Magnetic flux ropes and convection

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Abstract
Three-dimensional cellular convection concentrates magnetic flux into ropes when the magnetic Reynolds number is large. Amplification of the magnetic field is limited by the Lorentz force and the maximum field in a flux rope can be estimated. Boundary-layer analysis yields a completely self-consistent solution for a model of convection driven by imposed horizontal temperature gradients, and the transition from a kinematic to a dynamic regime can be followed in detail. The maximum value of the amplified field is proportional to the square root of the ratio of the viscous to the magnetic diffusivity.