Effect of dynamical friction on nonlinear energetic particle modes

Lilley, Matthew; Breǐzman, B. N.; Sharapov, S. E.

doi:10.1063/1.3486535

Cited by 71 publications

(115 citation statements)

References 21 publications

(27 reference statements)

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“…The Berk-Breizman scenario has been proved to be successful in explaining the frequency chirping events observed in experiments with AEs [14,15]. Moreover, the effect of different types of relaxation processes on the nonlinear evolution has been investigated in [16] and [17], with the BOT code introduced in the latter. All the mentioned models are based on the assumption that the range of frequency chirping is short and the mode structure is fixed.…”

Section: Introductionmentioning

confidence: 99%

Impact of energetic particle orbits on long range frequency chirping of BGK modes

Hezaveh¹,

Qu²,

Layden³

et al. 2017

Nucl. Fusion

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Abstract.Long range frequency chirping of Bernstein-Greene-Kruskal modes, whose existence is determined by the fast particles, is investigated in cases where these particles do not move freely and their motion is bounded to restricted orbits. An equilibrium oscillating potential, which creates different orbit topologies of energetic particles, is included into the bump-on-tail instability problem of a plasma wave. With respect to fast particles dynamics, the extended model captures the range of particles motion (trapped/passing) with energy and thus represents a more realistic 1D picture of the long range sweeping events observed for weakly damped modes, e.g. global Alfven eigenmodes, in tokamaks. The Poisson equation is solved numerically along with bounce averaging the Vlasov equation in the adiabatic regime. We demonstrate that the shape and the saturation amplitude of the nonlinear mode structure depends not only on the amount of deviation from the initial eigenfrequency but also on the initial energy of the resonant electrons in the equilibrium potential. Similarly, the results reveal that the resonant electrons following different equilibrium orbits in the electrostatic potential lead to different rates of frequency evolution. As compared to the previous model [Breizman B.N. 2010 Nucl. Fusion 50 084014], it is shown that the frequency sweeps with lower rates. The additional physics included in the model enables a more complete 1D description of the range of phenomena observed in experiments.Hard nonlinear evolution in the presence of particle orbits 2

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Section: Introductionmentioning

confidence: 99%

Impact of energetic particle orbits on long range frequency chirping of BGK modes

Hezaveh¹,

Qu²,

Layden³

et al. 2017

Nucl. Fusion

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“…[6], and frequently exhibits chirping patterns in the wave frequency away from the normal modes of the bulk plasma. Extensive modeling over the years, in simplified systems [7][8][9][10] and in more realistic geometries [11], has revealed that the frequency shifts can be attributed to the formation and subsequent evolution of long-living structures in the fast particle distribution, so called holes (a depletion of particles) and clumps (an excess of particles). The holes and clumps form in the proximity of the wave-particle resonances of a kinetically unstable bulk plasma mode, and once firmly established, they represent nonlinear waves of so-called BGK type [12] whose frequencies are slightly up-and down-shifted with respect to that of the initial instability.…”

mentioning

confidence: 99%

Formation of Phase Space Holes and Clumps

Lilley

Nyqvist

2014

Phys. Rev. Lett.

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It is shown that the formation of phase space holes and clumps in kinetically driven, dissipative systems is not restricted to the near threshold regime, as previously reported and widely believed. Specifically, we observe hole-clump generation from the edges of an unmodulated phase space plateau, created via excitation, phase mixing and subsequent dissipative decay of a linearly unstable bulk plasma mode in the electrostatic bump-on-tail model. This has now allowed us to elucidate the underlying physics of the holeclump formation process for the first time. Holes and clumps develop from negative energy waves that arise due to the sharp gradients at the interface between the plateau and the nearly unperturbed, ambient distribution and destabilize in the presence of dissipation in the bulk plasma. We confirm this picture by demonstrating that the formation of such nonlinear structures in general does not rely on a "seed" wave, only on the ability of the system to generate a plateau. In addition, we observe repetitive cycles of plateau generation and erosion, the latter due to hole-clump formation and detachment, which appear to be insensitive to initial conditions and can persist for a long time. We present an intuitive discussion of why this continual regeneration occurs.

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“…T(1, 2) requires closure calculation for the triplet nonlinearity. The closure calculation 16,32 can be implemented by calculating phase coherent response of the two point correlation function to E Â B velocity, i.e., df ð2Þe v EÂB ð1Þ Á r 1 df ð1Þ ffi r 1 Á ðe vð1Þðdf i ð1Þdf i ð2ÞÞ c Þ; (10) where (6)) and resonant particles. The arrows indicate unperturbed trajectory of the resonant particles, initially located at (0, 0).…”

Section: Evolution Of Two Point Phase Space Density Correlationmentioning

confidence: 99%

“…At the nonlinear stage, as turbulent amplitude increases, an increasing number of resonant particles are trapped in waves. In this case, the system shows rich nonlinear behavior, such as the formation of BGK vortices, 1 phase space density holes, [2][3][4][5][6] pairs of clumps and holes, [7][8][9][10][11][12][13] and phase space density granulations. [14][15][16][17] More recently, state-of-the-art numerical scheme and computational power were applied to study simplified models, such as bump-on-tail 18 and ion-acoustic turbulence.…”

Section: Introductionmentioning

confidence: 99%

Ion temperature gradient driven turbulence with strong trapped ion resonance

et al. 2014

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A theory to describe basic characterization of ion temperature gradient driven turbulence with strong trapped ion resonance is presented. The role of trapped ion granulations, clusters of trapped ions correlated by precession resonance, is the focus. Microscopically, the presence of trapped ion granulations leads to a sharp (logarithmic) divergence of two point phase space density correlation at small scales. Macroscopically, trapped ion granulations excite potential fluctuations that do not satisfy dispersion relation and so broaden frequency spectrum. The line width from emission due only to trapped ion granulations is calculated. The result shows that the line width depends on ion free energy and electron dissipation, which implies that non-adiabatic electrons are essential to recover non-trivial dynamics of trapped ion granulations. Relevant testable predictions are summarized. V C 2014 AIP Publishing LLC. [http://dx

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Effect of dynamical friction on nonlinear energetic particle modes

Cited by 71 publications

References 21 publications

Impact of energetic particle orbits on long range frequency chirping of BGK modes

Impact of energetic particle orbits on long range frequency chirping of BGK modes

Formation of Phase Space Holes and Clumps

Ion temperature gradient driven turbulence with strong trapped ion resonance

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