Coherent transport structures in magnetized plasmas. I. Theory

Giannatale, G. Di; Falessi, Matteo Valerio; Grasso, D.; Пегораро, Ф.; Schep, T. J.

doi:10.1063/1.5020163

Cited by 15 publications

(32 citation statements)

References 54 publications

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“…Lagrangian coherent structures are a generalization of dynamical structures observed in autonomous and periodic systems, e.g. invariant manifolds, to temporally aperiodic flows and allow one to identify phase-space regions distinguished by qualitatively different behaviour of particle motion (see Haller (2015), Falessi, Pegoraro & Schep (2015), Carlevaro et al (2015), Di Giannatale et al (2018a and Pegoraro et al (2019) for applications to plasma physics). Following the work of Haller (2015), we define LCSs as the most repulsive or attractive material lines (one-dimensional ensemble of material points, i.e.…”

Section: Lagrangian Coherent Structure Analysismentioning

confidence: 99%

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Resonance overlap and nonlinear features of the beam–plasma system

2020

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The beam–plasma instability can be addressed as a reduced model in several contexts of plasma physics, from space to fusion plasma. In this paper, we review and refine some nonlinear features of this model. Specifically, by analysing the dependence of the nonlinear velocity spread as a function of the linear growth rate, we discuss the effective size of the resonance in view of its role in the spectral overlap at saturation. The relevance of this characterization relies on the necessity of a quantitative determination of the overlap degree to discriminate among different transport regimes of the self-consistent dynamics. The analysis is enriched with a study of the phase-space dynamics by means of the Lagrangian coherent structure technique, in order to define the transport barriers of the system describing the relevant features of the overlap process. Finally, we discuss relevant features related to the mode saturation levels.

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Section: Lagrangian Coherent Structure Analysismentioning

confidence: 99%

“…(2015), Di Giannatale et al. (2018 a , b ) and Pegoraro et al. (2019) for applications to plasma physics).…”

Section: Lagrangian Coherent Structure Analysismentioning

confidence: 99%

Resonance overlap and nonlinear features of the beam–plasma system

2020

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“…The continuous trapping/de-trapping phenomenon can also be observed by resorting to the Lagrangian Coherent Structure (LCS) technique [29][30][31][32][33]. It is well known that these the island from the lower edge and an outgoing flow of particles, destined to become detrapped, from the upper edge.…”

Section: Trapping/de-trapping Processmentioning

confidence: 99%

Analysis of the nonlinear dynamics of a chirping-frequency Alfvén mode in a Tokamak equilibrium

Wang¹,

Briguglio²,

Troia³

et al. 2021

Preprint

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Chirping Alfvén modes are considered as potentially harmful for the confinement of energetic particles in burning Tokamak plasmas because of their capability, by modifying their frequency, of extracting as much power as possible from such particles and, in turn, enhancing their transport.In this paper, the nonlinear evolution of a single-toroidal-number chirping mode is analysed by numerical particle simulation. This analysis can be simplified if the different resonant phase-space structures can be investigated as isolated ones; that is, if the phase space can be cut into slices that do not exchange particles and interact with the mode independently of each other. This can be done adopting a coordinate system that includes two global invariants of the system or, if it is not possible to identify these invariants (this is generally the case for chirping modes), two constants of motion. In the frame of a numerical simulation approach, we adopt as constants of motion, the magnetic momentum and a suited function of the initial particle coordinates. The relevant resonant structures are then identified. The analysis is focused on the dynamics of two of them: namely, those yielding the largest drive during, respectively, the linear phase and the nonlinear one. It is shown that, for each resonant structure, a density-flattening region is formed around the respective resonance radius, with radial width that increases as the mode amplitude grows. It is delimited by two large negative density gradients, drifting inward and outward. If the mode frequency were constant, this density flattening would be responsible for the exhausting of the drive yielded by the resonant structure, which would occur as the large negative density gradients leave the resonance region. causes the resonance radius and the resonance region to drift inward. This drift, along with a relevant resonance broadening, delays the moment in which the inner density gradient reaches the inner boundary of the resonance region, leaving it. On the other side, the island reconstitutes around the new resonance radius; as a consequence, the large negative density gradient further moves inward. This process continues as long as it allows to keep the large gradient within the resonance region. When this is no longer possible, the resonant structure ceases to be effective in driving the mode. To further grow, the mode has to tap a different resonant structure, possibly making use of additional frequency variations.

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“…In order to solve this problem, when the curves satisfying the conditions (I-IV) have been obtained, they are evolved backward, that is the trajectories of the points belonging to the LCSs are evolved under the flow map Φ reversing the sign of "time" in Eq. 2 (for our studies, the direction along the toroidal direction during the field line trajectories computation 14 ). To explain properly such concept, let us to refer to a Hamiltonian system, where it is known that LCSs try to mark stable manifolds, or at least their equivalent for finite time.…”

Section: Backward Integrationmentioning

confidence: 99%

“…Even though magnetic chaos may lead to a degradation of the confinement properties, magnetic barriers can emerge also in a chaotic region, preventing ergodicity [13][14][15][16][17][18][19][20] . Such barriers may account for the formation of internal electron transport barriers that have been experimentally observed in the RFX device 21 .…”

Section: Introductionmentioning

confidence: 99%

Prediction of temperature barriers in weakly collisional plasmas by a Lagrangian Coherent Structures computational tool

Di Giannatale,

Bonfiglio,

Cappello

et al. 2021

Preprint

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Coherent transport structures in magnetized plasmas. I. Theory

Cited by 15 publications

References 54 publications

Resonance overlap and nonlinear features of the beam–plasma system

Resonance overlap and nonlinear features of the beam–plasma system

Analysis of the nonlinear dynamics of a chirping-frequency Alfvén mode in a Tokamak equilibrium

Prediction of temperature barriers in weakly collisional plasmas by a Lagrangian Coherent Structures computational tool

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