One dimensional analytical solutions of the transport equations for incompressible magnetohydrodynamic (MHD) turbulence

TL;DR

This paper derives one-dimensional analytical solutions for the transport equations of incompressible MHD turbulence, enabling simplified analysis of turbulence evolution and particle diffusion in space and astrophysical environments.

Contribution

It presents new 1D analytical solutions for MHD turbulence transport equations applicable to arbitrary background speeds, under near equipartition conditions.

Findings

Solutions are suitable for arbitrary background convection and Alfvén speeds.

They facilitate investigation of turbulence evolution in simple geometries.

The solutions help estimate energetic particle diffusion coefficients.

Abstract

We derive one dimensional (1D) analytical solutions for the transport equations of incompressible magnetohydrodynamic (MHD) turbulence developed by Zank et al. [2012], Adhikari et al. [2023], including the Els\"asser energies and the correlation lengths. The solutions are suitable for an arbitrary given background convection speed and Alfv\'en speed profiles but require near equipartition of turbulent kinetic energy and magnetic field energy. These analytical solutions provide a simple tool to investigate the evolution of turbulence and resulting energetic particle diffusion coefficients in various space and astrophysical environments that possess simple geometry.