Stabilization of Alfvén Eigenmodes in DIII-D via Controlled Energetic Ion Density Ramp and Validation of Theory and Simulations

Tang, Shawn; Carter, Troy; Crocker, N. A.; Heidbrink, W. W.; Lestz, Jeff; Pinsker, R. I.; Thome, K. E.; Zeeland, M. A. Van; Белова, Е. В.

doi:10.1103/physrevlett.126.155001

Cited by 17 publications

(30 citation statements)

References 26 publications

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“…For instance, cntr-GAEs were routinely excited in the early operation of NSTX-U [9] with v 0 /v A ≈ 1-2, while co-CAEs were rarely observed. In addition, cntr-propagating sub-cyclotron modes have also been observed in dedicated low-field DIII-D discharges [13,14] with v 0 /v A ≈ 1, in agreement with the corresponding HYM simulations [48].…”

Section: Interpretation Of Simulation Resultssupporting

confidence: 85%

“…These critical densities imply thermal damping rates of γ damp /ω ci = 0.02-0.05, corresponding to 20%-60% of the fast-ion drive for the case with a nominal experimental fast ion density of n b /n e = 0.053. A beam density threshold for a cntr-GAE was recently demonstrated in DIII-D experiments, taking advantage of the unique variable beam perveance capability [14,52].…”

Section: Rate Of Mode Damping On the Thermal Plasmamentioning

confidence: 99%

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Hybrid simulations of sub-cyclotron compressional and global Alfvén eigenmode stability in spherical tokamaks

Lestz¹,

Белова²,

Gorelenkov³

2021

Nucl. Fusion

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A comprehensive numerical study has been conducted in order to investigate the stability of beam-driven, sub-cyclotron-frequency compressional Alfvén eigenmodes (CAEs) and global Alfvén eigenmodes (GAEs) in low-aspect-ratio plasmas for a wide range of beam parameters. The presence of CAEs and GAEs has previously been linked to anomalous electron temperature profile flattening at high beam powers in NSTX experiments, prompting a further examination of the conditions necessary for their excitation. Linear simulations have been performed with the hybrid MHD–kinetic initial value code in order to capture the general Doppler-shifted cyclotron resonance that drives the modes. Three distinct types of modes were found in the simulations—co-CAEs, cntr-GAEs, and co-GAEs—with differing spectral and stability properties. The simulations revealed that unstable GAEs are more ubiquitous than unstable CAEs, which is consistent with experimental observations, as they are excited at lower beam energies and generally have larger growth rates. Local analytic theory is used to explain key features of the simulation results, including the preferential excitation of different modes based on beam injection geometry and the growth rate dependence on the beam injection velocity, critical velocity, and degree of velocity space anisotropy. The background damping rate is inferred from the simulations and analytically estimated for relevant sources absent from the simulation model, indicating that co-CAEs are closer to marginal stability than modes driven by the cyclotron resonances.

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Section: Interpretation Of Simulation Resultssupporting

confidence: 85%

Section: Rate Of Mode Damping On the Thermal Plasmamentioning

confidence: 99%

Hybrid simulations of sub-cyclotron compressional and global Alfvén eigenmode stability in spherical tokamaks

Lestz¹,

Белова²,

Gorelenkov³

2021

Nucl. Fusion

Self Cite

View full text Add to dashboard Cite

show abstract

“…For instance, cntr-GAEs were routinely excited in early operation of NSTX-U 9 with v 0 /v A ≈ 1 − 2, while co-CAEs were rarely observed. In addition, cntr-propagating, sub-cyclotron modes have also been observed in dedicated low field DIII-D discharges 13,14 with v 0 /v A ≈ 1, in agreement with corresponding HYM simulations. 45…”

Section: A Interpretation Of Simulation Resultssupporting

confidence: 86%

“…High frequency (ω ω ci ) compressional (CAE) and global (GAE) Alfvén Eigenmodes are routinely driven unstable by super-Alfvénic beam ions in the spherical tokamaks NSTX, [1][2][3][4][5][6][7][8] NSTX-U, 9,10 and MAST. 11,12 They have also been observed in the conventional aspect ratio tokamaks DIII-D 13,14 and ASDEX Upgrade, 15 with barely Alfvénic or sub-Alfvénic fast ions. The CAEs/GAEs have been observed in the broad frequency range 0.1 < ω/ω ci < 1.2 with a wide range of toroidal mode numbers |n| = 1 − 15, and may propagate toroidally either with (co-propagation) or against (cntrpropagation) the direction of the plasma current and beam injection.…”

Section: Introductionmentioning

confidence: 89%

“…A beam density threshold for a cntr-GAE was recently demonstrated in DIII-D experiments, taking advantage of the unique variable beam perveance capability. 14,49 Given this relatively large damping rate, it is natural to consider its primary source. The resistivity and viscosity in the simulations were varied to determine their influence on the damping.…”

Section: Rate Of Mode Damping On the Thermal Plasmamentioning

confidence: 99%

See 1 more Smart Citation

Hybrid simulations of sub-cyclotron compressional and global Alfvén Eigenmode stability in spherical tokamaks

Lestz¹,

Belova²,

Gorelenkov³

2021

Preprint

View full text Add to dashboard Cite

A comprehensive numerical study has been conducted in order to investigate the stability of beam-driven, subcyclotron frequency compressional (CAE) and global (GAE) Alfvén eigenmodes in low aspect ratio plasmas for a wide range of beam parameters. The presence of CAEs and GAEs has previously been linked to anomalous electron temperature profile flattening at high beam power in NSTX experiments, prompting further examination of the conditions for their excitation. Linear simulations are performed with the hybrid MHD-kinetic initial value code HYM in order to capture the general Doppler-shifted cyclotron resonance that drives the modes. Three distinct types of modes are found in simulations -co-CAEs, cntr-GAEs, and co-GAEs -with differing spectral and stability properties. The simulations reveal that unstable GAEs are more ubiquitous than unstable CAEs, consistent with experimental observations, as they are excited at lower beam energies and generally have larger growth rates. Local analytic theory is used to explain key features of the simulation results, including the preferential excitation of different modes based on beam injection geometry and the growth rate dependence on the beam injection velocity, critical velocity, and degree of velocity space anisotropy. The background damping rate is inferred from simulations and estimated analytically for relevant sources not present in the simulation model, indicating that co-CAEs are closer to marginal stability than modes driven by the cyclotron resonances.

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Physics-constrained machine learning for electrodynamics without gauge ambiguity based on Fourier transformed Maxwell’s equations

Leon,

Scheinker

2024

Sci Rep

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We utilize a Fourier transformation-based representation of Maxwell’s equations to develop physics-constrained neural networks for electrodynamics without gauge ambiguity, which we label the Fourier–Helmholtz–Maxwell neural operator method. In this approach, both of Gauss’s laws and Faraday’s law are built in as hard constraints, as well as the longitudinal component of Ampère–Maxwell in Fourier space, assuming the continuity equation. An encoder–decoder network acts as a solution operator for the transverse components of the Fourier transformed vector potential, $$\hat{{\textbf {A}}}_\perp ({\textbf {k}}, t)$$ A ^ ⊥ ( k , t ) , whose two degrees of freedom are used to predict the electromagnetic fields. This method was tested on two electron beam simulations. Among the models investigated, it was found that a U-Net architecture exhibited the best performance as it trained quicker, was more accurate and generalized better than the other architectures examined. We demonstrate that our approach is useful for solving Maxwell’s equations for the electromagnetic fields generated by intense relativistic charged particle beams and that it generalizes well to unseen test data, while being orders of magnitude quicker than conventional simulations. We show that the model can be re-trained to make highly accurate predictions in as few as 20 epochs on a previously unseen data set.

show abstract

Stabilization of Alfvén Eigenmodes in DIII-D via Controlled Energetic Ion Density Ramp and Validation of Theory and Simulations

Cited by 17 publications

References 26 publications

Hybrid simulations of sub-cyclotron compressional and global Alfvén eigenmode stability in spherical tokamaks

Hybrid simulations of sub-cyclotron compressional and global Alfvén eigenmode stability in spherical tokamaks

Hybrid simulations of sub-cyclotron compressional and global Alfvén Eigenmode stability in spherical tokamaks

Physics-constrained machine learning for electrodynamics without gauge ambiguity based on Fourier transformed Maxwell’s equations

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