From the momentum conservation equation with the MHD approximation [see (6.6)], and the generalized Ohm's law in the simplified form (6.10), but without considering the Hall effect term, derive the following equation:

Solve this equation, considering that E = 0 and p = constant, to show that the fluid velocity perpendicular to B is given by

where τ is a characteristic time for diffusion of the fluid across the magnetic field lines, given by

Equations

Transcribed Image Text:

Pm Du Dt = go (Ex B) + oo(u × B) x B - Vp