Analytic stability boundaries for compressional and global Alfvén eigenmodes driven by fast ions. II. Interaction via Landau resonance

Lestz, Jeff; Gorelenkov, N. N.; Белова, Е. В.; Tang, Shawn; Crocker, N. A.

doi:10.1063/1.5127552

Cited by 9 publications

(23 citation statements)

References 38 publications

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“…III.B.1 of Ref. 30, net drive for co-CAEs driven by beams with λ 0 = 0.7 and ∆λ = 0.3 requires v 0 /v A > 4.1, similar to what is found in HYM simulations. The co-GAEs also require relatively large v 0 /v A for excitation, due to the requirement of a sufficiently large Doppler shift k v ,res in order to satisfy the strong = −1 resonance which drives them.…”

Section: A Interpretation Of Simulation Resultssupporting

confidence: 74%

“…A comprehensive parameter scan of these quantities is performed for a wide range of toroidal mode numbers. The inferred stability boundaries and growth rate trends are interpreted with recently derived expressions for the local fast ion drive, 29,30 yielding very reasonable agreement. The effect of gradients in the fast ion distribution with respect to p φ , self-consistently included in the simulations but absent in the local theory used throughout the paper, is considered and found to resolve some discrepancies.…”

Section: Introductionmentioning

confidence: 55%

“…In the simulations, most of the drive comes from the high energy fast ions, though realistic two-fluid effects may make the Landau resonance of comparable importance in experiments. 30 Just as with the cntr-GAEs, the high frequency co-GAEs behave more like EPMs than MHD eigenmodes, exhibiting large changes in frequency in proportion to changes in v 0 /v A , without any significant changes to the mode structure (also shown on Fig. 7).…”

Section: Co-propagating Gaesmentioning

confidence: 78%

“…As explored in Ref. 30, this may be due to the fact that they have a similar instability condition to the co-CAEs, but with growth rate reduced by a typically small factor (ω/ω ci ) 2 . High frequency co-GAEs were never observed in NSTX, nor have they been documented in other devices.…”

Section: Co-propagating Gaesmentioning

confidence: 95%

“…Approximate stability boundaries with respect to beam injection parameters for CAEs and GAEs have recently been derived under conditions relevant to the simulated NSTX conditions. 29,30 Such boundaries apply when 0.2 ∆λ 0.8 (the NSTX(-U) value is ∆λ ≈ 0. 30 for the = 0 resonance in the small FLR regime are applicable to the unstable modes in NSTX simulations presented here.…”

Section: Approximate Stability Boundariesmentioning

confidence: 99%

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

Lestz¹,

Belova²,

Gorelenkov³

2021

Preprint

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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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Section: A Interpretation Of Simulation Resultssupporting

confidence: 74%

Section: Introductionmentioning

confidence: 55%

Section: Co-propagating Gaesmentioning

confidence: 78%

Section: Co-propagating Gaesmentioning

confidence: 95%

Section: Approximate Stability Boundariesmentioning

confidence: 99%

See 3 more Smart Citations

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

Lestz¹,

Belova²,

Gorelenkov³

2021

Preprint

Self Cite

View full text Add to dashboard Cite

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Analytic stability boundaries for compressional and global Alfvén eigenmodes driven by fast ions. I. Interaction via ordinary and anomalous cyclotron resonances

et al. 2020

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Conditions for net fast ion drive are derived for beam-driven, sub-cyclotron compressional (CAE) and global (GAE) Alfvén eigenmodes, such as those routinely observed in spherical tokamaks such as NSTX(-U) and MAST. Both co-and counter-propagating CAEs and GAEs are investigated, driven by the ordinary and anomalous Doppler-shifted cyclotron resonance with fast ions. Whereas prior results were restricted to vanishingly narrow distributions in velocity space, broad parameter regimes are identified in this work which enable an analytic treatment for realistic fast ion distributions generated by neutral beam injection. The simple, approximate conditions derived in these regimes for beam distributions of realistic width compare well to the numerical evaluation of the full analytic expressions for fast ion drive. Moreover, previous results in the very narrow beam case are corrected and generalized to retain all terms in ω/ω ci and k /k ⊥ , which are often assumed to be small parameters but can significantly modify the conditions of drive and damping when they are non-negligible. Favorable agreement is demonstrated between the approximate stability criterion, simulation results, and a large database of NSTX observations of cntr-GAEs. arXiv:1909.05462v1 [physics.plasm-ph]

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Nonlinear simulations of GAEs in NSTX-U

Belova,

Fredrickson,

Crocker

2024

Physics of Plasmas

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A set of nonlinear simulations has been performed in order to study the nonlinear evolution of unstable global Alfvén eigenmodes in the National Spherical Torus Experiment-Upgrade (NSTX-U). Results of the single toroidal mode number, n, simulations are compared with a full nonlinear simulation (all toroidal harmonics included). In single-n simulations, the conservation of two integrals of motion of a particle in a cyclotron resonance with a monochromatic wave is demonstrated, resulting in a one-dimensional evolution of the particle distribution in (E,μ,pϕ) phase-space. Nonlinear simulations (both single-n and full nonlinear) show a significant redistribution of the resonant fast ions, especially in the pitch parameter. Thus, the changes in the resonant particle's parallel and perpendicular energies can be several times larger than the total particle energy change, with only a small fraction transferring into the excitation of the mode itself. This implies that even a relatively small amplitude mode can significantly modify the beam distribution in the resonant region. For the NSTX-U case considered, the single-n simulation results are close to full nonlinear simulation only for the most unstable mode, in which case the saturation amplitudes and changes in the fast ion distribution are comparable. In contrast, peak amplitudes of subdominant modes in all-n simulations are smaller by a factor of 3–10 compared to single-n runs due to the flattening of the beam ion distribution by the fastest growing mode.

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Analytic stability boundaries for compressional and global Alfvén eigenmodes driven by fast ions. II. Interaction via Landau resonance

Cited by 9 publications

References 38 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

Analytic stability boundaries for compressional and global Alfvén eigenmodes driven by fast ions. I. Interaction via ordinary and anomalous cyclotron resonances

Nonlinear simulations of GAEs in NSTX-U

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