing the number of particles (N = 2, M = 1), integrability is lost and chaos develops. Our analyses identify the two standard ways for chaos to appear and grow (the homoclinic tangle born from a separatrix, and the resonance overlap near an elliptic fixed point). Moreover, a strong form of chaos occurs when the energy is high enough for the wave amplitude to vanish occasionally.

nlin.CD↗

arXiv2021

Transport barriers in symplectic maps

Chaotic transport is a subject of paramount importance in a variety of problems in plasma physics, specially those related to anomalous transport and turbulence. On the other hand, a great deal of information on chaotic transport can be obtained from simple dynamical systems like two-dimensional area-preserving (symplectic) maps, where powerful mathematical results like KAM theory are available. In this work we review recent works on transport barriers in area-preserving maps, focusing on systems which do not obey the so-called twist property. For such systems KAM theory no longer holds everywhere and novel dynamical features show up as non-resistive reconnection, shearless curves and shearless bifurcations. After presenting some general features using a standard nontwist mapping, we consider magnetic field line maps for magnetically confined plasmas in tokamaks.

physics.plasm-ph↗

arXiv2020

Influence of autapses on synchronisation in neural networks with chemical synapses

A great deal of research has been devoted on the investigation of neural dynamics in various network topologies. However, only a few studies have focused on the influence of autapses, synapses from a neuron onto itself via closed loops, on neural synchronisation. Here, we build a random network with adaptive exponential integrate-and-fire neurons coupled with chemical synapses, equipped with autapses, to study the effect of the latter on synchronous behaviour. We consider time delay in the conductance of the pre-synaptic neuron for excitatory and inhibitory connections. Interestingly, in neural networks consisting of both excitatory and inhibitory neurons, we uncover that synchronous behaviour depends on their synapse type. Our results provide evidence on the synchronous and desynchronous activities that emerge in random neural networks with chemical, inhibitory and excitatory synapses where neurons are equipped with autapses.

q-bio.NC↗

arXiv2020

Wave-particle interactions in a long traveling wave tube with upgraded helix

We investigate the interaction of electromagnetic waves and electron beams in a 4 meters long traveling wave tube (TWT). The device is specially designed to simulate beam-plasma experiments without appreciable noise. This TWT presents an upgraded slow wave structure (SWS) that results in more precise measurements and makes new experiments possible. We introduce a theoretical model describing wave propagation through the SWS and validated by the experimental dispersion relation, impedance, phase and group velocities. We analyze nonlinear effects arising from the beam-wave interaction, such as the modulation of the electron beam and the wave growth and saturation process. When the beam current is low, the wave growth coefficient and saturation amplitude follow the linear theory predictions. However, for high values of current, nonlinear space charge effects become important and these parameters deviate from the linear predictions, tending to a constant value. After saturation, we also observe trapping of the beam electrons, which alters the wave amplitude along the TWT.

physics.plasm-ph↗

arXiv2019

Dynamical thermalization in time-dependent Billiards

Numerical experiments of the statistical evolution of an ensemble of non-interacting particles in a time-dependent billiard with inelastic collisions, reveals the existence of three statistical regimes for the evolution of the speeds ensemble, namely, diffusion plateau, normal growth/exponential decay and stagnation. These regimes are linked numerically to the transition from Gauss-like to Boltzmann-like speed distributions. Further, the different evolution regimes are obtained analytically through velocity-space diffusion analysis. From these calculations the asymptotic root mean square of speed, initial plateau, and the growth/decay rates for intermediate number of collisions are determined in terms of the system parameters. The analytical calculations match the numerical experiments and point to a dynamical mechanism for thermalization, where inelastic collisions and a high-dimensional phase space lead to a bounded diffusion in the velocity space towards a stationary distribution function with a kind of reservoir temperature determined by the boundary oscillation amplitude and the restitution coefficient.

nlin.CD↗

arXiv2019

Bistable firing pattern in a neural network model

Excessively high, neural synchronisation has been associated with epileptic seizures, one of the most common brain diseases worldwide. A better understanding of neural synchronisation mechanisms can thus help control or even treat epilepsy. In this paper, we study neural synchronisation in a random network where nodes are neurons with excitatory and inhibitory synapses, and neural activity for each node is provided by the adaptive exponential integrate-and-fire model. In this framework, we verify that the decrease in the influence of inhibition can generate synchronisation originating from a pattern of desynchronised spikes. The transition from desynchronous spikes to synchronous bursts of activity, induced by varying the synaptic coupling, emerges in a hysteresis loop due to bistability where abnormal (excessively high synchronous) regimes exist. We verify that, for parameters in the bistability regime, a square current pulse can trigger excessively high (abnormal) synchronisation, a process that can reproduce features of epileptic seizures. Then, we show that it is possible to suppress such abnormal synchronisation by applying a small-amplitude external current on less than 10% of the neurons in the network. Our results demonstrate that external electrical stimulation not only can trigger synchronous behaviour, but more importantly, it can be used as a means to reduce abnormal synchronisation and thus, control or treat effectively epileptic seizures.

physics.bio-ph↗

arXiv2018

Influence of the Radial Electric Field on the Shearless Transport Barriers in Tokamaks

In tokamaks, internal transport barriers, produced by modifications of the plasma current profile, reduce particle transport and improve plasma confinement. The triggering of the internal transport barriers and their dependence on the plasma profiles is a key nonlinear dynamics problem still under investigation. We consider the onset of shearless invariant curves inside the plasma which create internal transport barriers. A non-integrable drift-kinetic model is used to describe particle transport driven by drift waves and to investigate these shearless barriers onset in tokamaks. We show that for some currently observed plasma profiles shearless particle transport barriers can be triggered by properly modifying the electric field profile and the influence of non-resonant modes in the barriers onset. In particular, we show that a broken barrier can be restored by enhancing non-resonant modes.

physics.plasm-ph↗