Dynamical control of the chaotic state of the current-driven ion acoustic instability in a laboratory plasma using delayed feedback

Abstract

Controlling chaos caused by the current-driven ion acoustic instability is attempted using delayed feedback, i.e., the time-delay auto synchronization (TDAS) method introduced by Pyragas [Phys. Lett. A 170, 421 (1992)] with flexibility. When the control parameter of the system Vm is increased, the current-driven ion acoustic instability is excited, and then, the system demonstrates chaotic oscillation in a certain range of the parameter. When the electronic circuit to control chaos based on the TDAS method is applied to the chaotic regime, the chaotic orbit changes to a periodic one maintaining the instability, that is, the chaotic state caused by the current-driven ion acoustic instability is well controlled using the TDAS method. Furthermore, it is shown that controlling chaos can be achieved when the delay time τ is chosen to be close to a fundamental frequency of the unstable periodic orbit embedding in the chaotic system.