Theory of Alfvén-slow frequency gaps and discovery of Alfvén-slow eigenmodes in tokamaks

Chio-Zong Cheng, G. J. Kramer, M. Podesta, R. Nazikian

Research output: Contribution to journalArticle

Abstract

An analytical theory based on the MHD model is presented for understanding the coupling between the shear Alfvén wave and the slow magnetosonic wave (or the so called slow mode) in the frequency range below the Toroidal Alfvén Eigenmode (TAE) continuum spectrum gap. In tokamak plasmas, coupling of the Alfvén m poloidal harmonic and the slow mode m ± 1 harmonics causes the Alfvén m harmonic continuous spectrum to be uplifted from the uncoupled Alfvén spectrum by an amount related to the plasma pressure and the geodesic magnetic field curvature. However, the frequency of one of the slow mode m ± 1 harmonics is reduced by the same pressure-curvature coupling effect. But the frequency of the other slow mode harmonic is relatively unaffected. As a result, the Alfvén-slow (AS) mode continuous spectrum is broken up into two Alfvén-Slow (AS) gaps below the TAE continuum gap. Coupling of the Alfvén m harmonic with the slow mode m ± 2 harmonics also creates additional AS gaps if their frequencies cross each other. The AS gap widths increase with the plasma pressure. The creation of AS gaps allows the existence of several new types of Alfvén-Slow Eigenmodes (ASEs). The radial structure of these new ASEs does not intersect with the continuous spectrum and thus does not suffer from continuum damping. The Beta-induced Alfvén-Acoustic Eigenmode (BAAE) is one type of ASEs with frequency in the lowest AS frequency gap. However, the BAAE usually interacts with the Alfvén-Slow continuum and suffers from continuum damping. The existence of ASEs is ubiquitous for normal and reserve safety factor profiles, broad range of plasma β values, different plasma shapes, and many different toroidal mode numbers. The newly discovered ASEs provide explanation for the experimentally observed Beta-induced Alfvén Eigenmodes destabilized by fast ions with frequencies below the TAE frequency gap.

Original languageEnglish
Article number082508
JournalPhysics of Plasmas
Volume26
Issue number8
DOIs
Publication statusPublished - 2019 Aug 1

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harmonics
continuums
continuous spectra
plasma pressure
damping
curvature
safety factors
acoustics
S waves
frequency ranges
causes
profiles
magnetic fields
ions

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics

Cite this

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title = "Theory of Alfv{\'e}n-slow frequency gaps and discovery of Alfv{\'e}n-slow eigenmodes in tokamaks",
abstract = "An analytical theory based on the MHD model is presented for understanding the coupling between the shear Alfv{\'e}n wave and the slow magnetosonic wave (or the so called slow mode) in the frequency range below the Toroidal Alfv{\'e}n Eigenmode (TAE) continuum spectrum gap. In tokamak plasmas, coupling of the Alfv{\'e}n m poloidal harmonic and the slow mode m ± 1 harmonics causes the Alfv{\'e}n m harmonic continuous spectrum to be uplifted from the uncoupled Alfv{\'e}n spectrum by an amount related to the plasma pressure and the geodesic magnetic field curvature. However, the frequency of one of the slow mode m ± 1 harmonics is reduced by the same pressure-curvature coupling effect. But the frequency of the other slow mode harmonic is relatively unaffected. As a result, the Alfv{\'e}n-slow (AS) mode continuous spectrum is broken up into two Alfv{\'e}n-Slow (AS) gaps below the TAE continuum gap. Coupling of the Alfv{\'e}n m harmonic with the slow mode m ± 2 harmonics also creates additional AS gaps if their frequencies cross each other. The AS gap widths increase with the plasma pressure. The creation of AS gaps allows the existence of several new types of Alfv{\'e}n-Slow Eigenmodes (ASEs). The radial structure of these new ASEs does not intersect with the continuous spectrum and thus does not suffer from continuum damping. The Beta-induced Alfv{\'e}n-Acoustic Eigenmode (BAAE) is one type of ASEs with frequency in the lowest AS frequency gap. However, the BAAE usually interacts with the Alfv{\'e}n-Slow continuum and suffers from continuum damping. The existence of ASEs is ubiquitous for normal and reserve safety factor profiles, broad range of plasma β values, different plasma shapes, and many different toroidal mode numbers. The newly discovered ASEs provide explanation for the experimentally observed Beta-induced Alfv{\'e}n Eigenmodes destabilized by fast ions with frequencies below the TAE frequency gap.",
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Theory of Alfvén-slow frequency gaps and discovery of Alfvén-slow eigenmodes in tokamaks. / Cheng, Chio-Zong; Kramer, G. J.; Podesta, M.; Nazikian, R.

In: Physics of Plasmas, Vol. 26, No. 8, 082508, 01.08.2019.

Research output: Contribution to journalArticle

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AB - An analytical theory based on the MHD model is presented for understanding the coupling between the shear Alfvén wave and the slow magnetosonic wave (or the so called slow mode) in the frequency range below the Toroidal Alfvén Eigenmode (TAE) continuum spectrum gap. In tokamak plasmas, coupling of the Alfvén m poloidal harmonic and the slow mode m ± 1 harmonics causes the Alfvén m harmonic continuous spectrum to be uplifted from the uncoupled Alfvén spectrum by an amount related to the plasma pressure and the geodesic magnetic field curvature. However, the frequency of one of the slow mode m ± 1 harmonics is reduced by the same pressure-curvature coupling effect. But the frequency of the other slow mode harmonic is relatively unaffected. As a result, the Alfvén-slow (AS) mode continuous spectrum is broken up into two Alfvén-Slow (AS) gaps below the TAE continuum gap. Coupling of the Alfvén m harmonic with the slow mode m ± 2 harmonics also creates additional AS gaps if their frequencies cross each other. The AS gap widths increase with the plasma pressure. The creation of AS gaps allows the existence of several new types of Alfvén-Slow Eigenmodes (ASEs). The radial structure of these new ASEs does not intersect with the continuous spectrum and thus does not suffer from continuum damping. The Beta-induced Alfvén-Acoustic Eigenmode (BAAE) is one type of ASEs with frequency in the lowest AS frequency gap. However, the BAAE usually interacts with the Alfvén-Slow continuum and suffers from continuum damping. The existence of ASEs is ubiquitous for normal and reserve safety factor profiles, broad range of plasma β values, different plasma shapes, and many different toroidal mode numbers. The newly discovered ASEs provide explanation for the experimentally observed Beta-induced Alfvén Eigenmodes destabilized by fast ions with frequencies below the TAE frequency gap.

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