Modeling of long range frequency sweeping for energetic particle modes

Nyqvist, Robert; Breǐzman, B. N.

doi:10.1063/1.4799781

Cited by 14 publications

(37 citation statements)

References 18 publications

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“…This indicates that for realistic geometries where particles interacting with the mode can follow different equilibrium orbits, an extended approach is required to calculate the perturbed density inside the holes and clumps. This extension can highly benefit from the method presented in [22]. However, it should be taken into account that the adiabatic invariant (phase-space area) at the separatrix can have both the shrinking and expanding behavior depending on the initial orbit of the energetic particles.…”

Section: Discussionmentioning

confidence: 99%

“…In the previous BOT models for long range chirping [21,26,22], V α,n,p is unity for the dominant resonance and is zero otherwise. In contrast, the presented approach enables investigation of different types of resonances in wave-particle interaction through a 1D model.…”

Section: The Linear Growth Ratementioning

confidence: 99%

“…As an extension, the adiabatic description of treating an expanding separatrix which traps the ambient particles is presented in [22] by Nyqvist and Breizman. In magnetized plasmas, e.g. magnetic confinement devices, the particles gyrate about the magnetic field lines and follow certain trajectories depending on their energy and the magnetic field inhomogeneity.…”

Section: Introductionmentioning

confidence: 99%

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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: Discussionmentioning

confidence: 99%

Section: The Linear Growth Ratementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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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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“…These structures represent nonlinear waves of so-called Bernstein-GreeneKruskal type [18] whose frequencies are slightly up-and down-shifted with respect to that of the initial instability. Their subsequent convective motion in phase space is synchronized to the change in wave frequency, thus leading to complex chirping patterns in dynamical spectra of unstable waves, as discussed in more details in [19][20][21]. This mechanism is frequently referred as Berk-Breizman model.…”

mentioning

confidence: 99%

“…Over the years, the hole and clump mechanism has been extensively examined to study and interpret the Alfven wave turbulence driven by high-energy beam ions or alpha particles in toroidal magnetic traps [17,[19][20][21][23][24][25][26][27][28]; as well as some other MHD processes, such as fishbone [17] and ion-acoustic [29] instabilities, have been considered.…”

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confidence: 99%

Observation of quasi-periodic frequency sweeping in electron cyclotron emission of nonequilibrium mirror-confined plasma

Viktorov¹,

Shalashov²,

Mansfeld³

et al. 2016

EPL

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-Chirping frequency patterns have been observed in the electron cyclotron emission from strongly nonequilibrium plasma confined in a table-top mirror magnetic trap. Such patterns are typical for the formation of nonlinear phase space structures in a proximity of the wave-particle resonances of a kinetically unstable plasma, also known as the "holes and clumps" mechanism. Our data provides the first experimental evidence for acting of this mechanism in the electron cyclotron frequency domain.Introduction. -Resonant interaction of electromagnetic waves and charged particles plays an important role in the dynamics of magnetoactive plasma confined in space and laboratory magnetic traps. One of the most intriguing manifestations of such interaction is emission of broadband radiation with regular variations of dynamical spectra, e.g. quasi-periodic bursts with a frequency sweeping, resulting from the development of kinetic plasma instabilities. Such events are common features of experimental plasmas. Kinetic instabilities are caused by the presence of positive gradients in the velocity distribution of resonant particles, whose formation is universal for both space and laboratory plasma. In space magnetic traps, the sources of free energy are formed due to different acceleration mechanisms of particles, such as betatron acceleration, plasma-wave turbulence and magnetic reconnection. Under laboratory conditions, the energetic particles with an anisotropic velocity distribution can be formed due to the features of plasma heating, when the energy of the external source is embedded in a specific region of the phase space, such as provided by resonant cyclotron heating or neutral beam injection in magnetic fusion experiment. Spatial gradients can also result in instabilities of waves for which the diffusion in real space is coupled to the diffusion in velocity space due to conservation of invariants of particle motion in inhomogeneous systems energy; this type of instability is exploited in the so-called alpha channeling proposals [1,2]. As a rule, plasma confined in laboratory traps consists of at least two components, one

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Kinetic theory of phase space plateaux in a non-thermal energetic particle distribution

2015

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The transformation of kinetically unstable plasma eigenmodes into hole-clump pairs with temporally evolving carrier frequencies was recently attributed to the emergence of an intermediate stage in the mode evolution cycle, that of an unmodulated plateau in the phase space distribution of fast particles. The role of the plateau as the hole-clump breeding ground is further substantiated in this article via consideration of its linear and nonlinear stability in the presence of fast particle collisions and sources, which are known to affect the production rates and subsequent frequency sweeping of holes and clumps. In particular, collisional relaxation, as mediated by e.g. velocity space diffusion or even simple Krook-type collisions, is found to inhibit hole-clump generation and detachment from the plateau, as it should. On the other hand, slowing down of the fast particles turns out to have an asymmetrically destabilizing/stabilizing effect, which explains the well-known result that collisional drag enhances holes and their sweeping rates but suppresses clumps. It is further demonstrated that relaxation of the plateau edge gradients has only a minor quantitative effect and does not change the plateau stability qualitatively, unless the edge region extends far into the plateau shelf and the corresponding Landau pole needs to be taken into account.

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Modeling of long range frequency sweeping for energetic particle modes

Cited by 14 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

Observation of quasi-periodic frequency sweeping in electron cyclotron emission of nonequilibrium mirror-confined plasma

Kinetic theory of phase space plateaux in a non-thermal energetic particle distribution

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