The constraint imposed by magnetic helicity conservation on the alpha effect is considered for both magnetically and flow dominated self-organizing plasmas. Direct numerical simulations are presented for a dominant contribution to the alpha effect, which can be cast in the functional form of a total divergence of an averaged helicity flux, called the helicity-flux-driven alpha ( H$alpha$) effect. Direct numerical simulations of the H$alpha$ effect are prese nted for two examples---the magnetically dominated toroidal plasma unstable to tearing modes, and the flow-dominated accretion disk.
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