Cascade models of anisotropic turbulence in magnetized plasma of solar wind

Abstract

We present a physical framework for Alfvénic solar wind turbulence in which the plasma is modeled as discrete domains with local rotational symmetry about the domain-mean magnetic field. Using this symmetry, we construct minimalist cascade models governed by two characteristic time scales, nonlinear and Alfvénic, associated, respectively, with the perpendicular and parallel directions relative to the domain-mean magnetic field. Within this partial symmetry, we also characterize the anisotropy of each domain by a single additional geometrical parameter, the alignment angle between the domain-mean velocity and magnetic fields. We introduce a stochastic renewal process with a bimodal waiting-time distribution based on these two time scales, yielding a two-branch renormalization solution for the total energy cascade: a statistically robust branch with an Iroshnikov-Kraichnan-like $k^{-3/2}$ spectrum, and a statistically marginal branch with a Kolmogorov-like $k^{-5/3}$ spectrum. Utilizing principles of causality and cascade stability, we show that the system selects the faster cascade rate between the two available whenever energy-flux fluctuations become supercritical, preventing intermittent flux accumulation. Consequently, during solar wind expansion, balanced domains (with low cross-helicity) undergo a first-order phase transition from the slow $k^{-3/2}$ cascade to the fast $k^{-5/3}$ cascade. The transition is accelerated by heterogeneous nucleation at switchbacks. Incorporating a forward magnetic helicity cascade slaved to the energy cascade, we show that the large-scale spectra decouple into a flat $k^{-3/4}$ magnetic spectrum and a $k^{-3/2}$ kinetic spectrum. Data from Voyager, Ulysses, Helios, Wind, and PSP confirm these spectral signatures across diverse heliospheric regions.