Plasma and Fusion Research

Volume 15, 2401049 (2020)

Regular Articles

Emphasis of Periodicity in the Dynamic Behavior of Ionization Waves
Faculty of Education, Nagasaki University, 1-14 Bunkyo-machi, Nagasaki 852-8521, Japan
(Received 28 November 2019 / Accepted 28 May 2020 / Published 2 July 2020)


The dynamic behavior of ionization waves in glow discharge plasma was examined, particularly with regard to periodicity. In a series of experiments, neon plasma was produced by the glow discharge between two electrodes after the glass tube was evacuated to high vacuum. Fluctuations in the light intensity were sampled with a line-scan camera and photodiodes as spatiotemporal signals for data analysis. The largest Lyapunov exponents were calculated from the time series of the experimental samples to quantitatively estimate the complexity of the system. The signal-to-noise ratio (SNR) became saturated as the intensity of the external force applied to the chaotic state was gradually increased because chaotic oscillations in the ionization wave synchronized to the external force. A periodic orbit in the chaos system was emphasized, and the oscillation became coherent as the state SNR reached its maximum value. When the periodicity was emphasized, the oscillation became coherent not only in time but also in space. Periodicity was also observed in system-induced feedback without an external force. Similar results were obtained with an external force and feedback; however, the former caused the chaos system to synchronize with the external force, while the latter yielded periodic oscillations from the chaos–chaos interaction.


glow discharge, ionization wave, chaos, periodicity, synchronization

DOI: 10.1585/pfr.15.2401049


  • [1] W. Boswell, Plasma Phys. Control. Fusion 27, 405 (1985).
  • [2] Y. Cheung, S. Donovan and A.Y. Wong, Phys. Rev. Lett. 61, 1360 (1988).
  • [3] N. Ohno, M. Tanaka, A. Komori and Y. Kawai, J. Phys. Soc. Jpn. 58, 28 (1989).
  • [4] T. Fukuyama, K. Ota and H. Sakamoto, Phys. Plasmas 25, 092303 (2018).
  • [5] K. Ohe and S. Takeda, Contrib. Plasma Phys. 14, 55 (1974).
  • [6] Th. Pierre, G. Bonhomme and A. Atipo, Phys. Rev. Lett. 76, 2290 (1996).
  • [7] T. Fukuyama, K. Ishida and H. Kanzaki, Plasma Fusion Res. 14, 3401070 (2019).
  • [8] K. Pyragas, Phys. Lett. A 170, 421 (1992).
  • [9] T. Fukuyama, H. Shirahama and Y. Kawai, Phys. Plasmas 9, 4525 (2002).
  • [10] H. Tsuchiya, H. Shirahama and Y Kawai, Jpn. J. Appl. Phys. 46, 6074 (2007).
  • [11] A. Wolf, J.B. Swift, H.L. Swinney and J.A. Vastano, Physica D 16, 285 (1985).