High‐Dimensional Interior Crisis in Plasmas

The study of periodic orbits and their invariant manifolds can be essential for a proper understanding of the onset of chaos and intermittent turbulence in space plasmas, as well as for monitoring and controlling instabilities in tokamak experiments. Plasma turbulence can be generated by an event known as crisis, characterized by the sudden expansion of a chaotic attractor due to the collision of the chaotic attractor with an unstable periodic orbit. Most previous analysis of crises are restricted to low‐dimensional dynamical systems described by maps or systems with a few ordinary differential equations. In this work we identify an interior crisis in a spatiotemporal model for plasma turbulence with a high‐dimensional representation in the Fourier space. We numerically solve the Kuramoto‐Sivashinsky partial differential equation, which was first derived to describe the nonlinear saturation of the collisional trapped‐ion mode in plasmas confined in toroidal devices. We numerically find an unstable periodic orbit and show that, after its collision with the coexisting chaotic attractor, the attractor is abruptly enlarged, with a respective jump in the value of the maximum Lyapunov exponent. The methodology presented in this work may be followed in further studies of high‐dimensional dynamical systems, and can be used to characterize crises in other strongly dissipative spatiotemporal systems.