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Let us consider two close concentric rings in an accretion disc, such that the difference in radii is much smaller than the average radius <math> r \gg \Delta r </math>. In isolation, each ring would rotate at a slightly different Keplerian rate <math> \approx \Omega_k </math>. 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 <math> V_A / \Delta r </math>. When this rate is smaller than the Keplerian frequency, then the accretion disc winds up the magnetic field lines and amplifies them. |
Let us consider two close concentric rings in an accretion disc, such that the difference in radii is much smaller than the average radius <math> r \gg \Delta r </math>. In isolation, each ring would rotate at a slightly different Keplerian rate <math> \approx \Omega_k </math>. 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 <math> V_A / \Delta r </math>. When this rate is smaller than the Keplerian frequency, then the accretion disc winds up the magnetic field lines and amplifies them. |
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Revision as of 10:47, 31 October 2017
Let us consider two close concentric rings in an accretion disc, such that the difference in radii is much smaller than the average radius . In isolation, each ring would rotate at a slightly different Keplerian rate . 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 . When this rate is smaller than the Keplerian frequency, then the accretion disc winds up the magnetic field lines and amplifies them.
