Author ORCID Identifier

https://orcid.org/0000-0002-2061-0004

Semester

Fall

Date of Graduation

2024

Document Type

Dissertation

Degree Type

PhD

College

Eberly College of Arts and Sciences

Department

Physics and Astronomy

Committee Chair

Mark Koepke

Committee Member

Paul Cassak

Committee Member

Weichao Tu

Committee Member

Jason Gross

Abstract

In magnetically-confined fusion devices, the toroidicity-induced Alfv´en eigenmode (TAE) is a well-studied, weakly stable solution of the linearized ideal magnetohydrodynamic (MHD) equations. Due to intrinsic coupling of poloidal harmonics of the shear Alfv´en wave (SAW) in toroidal geometry, the rotational transform of magnetic field lines modulates the effective index of refraction, ensuring gaps in the so-called “Alfv´en continuum.” Experimental verification of theoretical predictions for various parameters of interest (i.e., frequency, mode structure, instability threshold, etc.) is established in the literature.

We present the first systematic study of TAE-TAE phase coherence in an experimental device, using the DIII-D tokamak. Crucially, nonlinear wave-wave coupling is doc- umented within ensembles of TAE over a range of experimental conditions. Four dis- charges heated by neutral beam injection (NBI) are considered; a scan of fast-ion density gradient via NBI power (3, 4, & 5 MW) leads to observable changes in density, neutron emission, and temperature. Shot-to-shot variation of data is negligible prior to beam change.

Magnetic fluctuation spectra, toroidal modenumber spectra, spatially-resolved fluctuations, and wavenumber-frequency spectra are inferred from experimental data. Participating waves are seen to coexist in configuration space and satisfy simultaneous coupling conditions in frequency and wavevector, consistent with nonlinear generation. Partially automated analysis yields a portfolio of candidates for quadratic coupling, and equilibrium magnetic field reconstructions inform estimates of the Alfv´en continuum. We conclude that nonlinear TAE-TAE coupling is repeatedly documented in the experimental data.

Identification of phase-coherency between multiple TAE and nonlinearly-generated modes is facilitated by wavelet-based bicoherence analysis of time series from inductive coils. Biphase dynamics associated with prominent bispectral features are well-resolved in time and consistent with transient quadratic coupling. The onset and duration of the nonlinearity are correlated with enhanced amplitude of participating TAE, as reported by band pass filtering in frequencies implied by a peak value of bicoherence.

Notably, nonlinear difference frequency locking is observed to be contemporaneous with an enhanced bispectral modulus. Usage of zero-crossing analysis and analytic signal corroborate interpretation. In line with prediction, time-resolved bispectral signatures are augmented by an energetic particle (EP) pressure gradient, as generated with varying NBI power.

A novel platform for polyspectral analysis is also presented.

Download

Share

COinS