Theoretical and numerical studies of wave-packet propagation in tokamak plasmas

TL;DR

This paper combines theoretical and numerical methods to analyze the propagation of wave-packets in tokamak plasmas, revealing how geometry and boundary conditions influence wave structures and absorption.

Contribution

It introduces a novel approach using the 2D WKB and Mode Structure Decomposition methods to study wave-packet evolution and mode structures in tokamak plasmas.

Findings

Shaping effects significantly influence wave propagation and absorption.

The methods successfully reconstruct time-varying 2D mode structures.

Eigenmodes and eigenvalues are obtained from wave-packet asymptotic analysis.

Abstract

Theoretical and numerical studies of wave-packet propagation are presented to analyze the time varying 2D mode structures of electrostatic fluctuations in tokamak plasmas, using general flux coordinates. Instead of solving the 2D wave equations directly, the solution of the initial value problem is used to obtain the 2D mode structure, following the propagation of wave-packets generated by a source and reconstructing the time varying field. As application, the 2D WKB method is applied to investigate the shaping effects (elongation and triangularity) of tokamak geometry on the lower hybrid wave propagation and absorbtion. Meanwhile, the Mode Structure Decomposition (MSD) method is used to handle the boundary conditions and simplify the 2D problem to two nested 1D problems. The MSD method is related to that discussed earlier by Zonca and Chen [Phys. Fluids B 5, 3668 (1993)], and reduces to the well-known "ballooning formalism" [J. W. Connor, R. J. Hastie, and J. B. Taylor, Phys. Rev. Lett. 40, 396 (1978)], when spatial scale separation applies. This method is used to investigate the time varying 2D electrostatic ITG mode structure with a mixed WKB-full-wave technique. The time varying field pattern is reconstructed and the time asymptotic structure of the wave-packet propagation gives the 2D eigenmode and the corresponding eigenvalue. As a general approach to investigate 2D mode structures in tokamak plasmas, our method also applies for electromagnetic waves with general source/sink terms, either by an internal/external antenna or nonlinear wave interaction with zonal structures.