## FANDOM

157 Pages

Let us consider two close concentric rings in an accretion disc, such that the difference in radii is much smaller than the average radius $r \gg \Delta r$. In isolation, each ring would rotate at a slightly different Keplerian rate $\approx \Omega_k$. If the accretion disc is fully ionised, then the ambient magnetic field will act like a spring, trying to synchronise the two rings. The rate at which the magnetic field transfers energy and momentum is the Alfven velocity divided by the radius difference $V_A / \Delta r$. When this rate is smaller than the Keplerian frequency, then the accretion disc winds up the magnetic field lines and amplifies them.