Dimensional Relations in Magnetohydrodynamics

An analysis of the dimensional relations characteristic of electromagnetic phenomena in fluids of large dimensions is carried out. Most dimensionless quantities are found to be exceedingly small, or large, compared to unity, with resultant simplifications of the theory. We find that, in the absence of instabilities, the conditions for the acceleration of particles to the higher cosmic-ray energies are favorable only when the linear dimensions of the fluids involved are very large.