arXiv subjects

Xavier Leoncini

Publications and source records attributed to Xavier Leoncini.

At least 19 recordsLinked to original sources

arXiv2025

Magnetically confined charged particles: From steep density profiles to the breaking of the adiabatic invariant

This study examines the stability of Vlasov equilibrium solutions for magnetically confined plasmas, derived through the principle of maximum entropy. By treating the toroidal limit as a perturbation from an analytical cylindrical solution, we demonstrate that these equilibria align well with the inviscid magnetohydrodynamic (MHD) description. Using the aspect ratio as a perturbation parameter, we compute particle trajectories sampled from the kinetic equilibrium distribution, confirming the overall stability of the solutions. However, under burning plasma conditions, chaotic dynamics emerge for particles with supra-thermal and even thermal energies. This destroys the adiabatic invariance of the magnetic moment. The exact consequences are unclear, but they could undermine the foundational assumptions of gyrokinetic modelling in burning plasmas. Nevertheless, these results suggest the possibility of unaccounted transport losses in future burning plasma operations. The interplay between turbulence and energetic particles in the presence of Hamiltonian chaos certainly warrants further investigation.

physics.plasm-ph↗

arXiv2022

Full Self-Consistent Vlasov-Maxwell Solution

Full self-consistent stationary Vlasov-Maxwell solutions of magnetically confined plasmas are built for systems with cylindrical symmetries. The stationary solutions are thermodynamic equilibrium solutions. These are obtained by computing the equilibrium distribution function resulting from maximizing the entropy and closing the equations with source terms that are then computed by using the obtained distribution. This leads to a self-consistent problem corresponding to solving a set of two coupled second order non-linear differential equations. Relevant plasma parameters are introduced and a bifurcation leading to an improvement of plasma confinement is shown. Conversely in the improved confinement setting, we exhibit the emergence of a separatrix in the integrable motion of a charged particles.

physics.plasm-ph↗

arXiv2021

Fast collective oscillations and clustering phenomena in an antiferromagnetic mean-field model

We study the out-of-equilibrium properties of the antiferromagnetic Hamiltonian Mean-Field model at low energy. In this regime, the Hamiltonian dynamics exhibits the presence of a stationary state where the rotators are gathered in a bicluster. This state is not predicted by equilibrium statistical mechanics in the microcanonical ensemble. Performing a low kinetic energy approximation, we derive the explicit expression of the magnetization vector as a function of time. We find that the latter displays coherent oscillations, and we show numerically that the probability distribution for its phase is bimodal or quadrimodal. We then look at the individual rotator dynamics as a motion in an external time-dependent potential, given by the magnetization. This dynamics exhibits two distinct time scales, with the fast one associated to the oscillations of the global magnetization vector. Performing an average over the fast oscillations, we derive an expression for the effective force acting on the individual rotator. This force is always bimodal, and determines a low frequency oscillation of the rotators. Our approach leads to a self-consistent theory linking the time-dependence of the magnetization to the motion of the rotators, providing a heuristic explanation for the formation of the bicluster.

cond-mat.stat-mech↗

arXiv2020

Growth of a tree with allocations rules: Part 2 Dynamics

Following up on a previous work we examine a model of transportation network in some source-sink flow paradigm subjected to growth and resource allocation. The model is inspired from plants, and we add rules and factors that are analogous to what plants are subjected to. We study how different resource allocation schemes affect the tree and how the schemes interact with additional factors such as embedding the network into a 3D space and applying gravity or shading. The different outcomes are discussed. PACS. 05.45.-a Nonlinear dynamics and chaos-05.65.+b Self-organized systems

nlin.AO↗

arXiv2019

Influence of toroidal flow on stationary density of collisionless plasmas

Starting from the given passive particle equilibrium particle cylindrical profiles, we built self-consistent stationary conditions of the Maxwell-Vlasov equation at thermodynamic equilibrium with non-flat density profiles. The solutions to the obtained equations are then discussed. It appears that the presence of an azimuthal (poloidal) flow in the plasma can insure radial confinement, while the presence of a longitudinal (toroidal) flow can enhance greatly the confinement. Moreover in the global physically reasonable situation, we find that no unstable point can emerge in the effective integrable Hamiltonian of the individual particles, hinting at some stability of the confinement when considering a toroidal geometry in the large aspect ratio limit.

physics.plasm-ph↗

arXiv2019

Growth of a tree with allocations rules: Part 1 Kinematics

A non-local model describing the growth of a tree-like transportation network with given allocation rules is proposed. In this model we focus on tree like networks, and the network transports the very resource it needs to build itself. Some general results are given on the viability tree-like networks that produce an amount of resource based on its amount of leaves while having a maintenance cost for each node. Some analytical studies and numerical surveys of the model in "simple" situations are made. The different outcomes are discussed and possible extensions of the model are then discussed.

nlin.AO↗

arXiv2018

Tailoring steep density profile with unstable points

The mesoscopic properties of a plasma in a cylindrical magnetic field are investigated from the view point of test-particle dynamics. When the system has enough time and spatial symmetries, a Hamiltonian of a test particle is completely integrable and can be reduced to a single degree of freedom Hamiltonian for each initial state. The reduced Hamiltonian sometimes has unstable fixed points (saddle points) and associated separatrices. To choose among available dynamically compatible equilibrium states of the one particle density function of these systems we use a maximum entropy principle and discuss how the unstable fixed points affect the density profile or a local pressure gradient, and are able to create a steep profile that improves plasma confinement.

physics.plasm-ph↗

arXiv2016

Study on creation and destruction of transport barriers via effective safety factors for energetic particles

Charged particles with low kinetic energy move along magnetic field lines, but so do not energetic particles. We investigate the topological structure changes in the phase space of energetic particles with respect to the magnetic one. For this study cylindrical magnetic fields with non-monotonic safety factors that induce the magnetic internal transport barrier are considered. We show that the topological structure of the magnetic field line and of the particle trajectories can be quite different. We explain this difference using the concept of effective particle $q$-profile. Using this notion we can investigate the location and existence of resonances for particle orbits that are different from the magnetic ones. These are examined both numerically by integrating an equation of motion and theoretically by use of Alfvén's guiding center theory and by use of the effective reduced Hamiltonian for the integrable unperturbed system. It is clarified that, for the energetic particles, the grad $B$ drift effect shifts the resonances and the drift induced by curvature of the magnetic field line leads to the vanishing of the resonances. As a result, we give two different mechanisms that lead to the creation of transport barriers for energetic particles in the region where the magnetic field line is chaotic.

nlin.CD↗

arXiv2016

Full particle orbit effects in regular and stochastic magnetic fields

We present a numerical study of charged particle motion in a time-independent magnetic field in cylindrical geometry. The magnetic field model consists of an unperturbed reversed-shear helical part and a perturbation consisting of a superposition of modes. Contrary to most of the previous studies, the particle trajectories are computed by directly solving the full Lorentz force equations of motion in a six-dimensional phase space using a sixth-order, implicit, symplectic Gauss-Legendre method. The level of stochasticity in the particle orbits is diagnosed using averaged, effective Poincare sections. It is shown that when only one mode is present the particle orbits can be stochastic even though the magnetic field line orbits are not stochastic. The lack of integrability of the particle orbits in this case is related to separatrix crossing and the breakdown of the global conservation of the magnetic moment. Some perturbation consisting of two modes creates resonance overlapping, leading to Hamiltonian chaos in magnetic field lines. Then, the particle orbits exhibit a nontrivial dynamics depending on their energy and pitch angle. It is shown that the regions where the particle motion is stochastic decrease as the energy increases. The non-monotonicity of the $q$-profile implies the existence of magnetic ITBs which correspond to shearless flux surfaces located in the vicinity of the $q$-profile minimum. It is shown that depending on the energy, these magnetic ITBs might or might not confine particles. That is, magnetic ITBs act as an energy-dependent particle confinement filter. Magnetic field lines in reversed-shear configurations exhibit topological bifurcations due to separatrix reconnection. We show that a similar but more complex scenario appears in the case of particle orbits that depends in a non-trivial way on the energy and pitch angle of the particles.

nlin.CD↗

arXiv2016

Slowing down of so-called chaotic states: "Freezing" the initial state

The so-called chaotic states that emerge on the model of $XY$ interacting on regular critical range networks are analyzed. Typical time scales are extracted from the time series analysis of the global magnetization. The large spectrum confirms the chaotic nature of the observable, anyhow different peaks in the spectrum allows for typical characteristic time-scales to emerge. We find that these time scales $τ(N)$ display a critical slowing down, i.e they diverge as $N\rightarrow\infty$. The scaling law is analyzed for different energy densities and the behavior $τ(N)\sim\sqrt{N}$ is exhibited. This behavior is furthermore explained analytically using the formalism of thermodynamic-equations of the motion and analyzing the eigenvalues of the adjacency matrix.

cond-mat.stat-mech↗

arXiv2015

Anomalous transport and observable average in the standard map

The distribution of finite time observable averages and transport in low dimensional Hamiltonian systems is studied. Finite time observable average distributions are computed, from which an exponent $α$ characteristic of how the maximum of the distributions scales with time is extracted. To link this exponent to transport properties, the characteristic exponent $μ(q)$ of the time evolution of the different moments of order $q$ related to transport are computed. As a testbed for our study the standard map is used. The stochasticity parameter $K$ is chosen so that either phase space is mixed with a chaotic sea and islands of stability or with only a chaotic sea. Our observations lead to a proposition of a law relating the slope in $q=0$ of the function $μ(q)$ with the exponent $α$.

nlin.CD↗

arXiv2015

Emergence of a collective crystal in a classical system with long-range interactions

A one-dimensional long-range model of classical rotators with an extended degree of complexity, as compared to paradigmatic long-range systems, is introduced and studied. Working at constant density, in the thermodynamic limit one can prove the statistical equivalence with the Hamiltonian Mean Field model (HMF) and $α$-HMF: a second order phase transition is indeed observed at the critical energy threshold $\varepsilon_c=0.75$. Conversely, when the thermodynamic limit is performed at infinite density (while keeping the length of the hosting interval $L$ constant), the critical energy $\varepsilon_c$ is modulated as a function of $L$. At low energy, a self-organized collective crystal phase is reported to emerge, which converges to a perfect crystal in the limit $ε\rightarrow 0$. To analyze the phenomenon, the equilibrium one particle density function is analytically computed by maximizing the entropy. The transition and the associated critical energy between the gaseous and the crystal phase is computed. Molecular dynamics show that the crystal phase is apparently split into two distinct regimes, depending on the the energy per particle $\varepsilon$. For small $\varepsilon$, particles are exactly located on the lattice sites; above an energy threshold $\varepsilon{*}$, particles can travel from one site to another. However, $\varepsilon{*}$ does not signal a phase transition but reflects the finite time of observation: the perfect crystal observed for $\varepsilon >0$ corresponds to a long lasting dynamical transient, whose life time increases when the $\varepsilon >0$ approaches zero.

cond-mat.stat-mech↗

arXiv2015

Crafting networks to achieve, or not achieve, chaotic states

The influence of networks topology on collective properties of dynamical systems defined upon it is studied in the thermodynamic limit. A network model construction scheme is proposed where the number of links, the average eccentricity and the clustering coefficient are controlled. This is done by rewiring links of a regular one dimensional chain according to a probability $p$ within a specific range $r$, that can depend on the number of vertices $N$. We compute the thermodynamic behavior of a system defined on the network, the $XY-$rotors model, and monitor how it is affected by the topological changes. We identify the network dimension $d$ as a crucial parameter: topologies with $d\textless{}2$ exhibit no phase transitions while ones with $d\textgreater{}2$ display a second order phase transition. Topologies with $d=2$ exhibit states characterized by infinite susceptibility and macroscopic chaotic/turbulent dynamical behavior. These features are also captured by $d$ in the finite size context.

physics.soc-ph↗

arXiv2014

Chaotic motion of charged particles in toroidal magnetic configurations

We study the motion of a charged particle in a tokamak magnetic field and discuss its chaotic nature. Contrary to most of recent studies, we do not make any assumption on any constant of the motion and solve numerically the cyclotron gyration using Hamiltonian formalism. We take advantage of a symplectic integrator allowing us to make long-time simulations. First considering an idealized magnetic configuration, we add a non generic perturbation corresponding to a magnetic ripple, breaking one of the invariant of the motion. Chaotic motion is then observed and opens questions about the link between chaos of magnetic field lines and chaos of particle trajectories. Second, we return to a axi-symmetric configuration and tune the safety factor (magnetic configuration) in order to recover chaotic motion. In this last setting with two constants of the motion, the presence of chaos implies that no third global constant exists, we highlight this fact by looking at variations of the first order of the magnetic moment in this chaotic setting. We are facing a mixed phase space with both regular and chaotic regions and point out the difficulties in performing a global reduction such as gyrokinetics.

nlin.CD↗

arXiv2014

Mixing properties in the advection of passive tracers via recurrences and extreme value theory

In this paper we characterize the mixing properties in the advection of passive tracers by exploiting the extreme value theory for dynamical systems. With respect to classical techniques directly related to the Poincaré recurrences analysis, our method provides reliable estimations of the characteristic mixing times and distinguishes between barriers and unstable fixed points. The method is based on a check of convergence for extreme value laws on finite datasets. We define the mixing times in terms of the shortest time intervals such that extremes converge to the asymptotic (known) parameters of the Generalized Extreme Value distribution. Our technique is suitable for applications in the analysis of other systems where mixing time scales need to be determined and limited datasets are available.

nlin.CD↗

arXiv2013

Critical behaviour of the XY -rotors model on regular and small world networks

We study the XY-rotors model on small networks whose number of links scales with the system size $N_{links}\sim N^γ$, where $1\leγ\le2$. We first focus on regular one dimensional rings in the microcanonical ensemble. For $γ<1.5$ the model behaves like short-range one and no phase transition occurs. For $γ>1.5$, the system equilibrium properties are found to be identical to the mean field, which displays a second order phase transition at a critical energy density $\varepsilon=E/N, \varepsilon_{c}=0.75$. Moreover for $γ_{c}\simeq1.5$ we find that a non trivial state emerges, characterized by an infinite susceptibility. We then consider small world networks, using the Watts-Strogatz mechanism on the regular networks parametrized by $γ$. We first analyze the topology and find that the small world regime appears for rewiring probabilities which scale as $p_{SW}\propto1/N^γ$. Then considering the XY-rotors model on these networks, we find that a second order phase transition occurs at a critical energy $\varepsilon_{c}$ which logarithmically depends on the topological parameters $p$ and $γ$. We also define a critical probability $p_{MF}$, corresponding to the probability beyond which the mean field is quantitatively recovered, and we analyze its dependence on $γ$.

cond-mat.stat-mech↗

arXiv2013

Dynamics of vortices and drift waves: a point vortex model

The complex interactions of localized vortices with waves is investigated using a model of point vortices in the presence of a transverse or longitudinal wave. This simple model shows a rich dynamical behavior including oscillations of a dipole, splitting and merging of two like-circulation vortices, and chaos. The analytical and numerical results of this model have been found to predict under certain conditions, the behavior of more complex systems, such as the vortices of the Charney-Hasegawa-Mima equation, where the presence of waves strongly affects the evolution of large coherent structures.

physics.plasm-ph↗

arXiv2013

Emergence of a non trivial fluctuating phase in the XY model on regular networks

We study an XY-rotor model on regular one dimensional lattices by varying the number of neighbours. The parameter $2\geγ\ge1$ is defined. $γ=2$ corresponds to mean field and $γ=1$ to nearest neighbours coupling. We find that for $γ<1.5$ the system does not exhibit a phase transition, while for $γ> 1.5$ the mean field second order transition is recovered. For the critical value $γ=γ_c=1.5$, the systems can be in a non trivial fluctuating phase for whichthe magnetisation shows important fluctuations in a given temperature range, implying an infinite susceptibility. For all values of $γ$ the magnetisation is computed analytically in the low temperatures range and the magnetised versus non-magnetised state which depends on the value of $γ$ is recovered, confirming the critical value $γ_{c}=1.5$.

cond-mat.stat-mech↗