Quasi-periodic, explosive events and singularities in relevant nonlinear models

A nonlinear analytical model is presented to describe sequences of quasi-periodic explosive events (bursts) involving a primary explosive instability which can be moderated by a secondary mode driven by the primary instability when this exceeds an appropriate threshold. The relevant time dependent nonlinear equations, involving the primary instability and the amplitude of the secondary mode, have a characteristic singularity of which two main types are identified. Only one type is shown to lead to explosive events. The considered bursts refer, for instance, to heated or accelerated particle populations, the case of electrons heated by the slowing down of charged nuclei produced by fusion reactions being a particularly significant one. copyright 1999 American Institute of Physics