Alpha-Alfvén local dispersion relation and solutions

Hedrick, C.L.; Leboeuf, J. N.; Spong, D. A.

doi:10.1063/1.860344

Cited by 36 publications

(35 citation statements)

References 23 publications

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“…Equation (2) is derived from Ohm s law coupled with Faraday s law, equation (3) is obtained from the toroidal component of the momentum balance equation after applying the operator ∇ ∧ √ g, equation (4) is obtained from the thermal plasma continuity equation with compressibility effects and equation (5) is obtained from the parallel component of the momentum balance [69,70,71,83]. Equations (6) and (7) are obtained calculating the first two moments of the kinetic equation [74,75]. Here, U = √ g ∇ × ρ m √ gv ζ is the toroidal component of the vorticity, ρ m the ion and electron mass density, ρ = √ φ N the effective radius with φ N the normalized toroidal flux and θ the poloidal angle.…”

Section: Equations and Numerical Schemementioning

confidence: 99%

Effect of the tangential NBI current drive on the stability of pressure and energetic particle driven MHD modes in LHD plasma

Varela¹,

Cooper²,

Nagaoka³

et al. 2020

Nucl. Fusion

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The aim of the present study is to analyze the stability of the pressure gradient driven modes (PM) and Alfvén eigenmodes (AE) in the Large Helical Device (LHD) plasma if the rotational transform profile is modified by the current drive of the tangential neutral beam injectors (NBI). This study forms a basic search for optimized operation scenarios with reduced mode activity. The analysis is performed using the code FAR3d which solves the reduced MHD equations describing the linear evolution of the poloidal flux and the toroidal component of NBI current drive 2 the vorticity in a full 3D system, coupled with equations for density and parallel velocity moments of the energetic particle (EP) species, including the effect of the acoustic modes. The Landau damping and resonant destabilization effects are added via the closure relation. On-axis and off-axis NBI current drive modifies the rotational transform which becomes strongly distorted as the intensity of the neutral beam current drive (NBCD) increases, leading to wider continuum gaps and modifying the magnetic shear. The simulations with on-axis NBI injection show that a counter (ctr-) NBCD in inward shifted and default configurations leads to a lower growth rate of the PM, although strong n = 1 and 2 AEs can be destabilized. For the outward shifted configurations, a co-NBCD improves the AEs stability but the PM are further destabilized if the co-NBCD intensity is 30 kA/T. If the NBI injection is off-axis, the plasma stability is not significantly improved due to the further destabilization of the AE and energetic particle modes (EPM) in the middle and outer plasma region.

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Section: Equations and Numerical Schemementioning

confidence: 99%

Effect of the tangential NBI current drive on the stability of pressure and energetic particle driven MHD modes in LHD plasma

Varela¹,

Cooper²,

Nagaoka³

et al. 2020

Nucl. Fusion

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“…A methodology has been developed to calibrate Landauclosure models against more complete kinetic models and optimize the closure coefficients [35]. The model includes Landau resonance couplings, fast ion FLR [54] and Landau damping of the modes on the background ions/electrons [53], although we did not consider the last two for simplicity. This paper is organized as follows.…”

Section: Introductionmentioning

confidence: 99%

Analysis of the MHD stability and energetic particles effects on EIC events in LHD plasma using a Landau-closure model

et al. 2019

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The aim of this study is to perform a theoretical analysis of the magnetohydrodynamic (MHD) stability and energetic particle effects on a LHD equilibria, calculated during a discharge where energetic-ion-driven resistive interchange mode (EIC) events were triggered. We use the reduced MHD equations to describe the linear evolution of the poloidal flux and the toroidal component of the vorticity in a full 3D system, coupled with equations of density and parallel velocity moments for the energetic particles species, including the effect of the acoustic modes, multiple energetic particles (EP) species, helical couplings and helically trapped EP. We add the Landau damping and resonant destabilization effects using a closure relation. The simulations suggest that the helically trapped EP driven by the perpendicular neutral beam injector (NBI) further destabilizes the 1/1 MHD-like mode located at the plasma periphery (r/a = 0.88). If the β of the EP driven by the perpendicular NBI is larger than 0.0025 a 1/1 EIC with a frequency around 3 kHz is destabilized. If the effect of the passing EP driven by the tangential NBI is included on the model, any enhancement of the injection intensity of the tangential NBI below β = 0.025 leads to a decrease of the instability growth rate. The simulations indicate that the EIC in LHD 2 perpendicular NBI EP is the main driver of the EIC events, as it was observed in the experiment. If the effect of the helical couplings are added in the model, an 11/13 EIC is destabilized with a frequency around 9 kHz, inward shifted (r/a = 0.81) compared to the 1/1 EIC. Thus, one possible explanation for the EIC frequency chirping down from 9 to 3 kHz is a transition between the 11/13 to the 1/1 EIC due to a weakening of the destabilizing effect of the high n modes, caused by a decrease of the EP drive due to a loss of helically trapped EP or a change in the EP distribution function after the EIC burst. The experimental data during the EIC bursting phase shows a complex mode structure and an inward shift of the instability, although no direct evidence of the proposed transition has been observed yet.

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“…A methodology has been developed to calibrate Landauclosure models against more complete kinetic models and optimize the closure coefficients [79]. The model includes Landau resonance couplings, thermal ion and energetic particle FLR effects [78] as well as the Landau damping of the modes on the background ions/electrons [77]. This paper is organized as follows.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Alfven eigenmode destabilization in ITER using a Landau closure model

Varela

Garcia

2019

Nucl. Fusion

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Alfvén Eigenmodes (AE) can be destabilized during ITER discharges driven by neutral beam injection (NBI) energetic particles (EP) and alpha particles. The aim of the present study is to analyze the AE stability of different ITER operation scenarios considering multiple energetic particle species. We use the reduced magneto-hydrodynamic (MHD) equations to describe the linear evolution of the poloidal flux and the toroidal component of the vorticity in a full 3D system, coupled with equations of density and parallel velocity moments for the energetic particles species including the effect of the acoustic modes. The AEs driven by the NBI EP and alpha particles are stable in the configurations analyzed, only MHD-like modes with large toroidal couplings are unstable, although both can be destabilized if the EP β increases above a threshold. The threshold is two times the model β value for the NBI EP and alpha particles in the reverse shear case, leading to the destabilization of Beta induced AE (BAE) near the magnetic axis with a frequency of 25 − 35 kHz and Toroidal or Elliptical AE (TAE/EAE) in the reverse shear region with a frequency of 125 − 175 kHz, respectively. On the other hand, the hybrid and steady state configurations show a threshold 3 times larger with respect to the model β for the alpha particle and 40 times for the NBI EP, also destabilizing BAE and TAE between the inner and middle plasma region. In addition, a extended analysis of the reverse shear scenario where the β of both alpha particles and NBI EP are above the AE threshold, multiple EP damping effects are also identified as well as optimization trends regarding the resonance properties of the alpha particle and NBI EP with the bulk plasma.

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Alpha-Alfvén local dispersion relation and solutions

Cited by 36 publications

References 23 publications

Effect of the tangential NBI current drive on the stability of pressure and energetic particle driven MHD modes in LHD plasma

Effect of the tangential NBI current drive on the stability of pressure and energetic particle driven MHD modes in LHD plasma

Analysis of the MHD stability and energetic particles effects on EIC events in LHD plasma using a Landau-closure model

Analysis of Alfven eigenmode destabilization in ITER using a Landau closure model

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