A paradigm shift from stationary stability to dynamically evolving stability required from experimental fusion plasmas

A paradigm shift from the traditional concept of stationary stability to the new one of dynamically evolving stability is proposed in order to correctly deal with dynamically evolving experimental plasmas. A new process to derive generalized simultaneous eigenvalue equations is presented by the use of a generalized theory of self-organization. The final simultaneous eigenvalue equations are shown to be a good candidate for the proposed paradigm shift because their mathematical forms exactly describe the self-similarly evolving and dynamically stable states available to various dynamic systems. Typical numerical configurations of mutually dependent, dynamically stable, and self-similarly evolving physical quantities are presented for the reversed-field pinch plasmas in cylindrical geometry by solving a set of simultaneous eigenvalue equations for the two-fluid model. A new algorithm is presented to find the dynamically stable, self-similarly evolving and self-organized configurations and to investigate quantitatively the robust dynamical stability of these configurations.