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Intrinsically explosive growth of a ballooning finger is demonstrated innonlinear magnetohydrodynamic calculations of high-$\beta$ disruptions intokamaks. The explosive finger is formed by an ideally unstable n=1 mode,dominated by an m/n=2/1 component. The quadrupole geometry of the 2/1 perturbedpressure field provides a generic mechanism for the formation of the initialballooning finger and its subsequent transition from exponential to explosivegrowth, without relying on secondary processes. The explosive ejection of thehot plasma from the core and stochastization of the magnetic field occur inAlfv\'enic time scales, accounting for the extremely fast growth of theprecursor oscillations and the rapidity of the thermal quench in somehigh-$\beta$ disruptions.

Role of explosive instabilities in high-$\beta$ disruptions in tokamaks