In this paper we present an analytical study of a subgrid scale turbulence model of the threedimensional magnetohydrodynamic (MHD) equations, inspired by the Navier-Stokes-α (also known as the viscous Camassa-Holm equations or the Lagrangian-averaged Navier-Stokes-α model. Specifically, we show the global well-posedness and regularity of solutions of a certain MHD-α model (which is a particular...