  We propose a one-dimensional (1D) model for the three-dimensional(3D)
incompressible ideal magnetohydrodynamics. We establish a regularity criterion
of the Beale-Kato-Majda type for this 1D model. Without the stretching effect,
the model with only transport effect equipped with a proper sign is shown to
have global in time strong solution. Some numerical simulations suggest that
solutions of this model with smooth periodic initial data do not tend to
develop singularities at finite time.
