Faculty of Sciences. Physics
Department of Physics
Cambridge :Electromagnetics Academy, 2007[*]2007
Engineering sciences. Technology
Progress in Electromagnetics Research Symposium (PIERS 2007), March 26-30, 2007, Beijing, Peoples Republic of China
University of Antwerp
Magneto-hydrodynamics (MHD) as conceived by Alfven is based on the evolution equation for the magnetic field. The main applications concern the magnetic fields in flows and dynamo mechanisms. Various extensions have been made. Here we consider the contribution due to the displacement current of Maxwell. This adds a term proportional to is an element of mu = c(-2) and thus is expected to be very small at low frequencies. Using the exact solution of the evolution equation obtained by Callebaut we may calculate precisely the correction and iterate if necessary. Thus we have compared the displacement current with the MHD current. The displacement current may become comparable to and exceed the MHD current at high frequencies and slowly varying structures in space. It is stressed that the space charge is an independent variable. We introduce a dimensionless quantity as a measure for it. This post-MHD may be particularly relevant in connection with the non-linear Fourier-Callebaut' analysis showing that the accumulation of some small oscillations (however, including the nonlinear terms) may lead, in narrow strips to very large, even divergent, velocities. In those strips turbulent resistivity may occur which allow the dissipation times to be 4 to 5 orders of magnitude shorter than those of ordinary MHD. This may explain the short explosion times for solar flares, coronal mass ejections (CMEs), etc.