Transitions to improved confinement regimes induced by changes in heating in zero-dimensional models for tokamak plasmas

It is shown that rapid substantial changes in heating rate can induce transitions to improved energy confinement regimes in zero-dimensional models for tokamak plasma phenomenology. We examine for the first time the effect of step changes in heating rate in the models of Kim and Diamond [Phys. Rev. Lett. 90, 185006 (2003)] and Malkov and Diamond [Phys. Plasmas 16, 012504 (2009)], which nonlinearly couple the evolving temperature gradient, micro-turbulence, and a mesoscale flow; and in the extension of Zhu et al. [Phys. Plasmas 20, 042302 (2013)], which couples to a second mesoscale flow component. The temperature gradient rises, as does the confinement time defined by analogy with the fusion context, while micro-turbulence is suppressed. This outcome is robust against variation of heating rise time and against introduction of an additional variable into the model. It is also demonstrated that oscillating changes in heating rate can drive the level of micro-turbulence through a period-doubling path to chaos, where the amplitude of the oscillatory component of the heating rate is the control parameter