Simulation and theory of spontaneous TAE frequency sweeping

Wang, Ge; Berk, H. L.

doi:10.1088/0029-5515/52/9/094003

Cited by 18 publications

(17 citation statements)

References 14 publications

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“…The interaction with the shear Alfén continuous spectra affects also the time evolution of the gap modes such as TAE and RSAE when they have the continuum damping and/ or the chirping frequency hits the continuum. A theoretical model of the frequency chirping of AEs with the interaction with shear Alfvén continua has been developed (Wang and Berk 2012).…”

Section: Discussion and Summarymentioning

confidence: 99%

Introduction to the interaction between energetic particles and Alfven eigenmodes in toroidal plasmas

Todo

2018

Rev. Mod. Plasma Phys.

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This article is a tutorial review of the interaction between energetic particles and Alfvén eigenmodes (AEs) which is one of the important research issues for fusion burning plasmas. The destabilization mechanism of AEs is a kind of inverse Landau damping through the resonant interaction with energetic particles. The important properties of the AE instability, such as resonance condition, conserved variable during the interaction, and particle trapping by the AE, are explained. The time evolution of AEs is classified into various types, steady state, frequency splitting, frequency chirping, and recurrent bursts. Berk and Breizman presented both a onedimensional weakly nonlinear theory for marginal stability and a reduced simulation model that qualitatively explain the various types of time evolution. Berk-Breizman's theory and reduced simulation model are introduced, and their limitations and the future works are discussed in this article. In addition, energetic particle transport by AEs is illustrated with surface-of-section plots. The particle trapping by the AE creates phase space islands and leads to the local flattening of the energetic particle spatial profile. The resonance overlap of multiple AEs and the overlap of higherorder resonances of a single AE lead to the emergence of stochasticity in phase space and the global transport of energetic particles.

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Section: Discussion and Summarymentioning

confidence: 99%

Introduction to the interaction between energetic particles and Alfven eigenmodes in toroidal plasmas

Todo

2018

Rev. Mod. Plasma Phys.

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“…EP transport in velocity space occurs in 'buckets' [87], similar to 'bucket' EP transport in real space introduced in [88]. 5 Note that the original adiabatic theory of [84] has been recently extended in [85,86], but still remains local in the sense discussed in section 2.1 and hereafter. More detailed discussions of this point are given in [15,27].…”

Section: Phase Locking and Nonadiabatic Phase Space Dynamicsmentioning

confidence: 96%

“…These physics have been extensively investigated since the pioneering work of Bernstein, Greene and Kruskal (BGK) [42]; and used for analyzing nonlinear behaviors of 1D uniform Vlasov plasmas [43][44][45][46][47][48], including sources and collisional dissipation [71,79,80]. If the frequency of hole/clump pairs slowly evolves in time [81][82][83][84][85][86], it happens adiabatically at a rate ω ω | | ≪ B 2 , set by balancing the rate of energy extraction of the moving holes/clumps in the phase space with fixed background dissipation 5 . EP transport in velocity space occurs in 'buckets' [87], similar to 'bucket' EP transport in real space introduced in [88].…”

Section: Phase Locking and Nonadiabatic Phase Space Dynamicsmentioning

confidence: 99%

Nonlinear dynamics of phase space zonal structures and energetic particle physics in fusion plasmas

et al. 2015

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A general theoretical framework for investigating the nonlinear dynamics of phase space zonal structures is presented in this work. It is then, more specifically, applied to the limit where the nonlinear evolution time scale is smaller or comparable to the wave-particle trapping period. In this limit, both theoretical and numerical simulation studies show that nonadiabatic frequency chirping and phase locking could lead to secular resonant particle transport on meso-or macro-scales. The interplay between mode structures and resonant particles then provides the crucial ingredient to properly understand and analyze the nonlinear dynamics of Alfvén wave instabilities excited by nonperturbative energetic particles in burning fusion plasmas. Analogies with autoresonance in nonlinear dynamics and with superradiance in free-electron lasers are also briefly discussed.

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“…In the limit of deeply passing particles, Eqs. (11) (with h = 1) and (43) are used to find the linear dispersion relation of the mode given by…”

Section: Linear Regime the Linearized Vlasov Equation For The P-th Rementioning

confidence: 99%

“…It is shown that the square root dependency holds for the very early stages of frequency chirping. The adiabatic condition represented in subsection 3.4.2, which is implemented for the formalism, needs to be validated if it remains satisfied [23,40,43]. Eq.…”

Section: Chirping Rate Structure Evolution and Adiabaticity Validationmentioning

confidence: 99%

Long range frequency chirping of Alfvén eigenmodes

Hezaveh

Breǐzman

et al. 2020

Nucl. Fusion

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A theoretical framework has been developed for an NBI scenario to model the hard nonlinear evolution of Global Alfvén Eigenmodes (GAEs) where the adiabatic motion of phasespace sturctures (holes and clumps), associated with the frequency chirping, occurs in generalized phase-space of slowing down energetic particles. The radial profile of the GAE is expanded using finite elements which allows update of the mode structure as the mode frequency chirps. Constants of motion are introduced to track the dynamics of energetic particles during frequency chirping by implementing proper Action-Angle variables and canonical transformations which reduce the dynamics essentially to 1D. Consequently, we specify whether the particles are drifting inward/outward as the frequency deviates from the initial MHD eigenfrequency. Using the principle of least action, we have derived the nonlinear equation describing the evolution of the radial profile by varying the total Lagrangian of the system with respect to the weights of finite elements. For the choice of parameters in this work, it is shown that the peak of the radial profile is shifted and also broadens due to frequency chirping. The time rate of frequency change is also calculated using the energy balance and we show that the adiabatic condition remains valid once it is satisfied. This model clearly illustrates the theoretical treatment to study the long range adiabatic frequency sweeping events observed for Alfvén gap modes in real experiments.

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Simulation and theory of spontaneous TAE frequency sweeping

Cited by 18 publications

References 14 publications

Introduction to the interaction between energetic particles and Alfven eigenmodes in toroidal plasmas

Introduction to the interaction between energetic particles and Alfven eigenmodes in toroidal plasmas

Nonlinear dynamics of phase space zonal structures and energetic particle physics in fusion plasmas

Long range frequency chirping of Alfvén eigenmodes

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