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

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.