7th Asia-Pacific Conference on Plasma Physics, 12-17 Nov, 2023 at Port Messe Nagoya

The nonlinear dynamic behaviors in an undriven direct current glow discharge:
bifurcation-remerging process, intermittency and hysteresis
Chengxun Yuan1,2, Jingfeng Yao1,2 and Zijia Chu1
1
School of Physics, Harbin Institute of Technology, 2 Heilongjiang Provincial Key Laboratory ofPlasma Physics and Application Technology
e-mail (speaker): Chengxun Yuan

It is widely believed that a nonlinear physical system
which far from thermodynamic equilibrium state canexhibit complex dynamic behaviors with regular orirregular structures in time and/or space domains. As atypically complex nonlinear medium, deterministic chaosin laboratory plasmas has been extensively demonstrated
both experimentally and numerically over the last
decades1-3.
Due to the existence of the negative differential
conductivity (NDC), discharge plasmas operating in thesubnormal glow discharge regime can exhibit
self-sustained oscillations regardless of the presence ofthe external driving forces, which can be observed byrecording the macroscopic electrical signals4,5. The
charge-breakdown-discharge process is repeated within
the system during the self-sustained oscillation.
Meanwhile, it has been suggested that a variety ofcomplex bifurcations can be observed as the dischargeparameter changes. Several transition routes to chaos
have been reported, such as the period-doublingbifurcation sequence, the quasi-periodicity route, and theintermittent chaos route. Although outstandingachievements in the study of the complexities of gas
discharge plasma have been made, most previous studies
only go as far as describing experimental phenomena.
Due to the limitation of measurement accuracy and theinevitable influence of noise, some discharge phenomena
have not been consistently and reasonably explained, andthe variation of discharge modes with external control
parameters is not entirely clear. The study of nonlinear
phenomena in gas discharge plasma contributes to ourunderstanding of the plasma discharge process with theaim of eventually controlling chaos in low-temperatureplasma. In addition, it is also important for research on
relaxation oscillators in the fields of electronic circuits
and neurodynamic.
In this study, a two-dimensional plasma fluid model isestablished coupled with a circuit model as a boundary
condition. Using the applied voltage U0 as the firstcontrol parameter in the simulation, the complete
period-doublingbifurcation
andtheinverse
period-doubling bifurcation processes in the oscillatory
region are found (as shown in Fig.1(a)-(c)). A series ofperiodic windows are present in the chaotic region andthe type-I intermittent chaos appears near the periodic
window. Then the pressure is chosen as the second
control parameter, and the influence of pressure on thedynamic behavior is investigated. A two-parameter mapof the dynamic behavior is obtained by introducing thepressure as the second parameter and the influence of thepressure on the dynamic behavior is studied. The results
show that increasing the pressure can have a similareffect on the discharge mode transition processes asincreasing the applied voltage U0 and the chaotic
oscillations exist only under certain parameter range. Inaddition, it was found that the dynamic behavior of thesystem also depends on the initial condition and there isa hysteresis between the oscillatory regime and thestationary regime.
References[1] Braun T, Lisboa J A, Francke R E and Gallas J A C
Physical Review Letters 1987 59 613-616[2] Akhmet M, Rafatov I and Fen M O Chaos 2014 24043127[3] Alex P, Perumal M and Sinha S K Nonlinear
Dynamics 2020 101 655-673[4] Chabert P, Lazzaroni C and Rousseau A Journal ofApplied Physics 2010 108[5] Lazzaroni C and Chabert P Journal of Applied
Physics 2012 111

Figure 1. (a) Amplitude bifurcation diagram (b)Period-doubling bifurcation process. (c) Inverse
period-doubling bifurcation process.