Abstract
Abstract Numerical solutions have been calculated for the non-linear Rayleigh-Benard convection problem in a cylindrical geometry, including the effect of a magnetic field. The development of the field is governed by the induction equation and its back reaction on the motion is determined via the Lorentz force in the momentum equation. If the input field B 0 is weak a thin fluxrope is formed on the axis, and when B 0 is increased the amplified field reaches a maximum value as this region becomes stagnant. The equipartition value B e [tbnd] (μ o ρU2 )½ is easily exceeded. When Bo is stronger, heat transport is reduced and osciliations can occur; there are hysteresis effects, and erratic hehaviour is found for high magnetic Prandtl numbers. These results help to interpret ohserved flux concentrations on the Sun, and provide models for some subsidiary features of sunspots.
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