Post-MHD and Solar Atmosphere

In magnetohydrodynamics (MHD) one neglects the displacement current, which is usually an excellent approximation. However, when dealing with "small' scale phenomena and/or "fast" phenomena this displacement current plays a role. After solving the MHD evolution equation one may verify the approximation by using Maxwell's equations to calculate the displacement current (and the charges associated with it). The exact solution of the evolution equation obtained by Callebaut allows an exact calculation of the neglected terms. Examples are given. An iteration may yield a correction. For filamentation and sheet currents this may be important as it may facilitate turbulent resistivity and thus the onset of flares, CMEs, etc.