We present the simplest extension of the Burgers equation to include the effects of magnetic pressure. For unity magnetic Prandtl number, an exact solution exists that describes Alfvenic shock waves. For forced turbulence with arbitrary diffusivities, renormalized perturbation theory is used to show that the only stable, physically accessible fixed point corresponds to a state of equidissipation. Energy equipartition, however, requires the equality of the forcing functions. Implications for the spectra of turbulence and self-organization phenomena in magnetohydrodynamics are discussed.

• Received 10 March 1998

DOI:https://doi.org/10.1103/PhysRevE.58.R2709