Model for spontaneous frequency sweeping of an Alfvén wave in a toroidal plasma

Wang, Ge; Berk, H. L.

doi:10.1016/j.cnsns.2011.08.001

Cited by 7 publications

(9 citation statements)

References 18 publications

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“…For the case that new electrons are trapped into an expanding separatrix, it is required that the value of the distribution function of newly trapped particles is set to the value of the ambient distribution. The latter case is not the subject of this paper and the reader is referred to [22,29,31] where the subject of expanding separatrices is addressed.…”

Section: Resultsmentioning

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: Resultsmentioning

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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show abstract

“…For a sufficiently small perturbation, one can isolate a single resonance and select a transformation to the frame of the resonance structure, in the process of reducing the dynamics of the motion to a single action variable and its conjugate angle variable. One finds the following Hamiltonian [5] for a frequency sweeping structure,…”

Section: Adiabatic Modelmentioning

confidence: 99%

“…The form for the RHS was derived in [3,12]. The resulting adiabatic equations are given by In the absence of dissipation and drive (η = 0), one finds (see [1,5]) from the linear theory of equations (1) and (2) that the linear frequency ω 0 is given by ω 0 = ( 2 r − 1)/( 2 r + 1). When we take into account drive and dissipation under the assumption γ L 1, we find a growth rate γ given by 2 .…”

Section: Adiabatic Modelmentioning

confidence: 99%

“…whose values, as the magnitude of α goes from 0 to 1, vary from 1 3 to 3 14 for c 1 (α) and from 1 to 3 10 for c 2 (α) along the separatrix determined from the normalized Hamiltonian equation (5). We also note that there is error in [12] for values of c 1 and c 2 as |α| approaches unity, and in particular c 1 does not change sign in contrast to [12] as |α| goes from 0 to 1.…”

Section: Adiabatic Modelmentioning

confidence: 99%

“…Using the Fourier transform, the frequency form can be converted to a convolution integral with a temporal kernel producing a non-local time response for the wave. The governing theory for the time representation of the RBV tip model has been described in a recent paper [5]. In this paper we show how to develop an adiabatic theory for the RBVresonant particles and waves.…”

Section: Introductionmentioning

confidence: 97%

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Simulation and theory of spontaneous TAE frequency sweeping

Wang

Berk

2012

Nucl. Fusion

Self Cite

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A simulation model, based on the linear tip model of Rosenbluth, Berk and Van Dam (RBV), is developed to study frequency sweeping of toroidal Alfvén eigenmodes (TAEs). The time response of the background wave in the RBV model is given by a Volterra integral equation. This model captures the properties of TAE waves both in the gap and in the continuum. The simulation shows that phase space structures form spontaneously at frequencies close to the linearly predicted frequency, due to resonant particle-wave interactions and background dissipation. The frequency sweeping signals are found to chirp towards the upper and lower continua. However, the chirping signals penetrate only the lower continuum, whereupon the frequency chirps and mode amplitude increases in synchronism to produce an explosive solution. An adiabatic theory describing the evolution of a chirping signal is developed which replicates the chirping dynamics of the simulation in the lower continuum. This theory predicts that a decaying chirping signal will terminate at the upper continuum though in the numerical simulation the hole disintegrates before the upper continuum is reached.

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A hybrid Eulerian-Lagrangian Vlasov method for nonlinear wave-particle interaction in weakly inhomogeneous magnetic field

Zheng,

Wang,

2025

Computer Physics Communications

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Model for spontaneous frequency sweeping of an Alfvén wave in a toroidal plasma

Cited by 7 publications

References 18 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

Simulation and theory of spontaneous TAE frequency sweeping

A hybrid Eulerian-Lagrangian Vlasov method for nonlinear wave-particle interaction in weakly inhomogeneous magnetic field

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