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The onset of a solar eruption is formulated here as either a magneticcatastrophe or as an instability. Both start with the same equation of forcebalance governing the underlying equilibria. Using a toroidal flux rope in anexternal bipolar or quadrupolar field as a model for the current-carrying flux,we demonstrate the occurrence of a fold catastrophe by loss of equilibrium forseveral representative evolutionary sequences in the stable domain of parameterspace. We verify that this catastrophe and the torus instability occur at thesame point; they are thus equivalent descriptions for the onset condition ofsolar eruptions.

Catastrophe versus instability for the eruption of a toroidal solar magnetic flux rope