Plasmas have been recently studied as topological materials. However, a comprehensive picture of topological phases and topological phase transitions in cold magnetized plasmas is still missing. Here we systematically map out all the topological phases and establish the bulk-edge correspondence in cold magnetized plasmas. We find that for the linear eigenmodes, there are 10 topological phases in the parameter space of density n, magnetic field B, and parallel wavenumber kz, separated by the surfaces of Langmuir wave-L wave resonance, Langmuir wave-cyclotron wave resonance, and zero magnetic field. For fixed B and kz, only the phase transition at the Langmuir wave-cyclotron wave resonance corresponds to edge modes. A sufficient and necessary condition for the existence of this type of edge modes is given and verified by numerical solutions. We demonstrate that edge modes exist not only on a plasma-vacuum interface but also on more general plasma-plasma interfaces. This finding broadens the possible applications of these exotic excitations in space and laboratory plasmas.

Real-time feedback control based on machine learning algorithms (MLA) was successfully developed and tested on DIII-D plasmas to avoid tearing modes and disruptions while maximizing the plasma performance, which is measured by normalized plasma beta. The control uses MLAs that were trained with ensemble learning methods using only the data available to the real-time Plasma Control System (PCS) from several thousand DIII-D discharges. A “tearability” metric that quantifies the likelihood of the onset of 2/1 tearing modes in a given time window, and a “disruptivity” metric that quantifies the likelihood of the onset of plasma disruptions were first tested off-line and then implemented on the PCS. A real-time control system based on these MLAs was successfully tested on DIII-D discharges, using feedback algorithms to maximize βN while avoiding tearing modes and to dynamically adjust ramp down to avoid high-current disruptions in ramp down.

We show that the dynamical system of an inviscid fluid with velocity shear admits parity-time (PT) symmetry, which provides a physical explanation of the well-known observation that the spectrum of the perturbation eigenmodes of the system is symmetric with respect to the real axis. It is found that the Kelvin–Helmholtz instability is triggered when and only when the PT symmetry is spontaneously broken. The analysis of PT symmetry also reveals that the relative phase between parallel velocity and pressure perturbations needs to be locked at π/2 when the instability is suppressed.