Nonlinear Splitting of Fast Particle Driven Waves in a Plasma: Observation and Theory

Fasoli, A.; Breǐzman, B. N.; Borba, D.; Heeter, R. F.; Pekker, M.; Sharapov, S. E.

doi:10.1103/physrevlett.81.5564

Cited by 101 publications

(128 citation statements)

References 9 publications

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“…Unlike the complicated 'tornado' spectra in JT-60U [54], the 'chirping' spectra in TFTR [47] and the 'pitchfork' spectra in JET [46], the Alfvén spectra in our experiments usually consist of a single steady mode. (Occasionally two modes briefly coexist.)…”

Section: Discussionmentioning

confidence: 99%

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High harmonic ion cyclotron heating in DIII-D: Beam ion absorption and sawtooth stabilization

et al. 1999

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Abstract. Combined neutral beam injection and fast wave heating at the fourth cyclotron harmonic produce an energetic deuterium beam ion tail in the DIII-D tokamak. When the concentration of thermal hydrogen exceeds ∼5%, the beam ion absorption is suppressed in favour of second harmonic hydrogen absorption. As theoretically expected, the beam absorption increases with beam ion gyroradius; also, central absorption at the fifth harmonic is weaker than central absorption at the fourth harmonic. For central heating at the fourth harmonic, an energetic, perpendicular, beam population forms inside the q = 1 surface. The beam ion tail transiently stabilizes the sawtooth instability but destabilizes toroidicity induced Alfvén eigenmodes (TAEs). Saturation of the central heating correlates with the onset of the TAEs. Continued expansion of the q = 1 radius eventually precipitates a sawtooth crash; complete magnetic reconnection is observed.

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Section: Discussionmentioning

confidence: 99%

“…The toroidal mode number ranges from n = 4 to n = 7, with n = 6 typically observed. In unstable beam heated discharges in DIII-D, the TAE toroidal mode number is usually n = 3-5 [44] while, during RF heating in larger tokamaks [45][46][47], n 10 is typical.…”

Section: Alfvén Modesmentioning

confidence: 99%

High harmonic ion cyclotron heating in DIII-D: Beam ion absorption and sawtooth stabilization

et al. 1999

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“…AEs excited by ion cyclotron resonance heating ͑ICRH͒-produced ions show usually the "soft" excitation regimes. [3][4][5][6][7][8] In these nonlinear scenarios, the mode frequency remains close to the linear AE eigenfrequency and the structure of the mode remains similar to the linear one. In contrast, in the case of neutral beam injection ͑NBI͒, a "hard" nonlinear regime is observed more often, resulting in bursting amplitude evolution and in rapid frequency sweeping.…”

Section: Introductionmentioning

confidence: 99%

“…In the past, such a model was successfully used to explain nonlinear bifurcations and frequency sweeping events observed in various AE experiments. 3,4,9 It was found 16 that the mode grows explosively when dynamical friction ͑drag͒ dominates over velocity space diffusion in the vicinity of the wave-particle resonance. This previous analysis was limited to a weakly nonlinear regime with a perturbative treatment of the energetic particle response to the wave field.…”

Section: Introductionmentioning

confidence: 99%

Effect of dynamical friction on nonlinear energetic particle modes

Lilley¹,

Breǐzman²,

Sharapov³

2010

Physics of Plasmas

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106

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A fully nonlinear model is developed for the bump-on-tail instability including the effects of dynamical friction ͑drag͒ and velocity space diffusion on the energetic particles driving the wave. The results show that drag provides a destabilizing effect on the nonlinear evolution of waves. Specifically, in the early nonlinear phase of the instability, the drag facilitates the explosive scenario of the wave evolution, leading to the creation of phase space holes and clumps that move away from the original eigenfrequency. Later in time, the electric field associated with a hole is found to be enhanced by the drag, whereas for a clump it is reduced. This leads to an asymmetry of the frequency evolution between holes and clumps. The combined effect of drag and diffusion produces a diverse range of nonlinear behaviors including hooked frequency chirping, undulating, and steady state regimes. An analytical model is presented, which explains the aforementioned diversity. A continuous production of hole-clump pairs in the absence of collisions is also observed.

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“…It should be mentioned that holes and clumps form not only in case of a weakly unstable mode but also with any amount of background dissipation [13]. 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.…”

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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Nonlinear Splitting of Fast Particle Driven Waves in a Plasma: Observation and Theory

Cited by 101 publications

References 9 publications

High harmonic ion cyclotron heating in DIII-D: Beam ion absorption and sawtooth stabilization

High harmonic ion cyclotron heating in DIII-D: Beam ion absorption and sawtooth stabilization

Effect of dynamical friction on nonlinear energetic particle modes

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

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