The Role of Phase and Spatial Modes in Wave-Induced Plasma Transport

TL;DR

This work addresses drift-wave–driven particle transport at the plasma edge by deriving a two-dimensional symplectic map from a multi-wave drift-wave potential with fixed amplitudes, spatial modes, and relative phases. It analyzes a reduced two-wave model for identical and distinct spatial modes, using transmissivity and phase-space diagnostics to quantify confinement and boundary complexity. The key finding is that phase alignment can either suppress transport through destructive interference or promote transport via mode mismatch, which also yields fractal-like transport boundaries quantified by box-counting dimensions. The results connect the spectral content and phase of edge perturbations to confinement outcomes, offering guidance for controlling transport in fusion plasmas, albeit within a fixed-amplitude, non-self-consistent framework with a path forward to incorporate nonlinear wave dynamics.

Abstract

We derive a two-dimensional symplectic map for particle motion at the plasma edge by modeling the electrostatic potential as a superposition of integer spatial harmonics with relative phase shift, then reduce it to a two-wave model to study the transport dependence on the perturbation amplitudes, relative phase, and spatial-mode choice. Using particle transmissivity as a confinement criterion, identical-mode pairs exhibit phase-controlled behavior: anti-phase waves produce destructive interference and strong confinement while in-phase waves add constructively and drive chaotic transport. Mode-mismatched pairs produce richer phase-space structure with higher-order resonances and sticky regions; the transmissivity boundaries become geometrically complex. Box-counting dimensions quantify this: integer dimension smooth boundaries for identical modes versus non-integer fractal-like dimension for distinct modes, demonstrating that phase and spectral content of waves jointly determine whether interference suppresses or promotes transport.

Figures (6)

• Figure 1: Evolution of phase space and corresponding winding number profiles for a single wave ($\alpha_2 = 0$) with increasing amplitude $\alpha_1$. Left column (a1-d1): Phase portraits for $\alpha_1 = 0, 0.09, 0.12, 0.18$. Right column (a2-d2): The associated winding number $\Omega(I)$. In all panels, the shearless curve and its corresponding extremum in the winding profile are highlighted in red.
• Figure 2: Phase space portraits in action-angle coordinates $(I, \Psi)$ for a fixed amplitude $\alpha_{1,2} = 0.09$, demonstrating the impact of wave interference. (a) Constructive interference ($\nu = 0$), (b) Intermediate phase ($\nu = \pi/2$), (c) Destructive interference ($\nu = \pi$). The STB is highlighted in red in each case.
• Figure 3: For $\eta_{1,2} = 1$ the transmissivity across different parameter spaces. (a) Phase-amplitude space $(\nu, \alpha_{1,2})$. (b, c) Amplitude-amplitude space $(\alpha_2, \alpha_1)$ for a fixed phase difference of (b) $\nu = 0$ and (c) $\nu = \pi/2$. In all panels, black denotes parameter combinations resulting in no transport.
• Figure 4: Impact of a secondary wave on phase space structure. Portraits in action-angle coordinates $(I, \Psi)$ for a fixed $\alpha_1 = 0.2$ with increasing amplitude of the second wave: (a) $\alpha_2 = 0.05$, (b) $\alpha_2 = 0.1$, (c) $\alpha_2 = 0.2$, (d) $\alpha_2 = 0.3$. The STB is highlighted in red in each panel.
• Figure 5: Transmissivity across different parameter spaces for $\eta_1 = 2$ and $\eta_2 = 3$. (a) Phase-amplitude space $(\nu, \alpha_{1,2})$. (b, c) Amplitude-amplitude space $(\alpha_2, \alpha_1)$ for a fixed phase difference of (b) $\nu = 0$ and (c) $\nu = \pi/2$. In all panels, black denotes parameter combinations resulting in no transport.