Development of magnetohydrodynamic modes during sawteeth in tokamak plasmas

Firpo, Marie-Christine; Ettoumi, Wahb; Farengo, Ricardo; Ferrari, Hugo; García-Martínez, Pablo; Lifschitz, Agustín

doi:10.1063/1.4816025

Cited by 4 publications

(6 citation statements)

References 23 publications

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“…4, we directly see that this is likely not the case. However this remark, lead to numerous studies on the chaoticity of magnetic field lines, having in mind a picture very much like the advection of passive tracers in a stationary three dimensional flows, where passive tracers simply follows velocity field lines 21,[24][25][26][27][28][29][30][31][32][33] . The tokamak being a three dimensional object, it has been shown for a long time that field lines of flux conservative fields are generically chaotic in three dimensions.…”

Section: B the Ripple Effectmentioning

confidence: 99%

Chaotic motion of charged particles in toroidal magnetic configurations

Cambon

Leoncini

Vittot

et al. 2014

Chaos: An Interdisciplinary Journal of Nonlinear Science

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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 an axisymmetric 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.PACS numbers: 05.45.Ac, 52.25.Gj 1 Contrary to old studies, most of recent research dealing with hot magnetized fusion plasmas rely on numerical simulations. In the special case of a tokamak magnetic configuration, the majority of the numerical codes are based on the gyrokinetic theory. One of the assumptions made by this theory is to consider the magnetic moment of the particles moving in the magnetic field as an exact invariant of the motion. The straight consequence is to consider that all particle trajectories are integrable for axisymmetric configuration and no electric field.This assumption enables to make global reduction of the phase space and allows for faster numerical simulations. In fact, the magnetic moment is often an adiabatic invariant and it can present variations over very large-time scales. These remarks lay the ground for possible presence of Hamiltonian chaos in particle trajectory and a non-constant magnetic moment. In this paper, we solve numerically the motion of charged particles including the cyclotron gyration using Hamiltonian formalism in the sixth dimensional phase space, without using any assumption. We take advantage of a symplectic integrator allowing us to make long-time simulations. First, considering an axisymmetric magnetic configuration, we add a non-generic perturbation corresponding to a specific magnetic ripple, breaking one of the invariant of the motion. Chaotic motion is then observed whereas magnetic field lines are still integrable. So, we underline that the link between the two notions is not automatic. Second, we observe chaos of particle trajectories even in an axisymmetric configuration of the magnetic field. For this purpose, we study the limit case in which the major radius of the tokamak is infinite. The geometry becomes cylindrical. We tune the winding profile of magnetic field...

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Section: B the Ripple Effectmentioning

confidence: 99%

Chaotic motion of charged particles in toroidal magnetic configurations

Cambon

Leoncini

Vittot

et al. 2014

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…The time evolution of the displacement is phenomenologically reconstructed as in [18,26,27]. In the JET discharges of [20], sawteeth are in all likelihood triggered by excitation of the n=1 internal kink mode, whereas higher modes are nonlinearly triggered [24,28] as the n=1 mode develops. Higher order ¹ m n modes have even been experimentally measured [29].…”

Section: Frameworkmentioning

confidence: 99%

“…Important to our study is to recognize that there exist also non-axisymmetric integrable field-line Hamiltonians obtained from equation (8). For instance, if one assumes that the magnetic field perturbation affects only m=n modes, such as the dominant (1, 1) and (2, 2) modes, then the Hamiltonian may be expressed as a function of just two coordinates, namely Ψ and the helical angle q f -, and is thus integrable [23,24]. Then, in order to isolate the effect of the magnetic field line chaos on the motion of the nickel ions during the sawtooth crash, two different sets of magnetic field perturbations will be used [25].…”

Section: Frameworkmentioning

confidence: 99%

Evidence and relevance of spatially chaotic magnetic field lines in MCF devices

Firpo

Lifschitz

Ettoumi

et al. 2017

Plasma Phys. Control. Fusion

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Numerical evidence for the existence of spatially chaotic magnetic field lines about the collapse phase of tokamak sawteeth with incomplete reconnection is presented. This uses the results of extensive test particle simulations in different sets of electromagnetic perturbations tested against experimental JET measurements. In tokamak sawteeth, that form a laboratory prototype of magnetic reconnection, the relative magnetic perturbation dB B may reach a few percents. This does not apply to tokamak operating regimes dominated by turbulence where dB B is usually not larger than-10 4. However, this small magnetic perturbation being sustained by a large spectrum of modes is shown to be sufficient to ensure the existence of stochastic magnetic field lines. This has important consequences for magnetic confinement fusion where electrons are dominantly governed by the magnetic force. Indeed some overlap between magnetic resonances can locally induce chaotic magnetic field lines enabling the spatial redistribution of the electron population and of its thermal content. As they are the swiftest plasma particles, electrons feed back the most rapid perturbations of the magnetic field.

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“…Contrarily to macroscopic dramatic phenomena, such as the sawtooth crash, that may be related to the onset of the chaos of magnetic field lines due to some subset of longwavelength modes with different helicities (See e.g. [4][5][6][7], the consequences of the loss of the integrity of magnetic surfaces in the presence of plasma microturbulence have been observed in some gyrokinetic numerical simulations 3 to be normally benign or moderate. Yet, there is certainly some limit in the braiding of the magnetic field lines above which magnetic confinement breaks and a disruption occurs.…”

Section: Introduction and Objectivesmentioning

confidence: 99%

Microtearing turbulence: Magnetic braiding and disruption limit

Firpo

2015

Physics of Plasmas

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A realistic reduced model involving a large poloidal spectrum of microtearing modes is used to probe the existence of some stochasticity of magnetic field lines. Stochasticity is shown to occur even for the low values of the magnetic perturbation δB/B devoted to magnetic turbulence that have been experimentally measured. Because the diffusion coefficient may strongly depend on the radial (or magnetic-flux) coordinate, being very low near some resonant surfaces, and because its evaluation implicitly makes a normal diffusion hypothesis, one turns to another indicator appropriate to diagnose the confinement: the mean residence time of magnetic field lines. Their computation in the microturbulence frame points to the existence of a disruption limit, namely of a critical order of magnitude of δB/B above which stochasticity is no longer benign yet, leads to a macroscopic loss of confinement in some tens to hundred of electron toroidal excursions. Since the level of magnetic turbulence δB/B has been measured to grow with the plasma electron density, this would also be a density limit.

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Development of magnetohydrodynamic modes during sawteeth in tokamak plasmas

Cited by 4 publications

References 23 publications

Chaotic motion of charged particles in toroidal magnetic configurations

Chaotic motion of charged particles in toroidal magnetic configurations

Evidence and relevance of spatially chaotic magnetic field lines in MCF devices

Microtearing turbulence: Magnetic braiding and disruption limit

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