Drift Alfvén energetic particle stability with circulating particles

Li, Y.; Hu, Shiqiang; Zheng, Weiying; Xiao, Yong

doi:10.1063/5.0005727

Cited by 5 publications

(17 citation statements)

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“…In order to accurately address the complex magnetic geometry in a tokamak, a particular set of magnetic coordinates, i.e., the Boozer coordinates (ψ p , θ B , ζ B ) are used in the theoretical modelling and numeric calculation in this paper. The vorticity equation using the ballooning representation and the Boozer coordinates can be written as [14,25]…”

Section: Vorticity Equation and Gyrokinetic Equationmentioning

confidence: 99%

“…Recently both fluid-kinetic hybrid simulation and gyrokinetic simulation have been developed to looked into the linear and nonlinear BAE physics [6,[21][22][23][24], e.g., wave-particle trapping has been recently discovered to be the main saturation mechanism of BAE turbulence [24]. Here we employ a newly developed non-perturbative linear eigenvalue code named DAEPS [25] (drift Alfvén EP stability) to investigate the plasma shaping effect on the BAE instability.…”

Section: Introductionmentioning

confidence: 99%

“…The DAEPS code is based on the general fishbone-like dispersion relation (GFLDR) theoretical framework and uses the numerical method of finite element to calculate various unstable or stable drift Afvénic eigenmodes in toroidal plasmas [25]. This code uses an iteration method to solve the vorticity equation, as well as to obtain the complex frequency ω and asymptotic behaviour Λ with high precision.…”

Section: Introductionmentioning

confidence: 99%

“…In addition, it has used the Neumann boundary condition for accurate asymptotic wave behaviour in the inertial region of the Ballooning space, i.e., ∂ θ Ψ = iΛΨ. Furthermore, in order to speed up numerical integration, a reduced method based on drift center transformation has been developed in DAEPS to calculate the BAE stability [25]. Many numerical codes have investigated the AE physics by setting the perturbed magnetic potential Ψ = 0 as the boundary condition [26,27], which cannot accurately compute the asymptotic mode behaviour and then the eigen frequency on many occasions, especially for those damped modes or marginally unstable modes.…”

Section: Introductionmentioning

confidence: 99%

“…Most previous studies on the AEs are based on a model equilibrium with concircular magnetic flux surface [20,25]. However, the cross section of magnetic flux surface is generally not circular in modern tokamaks.…”

Section: Introductionmentioning

confidence: 99%

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Elongation effect on beta-induced Alfvén eigenmode

Xiao

2022

Nucl. Fusion

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Beta induced Alfvén eigenmode (BAE) can be an important candidate for ion loss in burning plasmas. Elongation effect on BAE has been investigated by the gyrokinetic eigenvalue code DAEPS in this work. We construct a shaped equilibrium model by modifying local s − α model with which the capability of the DAEPS code has been extended to study the elongation effect. It is discovered that the BAE growth rate first increases with elongation factor κ, reaches a maximum and then decreases. This trend occurs for many different values of η i. We find that, in the weak or moderate elongation region, the BAE instability is reactive type and mainly determined by the fluid/MHD effects, namely the combination of stabilizing field line bending term and destabilizing interchange drive in the vorticity equation. However, in the strong elongation region, the BAE instability becomes dissipative and is mainly driven by the wave–particle resonance effect embedded in δW k since the fluid driving damps away. It is also discovered that the wave–particle resonance decreases with elongation in this region, which is due to the decrease of the geodesic curvature with elongation and leads to the decrease in the growth rate of BAE.

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Section: Vorticity Equation and Gyrokinetic Equationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Elongation effect on beta-induced Alfvén eigenmode

Xiao

2022

Nucl. Fusion

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Effects of rotating magnetic island on the transport of trapped fast ions

et al. 2022

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The enhanced transport of trapped energetic ions (TEIs) in the presence of resonant interactions between trapped fast ions and a rotating magnetic island is investigated within a drift-kinetic framework. Gyro-orbit banana center model equations of resonances between the island rotation, the bounce motion of trapped fast ions, and their precession frequency (poloidal precession and precession in the helical direction) are constructed. There are two solutions for resonances in phase space for different mode numbers, with only one solution having low-energy resonant lines (<100 keV); the other has not only low-energy resonant lines but also high-energy lines (≥100 keV). Island rotation plays an important role in the low-energy region, especially near the trapped-passing boundary. The precession frequency is more important when resonances occur in the high-energy area. Thus, the effect of islands on TEI transport in a low-energy region is the focus of this paper. Transport fluxes caused by collisions, resonances, and symmetry breaking induced by an island are obtained. We divide transport fluxes into two types: [Formula: see text] arising from magnetic drift and [Formula: see text] arising from the island rotation. There is a discontinuity in [Formula: see text] with different island widths near the island separatrix. On the right-hand side of the (m = 2, n = 1) rational surface, [Formula: see text] is more important than [Formula: see text], and at the plasma boundary, the flux due to drift can suppress [Formula: see text], which makes fast ions move toward inner plasma. On the left-hand side of the rational surface, [Formula: see text] is dominant. When the island width is larger than a certain threshold, the fluxes oscillate, and [Formula: see text] is far larger than [Formula: see text].

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Physics of drift Alfvén instabilities and energetic particles in fusion plasmas

Falessi

Lauber

et al. 2023

Plasma Phys. Control. Fusion

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Shear Alfvén wave (SAW)/drift Alfvén wave (DAW) fluctuations can bedestabilized by energetic particles (EPs) as well as thermal plasmacomponents, which play a key role in the EP energy and momentumtransport processes in burning fusion plasmas. The drift Alfvénenergetic particle stability (`DAEPS`) code, which is an eigenvalue codeusing the finite element method (FEM), was developed to analyze Alfvéninstabilities excited by EPs. The model equations, consisting ofquasi-neutrality condition and Schrödinger-like form of vorticityequation, are derived within the general fishbone-like dispersionrelation (GFLDR) theoretical framework, which is widely used to analyzeSAW/DAW physics. The mode structure decomposition (MSD) approach andasymptotic matching between the inertial/singular layer and idealregions are adopted. Therefore, the `DAEPS` code can provide not onlyfrequency and growth/damping rate, but also the parallel mode structureas well as the asymptotic behavior corresponding to the singular layercontribution. Thus, it fully describes fluid and kinetic continuousspectra as well as unstable and damped modes. The model equations havebeen extended to include general axisymmetric geometry, and to solve forthe response of circulating and trapped particles by means of the actionangle approach. In this work, we discuss linear dispersion relation andparallel mode structure of drift Alfvén instabilities excited by EPs,computed by the `DAEPS` code with realistic experimental plasma profileand magnetic configuration. Based on this information, we adopt theDyson-Schrödinger Model (DSM) to further analyze EP energy and momentumflux. We will also briefly discuss how the parallel mode structure ofthe drift Alfvén instabilities can be used in the DSM to calculate thenonlinear radial envelope evolution and the EP transport.

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Drift Alfvén energetic particle stability with circulating particles

Cited by 5 publications

References 50 publications

Elongation effect on beta-induced Alfvén eigenmode

Elongation effect on beta-induced Alfvén eigenmode

Effects of rotating magnetic island on the transport of trapped fast ions

Physics of drift Alfvén instabilities and energetic particles in fusion plasmas

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