  In this paper, we utilize the maximum-principle-preserving flux limiting
technique, originally designed for high order weighted essentially
non-oscillatory (WENO) methods for scalar hyperbolic conservation laws, to
develop a class of high order positivity-preserving finite difference WENO
methods for the ideal magnetohydrodynamic (MHD) equations. Our schemes, under
the constrained transport (CT) framework, can achieve high order accuracy, a
discrete divergence-free condition and positivity of the numerical solution
simultaneously. Numerical examples in 1D, 2D and 3D are provided to demonstrate
the performance of the proposed method.
