The transition to magnetic-field self-generation in a turbulent, electrical
ly conducting fluid is shown to exhibit intermittent bursting characterized
by distinct scaling laws. This behavior is predicted on the basis of prior
analysis of a type of bifurcation (called a blowout bifurcation) occurring
in chaotic systems with an invariant phase space submanifold. The predicte
d scalings are shown to be consistent with numerical solutions of the gover
ning magnetohydrodynamic equations, and implications for recently implement
ed experimental programs are discussed.