×

Local and global bifurcations of L-mode to H-mode transition near plasma edge in tokamak. (English) Zbl 1147.76632

Summary: The mechanism of the L-mode to H-mode transition in tokamak is an important and difficult problem in a tokamak. In this paper, the local and global bifurcations of the Ginzburg-Landau type perturbed transport equation for the L-mode to H-mode transition near the plasma edge in a tokamak are investigated by using the theory of nonlinear dynamics. A new explanation is presented for the bifurcations of the L-mode to H-mode transition near the plasma edge in a tokamak. It is found that in a tokamak there exist not only the static L-mode to H-mode transition but also the dynamic L-mode to H-mode transition. The Hopf bifurcation and limit cycle oscillations are found for the L-mode to H-mode transition near the plasma edge in a tokamak. It is illustrated that in the case of choosing suitable parameters the normalized radial electric field near the plasma edge in a tokamak is stable.

MSC:

76X05 Ionized gas flow in electromagnetic fields; plasmic flow
37N10 Dynamical systems in fluid mechanics, oceanography and meteorology
76E20 Stability and instability of geophysical and astrophysical flows
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Wagner, F.; Becker, G., Regime of improved confinement and high beta in neutral-beam-heated divertor discharges of the ASDEX Tokamak, Phys Rev Lett, 49, 1408-1412 (1982)
[2] Shaing, K. C.; Crume, E. C., Bifurcation theory of poloidal rotation in Tokamaks: a model for L-H transition, Phys Rev Lett, 63, 2369-2372 (1989)
[3] Itoh, S. I.; Itoh, K., Model of L to H-Mode transition in Tokamak, Phys Rev Lett, 60, 2276-2279 (1988)
[4] Itoh SI, Itoh K, Fukuyama A. ELMs-H-mode as limit cycle and chaotic oscillation in Tokamak plasma. National Institute for Fusion Science of Japan, vol. 96, 1991.; Itoh SI, Itoh K, Fukuyama A. ELMs-H-mode as limit cycle and chaotic oscillation in Tokamak plasma. National Institute for Fusion Science of Japan, vol. 96, 1991.
[5] Itoh, S. I., Edge localized mode activity as a limit cycle in Tokamak plasmas, Phys Rev Lett, 67, 2485-2488 (1991)
[6] Itoh, S. I.; Itoh, K.; Fukuyama, A., The ELMy H mode as a limit cycle and the transient responses of H modes in Tokamaks, Nucl Fusion, 33, 1445-1457 (1993)
[7] Wang, X. M.; Cao, S. D.; Chen, Y. P., The stability and catastrophe of diffusion processes of plasma boundary layer, Sci China Ser A, 39, 430-441 (1996) · Zbl 0854.76039
[8] Itoh SI, Itoh K, Fukuyama A. ELMs-H-mode as limit cycle and transient responses of H-mode in Tokamak. National Institute for Fusion Science of Japan, vol. 221, 1993.; Itoh SI, Itoh K, Fukuyama A. ELMs-H-mode as limit cycle and transient responses of H-mode in Tokamak. National Institute for Fusion Science of Japan, vol. 221, 1993.
[9] Zhang, W., Further studies for nonlinear dynamics of one dimensional crystalline beam, Acta Phys Sin (Overseas Edition), 5, 409-422 (1996)
[10] Carreras, B. A., Dynamics of L to H bifurcation, Plasma Phys Controll Fusion, 36, A93-A98 (1994)
[11] Fujisawa, A., Observation of bifurcation properties of radial electric fields using a heavy ion beam probe, Nucl Fusion, 41, 575-584 (2001)
[12] Colchin, R. J., Physics of slow L-H transitions in DIII-D Tokamak, Nucl Fusion, 42, 1134-1143 (2002)
[13] Guzdar, P. N., Comparison of a low-to high-confinement transition theory with experimental data from DIII-D, Phys Rev Lett, 89, 265004 (2002)
[14] Bajaj, A. K., Bifurcations in a parametrically excited nonlinear oscillator, Int J Non-Linear Mech, 22, 47-59 (1987) · Zbl 0607.70026
[15] Sri Namachchivaya, N.; Ariaratnam, S. T., Periodically perturbed Hopf-bifurcation, SIAM J Appl Math, 47, 15-39 (1987) · Zbl 0625.70022
[16] Sanchez, N. E.; Nayfeh, A. H., Prediction of bifurcations in a parametrically excited Duffing oscillator, Int J Non-linear Mech, 25, 133-139 (1990) · Zbl 0711.70029
[17] Zhang, W.; Huo, Q. Z., Bifurcations of nonlinear oscillation system under combined parametric and forcing excitation, Acta Mech Sin, 23, 464-474 (1991)
[18] Zhang, W.; Huo, Q. Z., Degenerate bifurcations of codimension two in nonlinear oscillator under combined parametric and forcing excitation, Acta Mech Sin, 24, 717-727 (1992)
[19] Neal, H. L.; Nayfeh, A. H., Response of a parametrically excited system to a nonstationary excitation, J Vibrat Control, 1, 57-73 (1995) · Zbl 0949.70516
[20] Zhang, W.; Yu, P., Degenerate bifurcation analysis on a parametrically and externally mechanical system, Int J Bifurcat Chaos, 11, 3, 689-709 (2001)
[21] Nayfeh, A. H.; Mook, D. T., Nonlinear oscillations (1979), Wiley-Interscience: Wiley-Interscience New York
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.