Cascade models of anisotropic turbulence in magnetized plasma of solar wind

Abstract

The solar wind plasma is modeled as a collection of discrete domains, each possessing local rotational symmetry about its domain-mean magnetic field. Based on this partial symmetry, we construct cascade models governed by the nonlinear and Alfvénic time scales. We introduce a stochastic renewal process with a bimodal waiting-time distribution determined by these two time scales. This process yields a two-branch renormalization solution for the total energy: 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. Whenever energy-flux fluctuations become supercritical, the system selects the faster of the two available cascade rates, thereby preventing flux accumulation. During solar wind expansion, the system undergoes a dynamical first-order phase transition from the slow $k^{-3/2}$ cascade to the fast $k^{-5/3}$ cascade, with switchbacks accelerating the transition. The mixing of subcritical and supercritical domains in raw spacecraft measurements produces an apparent decoupling of the velocity and magnetic-field spectral indices. Incorporating a magnetic helicity cascade slaved to the energy cascade, we show that the large-scale spectra decouple into $k^{-3/4}$ magnetic and $k^{-3/2}$ kinetic spectra. For switchbacks inside the upper solar corona, the corresponding large-scale spectra instead decouple into $k^{-2/3}$ magnetic and $k^{-5/3}$ kinetic spectra. Data from Voyager, Ulysses, Helios, Wind, and PSP confirm the spectral signatures across heliospheric regions spanning heliocentric distances from 0.056 to 140 AU.

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