Volume 49 Number 3

The one-dimensional model of state transition in magnetized plasma based on bifurcation analysis

Thiti Aungcharoen^a, Danis Klanurak^a, Nopporn Poolyarat^b, Jiraporn Promping^b, Arlee Tamman^b, Apiwat Wisitsorasak^c, Ponkris Klaywittaphat^d, Boonyarit Chatthong^a,*

 
ABSTRACT:     The occurrence of limit-cycle oscillations during the low to high confinement mode transition in magnetically confined plasma is investigated using bifurcation theory. The fixed-point and stability analyses of the minimal temporal model are carried out, revealing two distinct critical external power thresholds. The first corresponds to the onset of limit-cycle oscillation via Hopf bifurcation in which plasma turbulence and zonal flow shear form a self regulating state. The second is associated with the transcritical bifurcation that drives the system into high confinement mode where mean flow shear sustains turbulence suppression. The minimal temporal model is extended to a spatio temporal model by coupling it to the energy transport equation and allowing for the turbulence spreading effect. In this model, the limit-cycle orbit originates at the plasma edge due to pressure gradient driven linear instability. During each cycle, the turbulence and zonal flow fronts also propagate radially inward due to turbulence spreading effect. Once the external power threshold surpasses the second critical value, an edge transport barrier is formed self-consistently at the edge of plasma pressure profile, providing rapidly strong mean flow shear that sustains local turbulence suppression and prevents the back-transition to the low confinement mode.

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* Corresponding author, E-mail: boonyarit.ch@psu.ac.th

Received 29 Dec 2025, Accepted 24 Aug 2026