CHEN Fang-qi, ZHOU Liang-qiang, WANG Xia, CHEN Yu-shu. Chaotic Motions for the Model of the L-Mode to H-Mode in Tokamak[J]. Applied Mathematics and Mechanics, 2009, 30(7): 757-765. doi: 10.3879/j.issn.1000-0887.2009.07.001
Citation: CHEN Fang-qi, ZHOU Liang-qiang, WANG Xia, CHEN Yu-shu. Chaotic Motions for the Model of the L-Mode to H-Mode in Tokamak[J]. Applied Mathematics and Mechanics, 2009, 30(7): 757-765. doi: 10.3879/j.issn.1000-0887.2009.07.001

Chaotic Motions for the Model of the L-Mode to H-Mode in Tokamak

doi: 10.3879/j.issn.1000-0887.2009.07.001
  • Received Date: 2008-10-17
  • Rev Recd Date: 2009-06-11
  • Publish Date: 2009-07-15
  • The chaotic dynamics of the transport equation for the L-mode to H-mode near plasma in Tokamak is studied in detail with Melnilov method.The transport equations represent a system with external and parametric excitation.The critical curves separating the chaotic regions and non-chaotic regions were presented for the system with periodically external excitation and linear parametric excitation,or cubic parametric excitation,respectively.The results obtained here show that there exist uncontrollable regions in which chaos always takes place via heteroclinic bifurcation for the system with linear or cubic parametric excitation.Especially,there exists a "controllable frequency" excited at which chaos doesn.toccur via homoclinic bifurcation no matter how large the excitation amplitude is for the system with cubic parametric excitation.Some complicated dynamical behaviors were obtained for this class of systems.
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  • [1]
    Wagner F,Becker G,Campbell D,et al.Regime of improved confinement and high beta in neutral- beam-heated divertor discharges of the ASDEX Tokamak[J].Physical Review Letters,1982,49(19):1408-1412. doi: 10.1103/PhysRevLett.49.1408
    [2]
    Shaing K, Crume J. Bifurcation theory of poloidal rotation in Tokamaks:a model for L-H transition[J].Physical Review Letters,1989,63(21):2369-2372. doi: 10.1103/PhysRevLett.63.2369
    [3]
    Itoh S, Itoh K. Model of L to H-mode transition in Tokamak[J].Physical Review Letters,1988,60(22):2276-2279. doi: 10.1103/PhysRevLett.60.2276
    [4]
    Itoh S,Itoh K,Fukuyama A,et al. Edge localized mode activity as a limit cycle in Tokamak plasmas[J].Physical Review Letters,1991,67(18):2485-2488. doi: 10.1103/PhysRevLett.67.2485
    [5]
    WANG Xian-min. The stability and catastrophe of diffusion processes of plasma boundary layer[J].Science in China,Ser A,1996,39(4):430-441.
    [6]
    ZHANG Wei. Further studies for nonlinear dynamics of one dimensinal crystalline beam[J].Acta Physica Sinica(Overseas Edition),1996,5(3):409-422. doi: 10.1088/1004-423X/5/6/002
    [7]
    Colchin R J,Carreras B A,Maingi R,et al. Physics of slow L-H transitions in DIII-D Tokamak[J].Nuclear Fusion,2002,42(9):1134-1143. doi: 10.1088/0029-5515/42/9/312
    [8]
    Guzdar P,Liu C S,Dong J Q,et al. Comparision of a slow-to high-confinement transition theory with experiment data from DIII-D[J].Physical Review Letters,2002,89(26):2650-2654.
    [9]
    ZHANG Wei, CAO Dong-xin. Local and global bifurcations of L-mode to H-mode transition near plasma edge in Tokamak[J].Chaos Solitons & Fractals,2006,29(1):223-232.
    [10]
    Silva E C, Caldas I L, Viana R L. Bifurcations and onset of chaos on the ergodic magnetic limiter mapping[J].Chaos Solitons & Fractals,2006,14(3):403-423.
    [11]
    Portela J S E, Viana R L, Caldas I L. Chaotic magnetic field lines in Tokamaks with ergidic limiters[J].Physica A,2003,317(3/4):411-431. doi: 10.1016/S0378-4371(02)01351-1
    [12]
    Kroetz T,Marcus F A,Roberto M,et al.Transport control in fusion plasmas by changing electric and magnetic field spatial profiles[J].Computer Physics Communications,2009,180(4):642-650. doi: 10.1016/j.cpc.2008.12.025
    [13]
    Viana R L.Chaotic magnetic field lines in a Tokamak with resonant helical windings[J].Chaos Solitons & Fractals,2000,11(5):765-778.
    [15]
    Wiggins S.Introduction to Applied Non-Linear Dynamical Systems and Chaos[M].New York:Springer, 1990.
    [16]
    Guckenheimer J, Holmes P J. Non-Linear Oscillations, Dynamical Systems and Bifurcation of Vector Fields[M].New York:Springer, 1983.
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