arXiv subjects

M. Leconte

Publications and source records attributed to M. Leconte.

14 recordsLinked to original sources

arXiv2026

Friction-induced scale-selection in the extended Cahn-Hilliard model for zonal staircase

In this work, we describe a possible mechanism to set the radial scale of zonal flows, which may be applicable to the $E \times B$ staircase found in the global full-f simulations such as [G. Dif-Pradalier et al. Phys. Rev. Lett. 114, 085004 (2015)]. 1D numerical simulation results of the Cahn-Hilliard model - extended to include zonal flow friction - can be understood from a heuristic nonlinear analysis. The staircase step-size $\Delta$ is found to decrease as the dimensionless zonal flow friction $\mu$ increases. It scales like $\Delta \sim \log \mu^\alpha$, with $\alpha \simeq -0.41$, up to a constant offset.

physics.plasm-ph↗

arXiv2023

Zonal density staircase formation in collisional drift-wave turbulence

Turbulence-driven quasi-stationnary structures known as 'staircase' are investigated using the collisional drift-wave model. Two-dimensional simulations show that the ability of zonal density corrugations to suppress turbulence are affected by the adiabaticity parameter (inversely proportional to collision frequency). As the adiabaticity parameter increases, zonal density becomes less efficient at suppressing turbulence, and zonal flows become dominant in the near-adiabatic regime. The nonlinear transport crossphase displays radial modulations associated to zonal density.

physics.plasm-ph↗

arXiv2022

Linear analysis and crossphase dynamics in the $\nabla T_e$-driven CTEM fluid model

Collisionless trapped-electron mode (CTEM) turbulence is an important contributor to heat and particle transport in fusion devices. The ITG/TEM fluid models are rarely treated analytically, due to the large number of transport channels involved, e.g. particle and ion/electron heat transport. The $\nabla T_e$-driven CTEM fluid model [Anderson et al, Plasma Phys. Control. Fusion 48, 651 (2006)] provides a simplified model, in the regime where the density gradient drive is negligeable compared to the electron temperature gradient drive ($\nabla T_e$). This provides an interesting model to study mechanisms associated to linear waves, such as crossphase dynamics, and its possible role in the formation of $E\times B$ staircase. Here, the $\nabla T_e$-driven CTEM fluid model is rigourously derived from the more general ITG/TEM model, and its linear dynamics is first analyzed and compared with CTEM gyrokinetic simulations with bounce-averaged kinetic electrons, while nonlinear analysis is left for future work. Comparisons of linear ITG spectrum are also made with other analytical models.

physics.plasm-ph↗

arXiv2021

Zonal profile corrugations and staircase formation: Role of the transport crossphase

Recently, quasi-stationary structures called $E \times B$ staircases were observed in gyrokinetic simulations, in all transport channels [Dif-Pradalier et al. Phys. Rev. Lett. 114, 085004 (2015)]. We present a novel analytical theory - supported by collisional drift-wave fluid simulations - for the generation of density profile corrugations (staircase), independent of the action of zonal flows: Turbulent fluctuations self-organize to generate quasi-stationary radial modulations $\Delta\theta(r,t)$ of the transport crossphase $\theta$ between density and electric potential fluctuations. The radial modulations of the associated particle flux drive zonal corrugations of the density profile, via a modulational instability. In turn, zonal density corrugations regulate the turbulence via nonlinear damping of the fluctuations.

physics.plasm-ph↗

arXiv2021

Limit Cycle Oscillations, response time and the time-dependent solution to the Lotka-Volterra Predator-Prey model

In this work, the time-dependent solution for the Lotka-Volterra Predator-Prey model is derived with the help of the Lambert W function. This allows an exact analytical expression for the period of the associated limit-cycle oscillations (LCO), and also for the response time between predator and prey population. These results are applied to the predator-prey interaction of zonal density corrugations and turbulent particle flux in gyrokinetic simulations of collisionless trapped-electron model (CTEM) turbulence. In the turbulence simulations, the response time is shown to increase when approaching the linear threshold, and the same trend is observed in the Lotka-Volterra model.

physics.plasm-ph↗

arXiv2020

Phase-mixing v.s. phase synchronization in the dynamics of flow-shear induced edge transport barrier

Nonlinear relaxation oscillations of flow-shear induced transport barriers can be qualitatively reproduced using a phenomenological critical-gradient model [M. Leconte, Y.M. Jeon and G.S. Yun, \emph{Contrib. Plasma Phys.} 56, 736 (2016]. Here, we give a more in-depth analysis of the mechanism of these nonlinear oscillations, associated to nonlinear \emph{phase synchronization}, in an extended version of the model including random fluctuations.

physics.plasm-ph↗

arXiv2019

Effects of zonal flows on transport crossphase in dissipative trapped-electron mode turbulence in edge plasmas

For H-mode, standard decorrelation theory predicts that it is the turbulence intensity $|\phi_k|^2$ that is mainly affected via flow-induced shearing of turbulent eddies. However, for other regimes (e.g. I-mode, characterized by high energy confinement but low particle confinement), this decrease of turbulence amplitude cannot explain the decoupling of particle v.s. thermal flux, since a suppression of turbulence intensity $|\phi_k|^2$ would necessarily affect both fluxes the same way. Here, we explore a possible new stabilizing mechanism: zonal flows may directly affect the transport crossphase. We show the effect of this novel mechanism on the turbulent particle flux, by using a simple fluid model [Baver et al., Phys. Plasmas \textbf{9}, 3318 (2002)] for dissipative trapped-electron mode (DTEM), including zonal flows. We first derive the evolution equation for the transport crossphase $\delta_k$ between density and potential fluctuations, including contributions from the $E \times B$ nonlinearity. By using a parametric interaction analysis, we obtain a predator-prey like system of equations for the pump amplitude $\phi_p$, the pump crossphase $\delta_p$, the zonal amplitude $\phi_z$ and the triad phase-mismatch $\Delta \delta$. The system displays limit-cycle oscillations where the instantaneous DTEM growth rate - proportional to the crossphase - shows quasi-periodic relaxations where it departs from that predicted by linear theory.

physics.plasm-ph↗

arXiv2018

Enhancement of zonal flow damping due to resonant magnetic perturbations in the background of an equilibrium $E \times B$ sheared flow

Using a parametric interaction formalism, we show that the equilibrium sheared rotation can enhance the zonal flow damping effect found in Ref. [M. Leconte and P.H. Diamond, \emph{Phys. Plasmas} 19, 055903 (2012)]. This additional damping contribution is proportional to $(L_s/L_V)^2 \times \delta B_r^2 / B^2$, where $L_s/L_V$ is the ratio of magnetic shear length to the scale-length of equilibrium $E \times B$ flow shear, and $\delta B_r / B$ is the amplitude of the external magnetic perturbation normalized to the background magnetic field.

physics.plasm-ph↗

arXiv2016

ExB flow-induced shearing-merging of filaments: a Ginzburg-Landau model of Edge-Localized Mode cycles

We derive and study a simple 1D nonlinear model for Edge Localized Mode (ELM) cycles. The nonlinear dynamics of a resistive ballooning mode is modeled via a single nonlinear equation of the Ginzburg-Landau type with a radial frequency gradient due to a prescribed ExB shear layer of finite extent. The nonlinearity is due to the feedback of the mode on the profile. We identify a novel mechanism, whereby the ELM only crosses the linear stability boundary once, and subsequently stays in the nonlinear regime for the full duration of the cycles. This is made possible by the shearing and merging of filaments by the ExB flow, which forces the system to oscillate between a radially-uniform solution and a non-uniform solitary - wave like solution. The model predicts a 'phase-jump' correlated with the ELM bursts.

physics.plasm-ph↗

arXiv2013

Impact of Resonant Magnetic Perturbations on Zonal Modes, Drift-Wave Turbulence and the L-H Transition Threshold

We study the effects of Resonant Magnetic Perturbations (RMPs) on turbulence, flows and confinement in the framework of resistive drift-wave turbulence. This work was motivated, in parts, by experiments reported at the IAEA 2010 conference [Y. Xu {\it et al}, Nucl. Fusion \textbf{51}, 062030] which showed a decrease of long-range correlations during the application of RMPs. We derive and apply a zero-dimensional predator-prey model coupling the Drift-Wave Zonal Mode system [M. Leconte and P.H. Diamond, Phys. Plasmas \textbf{19}, 055903] to the evolution of mean quantities. This model has both density gradient drive and RMP amplitude as control parameters and predicts a novel type of transport bifurcation in the presence of RMPs. This model allows a description of the full L-H transition evolution with RMPs, including the mean sheared flow evolution. The key results are: i) The L-I and I-H power thresholds \emph{both} increase with RMP amplitude $|\bx|$, the relative increase of the L-I threshold scales as $ΔP_{\rm LI} \propto |\bx|^2 ν_*^{-2} \gyro^{-2}$, where $ν_*$ is edge collisionality and $\gyro$ is the sound gyroradius. ii) RMPs are predicted to \emph{decrease} the hysteresis between the forward and back-transition. iii) Taking into account the mean density evolution, the density profile - sustained by the particle source - has an increased turbulent diffusion compared with the reference case without RMPs which provides one possible explanation for the \emph{density pump-out} effect.

physics.plasm-ph↗

arXiv2009

Control of Transport-barrier relaxations by Resonant Magnetic Perturbations

Transport-barrier relaxation oscillations in the presence of resonant magnetic perturbations are investigated using three-dimensional global fluid turbulence simulations from first principles at the edge of a tokamak. It is shown that resonant magnetic perturbations have a stabilizing effect on these relaxation oscillations and that this effect is due mainly to a modification of the pressure profile linked to the presence of both residual residual magnetic island chains and a stochastic layer.

physics.plasm-ph↗

arXiv2006

Maxwell demon in Granular gas: a new kind of bifurcation? The hypercritical bifurcation

This paper starts with the investigation of the behaviour of a set of two subsystems which are able to exchange some internal quantity according to a given flux function. It is found that this sytem exhibit a bifurcation when the flux passes through a maximum and that its kind (super-critical/sub-critical) depends on the dissymmetry of the flux function near the maximum. It is also found a new kind of bifurcation when the flux function is symmetric: we call it hypercritical bifurcation because it generates much stronger fluctuations than the super-critical one. The effect of a white noise is then investigated. We show that an experimental set-up, leading to the Maxwell demon in granular gas, displays all these kinds of bifurcation, just by changing the parameters of excitation. It means that this system is much less simple as it was thought.

physics.flu-dyn↗

arXiv2005

Autocatalytic reaction front in a pulsative periodic flow

Autocatalytic reaction fronts between reacted and unreacted species may propagate as solitary waves, namely at a constant front velocity and with a stationary concentration profile, resulting from a balance between molecular diffusion and chemical reaction. A velocity field in the supporting medium may affect the propagation of such fronts through different phenomena: convection, diffusion enhancement, front shape changes... We report here on an experimental study and lattice BGK numerical simulations of the effect of an oscillating flow on the autocatalytic reaction between iodate and arsenous acid in a Hele-Shaw cell. In the low frequency range covered by the experiments, the front behavior is controlled by the flow across the gap and can be reproduced with 2D numerical simulations. An analytical solution is also derived under the condition of a weak flow velocity, and is found to be in reasonable agreement with our data.

physics.flu-dyn↗

arXiv2003

Pattern of Reaction Diffusion Front in Laminar Flows

Autocatalytic reaction between reacted and unreacted species may propagate as solitary waves, namely at a constant front velocity and with a stationary concentration profile, resulting from a balance between molecular diffusion and chemical reaction. The effect of advective flow on the autocatalytic reaction between iodate and arsenous acid in cylindrical tubes and Hele-Shaw cells is analyzed experimentally and numerically using lattice BGK simulations. We do observe the existence of solitary waves with concentration profiles exhibiting a cusp and we delineate the eikonal and mixing regimes recently predicted.

physics.flu-dyn↗