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Hongsong Chou (Harvard)
Astrophysical dynamo theory studies the generation of large-scale magnetic fields from small-scale turbulence in many celestial objects. Mean-Field Electrodynamics, a kinematic dynamo theory, has been widely applied to solar dynamo, geodynamo contexts. But criticisms on different models of dynamo theory have existed ever since the early work by Parker(1955). We identify the recent questions on dynamo theory into the following three categories: (1) the back reaction of magnetic field on velocity field; (2) magnetic helicity constraints on dynamo \alpha- and \beta-effects; and (3) small-scale magnetic field in large magnetic Prandtl number systems. In this dissertation presentation, I will discuss all these three questions, and give our answers to each of them. To tackle the back reaction problem, we have to treat velocity field and magnetic field on equal footing. By assuming small de-correlation times of both the velocity field and the magnetic field, we developed a model that solves the momentum equation and induction equation altogether. By taking the back reaction of magnetic field into account, we provide a new derivation of the dynamo \alpha-effect. We also clarified the confusions over the constraints of the dynamics of magnetic helicity on dynamo effect. By considering both the time-dependent term and the boundary effect term in the equation of magnetic helicity, we are able to show, both analytically and numerically, that dynamo effect may not be quenched by large magnetic Reynolds numbers in astrphysical systems. Another open question on dynamo process is the concern that fast growing small-scale magnetic field would swamp velocity field entirely so that dynamo effect will not happen in systems of large magnetic Prandtl number, for example, the Galaxy. We have studied this problem numerically. We show that in driven turbulence, for at least moderate magnetic Prandtl number, magnetic field near the outer scale of the turbulence will grow even though the velocity field near the viscous cut-off scale is strongly suppressed by magnetic field at small scales.