Imbalanced RMHD turbulence

Magnetised plasma turbulence is ubiquitous throughout the Universe, regulating the transport and dissipation of energy in systems ranging from laboratory fusion plasmas to the solar corona and solar wind. In the presence of a strong mean magnetic field, its low-frequency Alfvénic component is often described by reduced magnetohydrodynamics (RMHD), in which turbulence is mediated by the interaction of Alfvén waves travelling in opposite directions along the mean field. When these two populations carry equal energies, the turbulence is said to be balanced; when one population dominates, it is imbalanced and possesses non-zero cross helicity. Such imbalance is common in naturally occurring plasmas where Alfvénic fluctuations are launched preferentially in one direction. The solar wind provides a particularly important example: Alfvénic fluctuations propagating away from the Sun typically dominate those propagating towards it, especially in the near-Sun environment [see, e.g., Podesta & Borovsky (2010); Chen (2016)]. Despite several decades of theoretical and numerical work, no generally accepted description of strong imbalanced turbulence exists. Competing theories disagree over the nonlinear interactions controlling the two cascades, the relationship between their energies and energy fluxes, and the resulting spectral scalings and anisotropy [see, e.g., Lithwick et al. (2007); Beresnyak & Lazarian (2008); Chandran (2008); Perez & Boldyrev (2009); Schekochihin (2022)]. Resolving these questions is also necessary for understanding how large-scale imbalance controls kinetic-scale processes such as the helicity barrier [see, e.g., Meyrand et al. (2021); Squire et al. (2022); McIntyre et al. (2025)]. In this project, the student will investigate the cascade physics of imbalanced RMHD turbulence using a combination of analytical theory and high-resolution numerical simulations. Particular emphasis will be placed on identifying which nonlinear interactions control the transfer of energy and cross helicity across scales, how these interactions change with the degree of imbalance, and the implications for decaying RMHD turbulence. Alongside conventional spectral diagnostics, the student will adapt exact scale-by-scale energy-flux decompositions and Fourier-space analyses of interacting triads developed in recent work on magnetohydrodynamic turbulence [see, e.g., Linkmann et al. (2016); Capocci et al. (2025)]. Prior familiarity with plasma physics, fluid dynamics, or numerical simulation would be advantageous but is not essential.