On the fast penetration of magnetic field into plasma

The fast penetration of a strong magnetic field into a plasma, caused by the Hall effect, is studied. The phenomenon is likely to govern the early evolution of the magnetic field not only in two‐dimensional geometry, to which previous studies were restricted, but also in three dimensions. This penetration mechanism is suppressed, if both the plasma and electrodes are collisionless, vAeτe≳a, where vAe is the electron Alfven velocity, τe−1 the collision frequency, and a the characteristic space‐scale. However, the collisionless penetration can occur in the case of a resistive cathode. The self‐consistent effect of ion motion is shown to be of importance only in a very special geometry. Then the penetration speed is limited by the value VA(aωpi/c)−1/3, where VA is the Alfven velocity and c/ωpi the ion skin depth.