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.