One-Dimensional Analytical Solutions of the Transport Equations for Incompressible Magnetohydrodynamic (MHD) Turbulence

We derive one-dimensional (1D) analytical solutions for the transport equations of incompressible magnetohydrodynamic (MHD) turbulence, including the Elsässer energies and the correlation lengths. The solutions are suitable for an arbitrary given background convection speed and Alfvén 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.