Hydromagnetic Equations for Two Isotopes in a Completely Ionized Gas

The hydromagnetic equation for a completely ionized gas of high density with a single isotope is given, and from it the two hydromagnetic equations with two isotopes is derived. The difference between the accelerations of the isotopes at any internal point is then equal to $\frac{\delta M}{M}$ times $\left(\frac{1}{\rho }\right)[\mathrm{j}\times \mathrm{B}]$, the force on the induced current per unit density due to the magnetic field.