Compressional Alfvén eigenmode structure in spherical tokamaks

Smith, H. M.; Verwichte, E.

doi:10.1088/0741-3335/51/7/075001

Cited by 28 publications

(49 citation statements)

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…According to the naming convention of [13], the five eigenmodes have the mode numbers (s = 1/2, m = 0), (s = 1, m = 1), (s = 1, m = −1), (s = 1, m = 2) and (s = 1, m = −2), respectively. However, we will for simplicity just number the eigenmodes in ascending order according to their eigenfrequencies, with the aid of the symbols seen in the figure.…”

Section: Results From Cae3b With Rotationmentioning

confidence: 99%

“…The term ρ 1 v 0 · ∇v 0 can therefore be neglected in (11), since it is of the order Ω 2 /ω 2 compared with the first term. Henceforth, it is assumed that perturbed quantities vary as exp(−inϕ − iωt), following the convention in [13]. Thus, v 0 · ∇v 1 = −inΩv 1 and the form of the rotation velocity v 0 = Ω(r)Rφ yields…”

Section: The Eigenmode Equationmentioning

confidence: 99%

“…Numerical studies have been able to more accurately include the magnetic-field geometry of the spherical tokamak [16,13]. However, these numerical studies also employ certain simplifying assumptions.…”

Section: Introductionmentioning

confidence: 99%

“…The simulations with the ideal MHD code NOVA [16] neglect the Hall term, which can be of importance since the eigenmode frequency is of the order of the ion cyclotron frequency ω ci . The CAE3B code (which was presented in [13] but not given a name there), on the other hand, includes the Hall term but excludes shear Alfvén waves by assuming that v 2 A /(ω 2 B 2 )(B · ∇) 2 ≪ 1 when operating on components of the perturbed magnetic field perpendicular to the background field. This restriction is lifted in the WHALES code [17], which is based on finite elements instead of finite differences as in CAE3B.…”

Section: Introductionmentioning

confidence: 99%

“…To this end, a new version of the CAE3B code is developed, which includes the effects of the plasma rotation on the eigenmodes. In Section 2 the eigenmode equation derived in [13] is extended to account for plasma rotation, and in Section 3 results from numerical solutions of this equation with the new code are presented and discussed.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Compressional Alfvén eigenmodes in rotating spherical tokamak plasmas

Smith

Fredrickson

2017

Plasma Phys. Control. Fusion

Self Cite

View full text Add to dashboard Cite

Abstract. Spherical tokamaks often have a considerable toroidal plasma rotation of several tens of kHz. Compressional Alfvén eigenmodes (CAEs) in such devices therefore experience a frequency shift, which if the plasma were rotating as a rigid body, would be a simple Doppler shift. However, since the rotation frequency depends on minor radius, the eigenmodes are affected in a more complicated way. The eigenmode solver CAE3B [Smith et al. Plasma Phys. Control. Fusion 51, 075001 (2009)] has been extended to account for toroidal plasma rotation. The results show that the eigenfrequency shift due to rotation can be approximated by a rigid body rotation with a frequency computed from a spatial average of the real rotation profile weighted with the eigenmode amplitude. To investigate the effect of extending the computational domain to the vessel wall, a simplified eigenmode equation, yet retaining plasma rotation, is solved by a modified version of the CAE code used in [Fredrickson et al. Phys. Plasmas 20, 042112 (2013)]. In summary, both solving the full eigenmode equation, as in the CAE3B code, and placing the boundary at the vessel wall, as in the CAE code, significantly influences the calculated eigenfrequencies.

show abstract

Section: Results From Cae3b With Rotationmentioning

confidence: 99%

Section: The Eigenmode Equationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Compressional Alfvén eigenmodes in rotating spherical tokamak plasmas

Smith

Fredrickson

2017

Plasma Phys. Control. Fusion

Self Cite

View full text Add to dashboard Cite

show abstract

Bi-directional Alfvén cyclotron instabilities in the mega-amp spherical tokamak

et al. 2014

View full text Add to dashboard Cite

Alfvén cyclotron instabilities excited by velocity gradients of energetic beam ions were investigated in MAST experiments with super-Alfvénic NBI over a wide range of toroidal magnetic fields from ~0.34 T to ~0.585 T. In MAST discharges with high magnetic field, a discrete spectrum of modes in the sub-cyclotron frequency range is excited toroidally propagating counter to the beam and plasma current (toroidal mode numbers n < 0). At lower magnetic field ≤ 0.45 T, a discrete spectrum of Compressional Alfvén Eigenmodes (CAEs) with n > 0 arises, in addition to the modes with n < 0. At lowest magnetic fields, the CAEs with n > 0 become dominant, they are observed in frequency range from ~250 kHz for 1 = n to ~3.5 MHz for 15 = n , well above the onaxis ion cyclotron frequency (~2.5 MHz). The data is interpreted in terms of normal and anomalous Doppler resonances modified by magnetic drift terms due to inhomogeneity and curvature of the magnetic field. A Hall MHD model is applied for computing the eigenfrequencies and the spatial mode structure of CAEs and a good agreement with the experimental frequencies is found.

show abstract

Nonlinear simulations of beam-driven compressional Alfvén eigenmodes in NSTX

et al. 2017

View full text Add to dashboard Cite

Results of 3D nonlinear simulations of neutral-beam-driven compressional Alfvén eigenmodes (CAEs) in the National Spherical Torus Experiment (NSTX) are presented. Hybrid MHD-particle simulations for the H-mode NSTX discharge (shot 141398) using the HYM code show unstable CAE modes for a range of toroidal mode numbers, n=4−9, and frequencies below the ion cyclotron frequency. It is found that the essential feature of CAEs is their coupling to kinetic Alfvén wave (KAW) that occurs on the high-field side at the Alfvén resonance location. High-frequency Alfvén eigenmodes are frequently observed in beam-heated NSTX plasmas, and have been linked to flattening of the electron temperature profiles at high beam power. Coupling between CAE and KAW suggests an energy channeling mechanism to explain these observations, in which beam-driven CAEs dissipate their energy at the resonance location, therefore significantly modifying the energy deposition profile. Nonlinear simulations demonstrate that CAEs can channel the energy of the beam ions from the injection region near the magnetic axis to the location of the resonant mode conversion at the edge of the beam density profile. A set of nonlinear simulations show that the CAE instability saturates due to nonlinear particle trapping, and a large fraction of beam energy can be transferred to several unstable CAEs of relatively large amplitudes and absorbed at the resonant location. Absorption rate shows a strong scaling with the beam power.

show abstract

Compressional Alfvén eigenmode structure in spherical tokamaks

Cited by 28 publications

References 35 publications

Compressional Alfvén eigenmodes in rotating spherical tokamak plasmas

Compressional Alfvén eigenmodes in rotating spherical tokamak plasmas

Bi-directional Alfvén cyclotron instabilities in the mega-amp spherical tokamak

Nonlinear simulations of beam-driven compressional Alfvén eigenmodes in NSTX

Contact Info

Product

Resources

About