Chaotic diffusion in multi-scale turbulence

This study investigates chaotic diffusion in multi-scale turbulence driven by nonlinear wave-particle resonance coupling. Turbulent waves with distinct characteristic wavelengths across scales coherently interact with charged particles when their phase velocities match the particles' velocities. A multi-wavenumber mapping framework is developed to model chaotic transport under multi-scale turbulence. By analytically deriving velocity correlation functions, we quantify the diffusion coefficient under conditions of cross-scale wave intensity parity. A critical analysis reveals that chaotic dynamics at smaller scales prove insufficient to completely erase phase-space correlations established by large-scale turbulent components. The largest-scale turbulence components dominate deviations from quasi-linear (QL) theory predictions, establishing a scale-dependent hierarchy in chaotic transport. Mere reduction of inter-wave phase velocity spacing for small-scale components cannot recover QL diffusion at finite wave amplitudes in multi-scale turbulence. Incorporating a larger-scale component into a small-scale-driven strong chaotic system can induce non-QL diffusion. Specifically, for two-scale turbulence, the QL approximation systematically underestimates transport. Increasing the number of smaller-scale components with strong overlap parameters drives convergence toward the QL approximation. This framework provides a methodology for analyzing resonance-driven turbulence in laboratory and astrophysical plasmas.