Study of nonlinear mode–mode couplings between Alfvénic modes by the Fourier bicoherence and Lissajous-curve technique in HL-2A
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摘要
Nonlinear couplings of various Alfvén modes driven by energetic particles in HL-2 A are addressed by employing the Fourier bicoherence and Lissajous-curve technique. Long-lived modes and high-frequency coherent modes are presented. Then the squared bicoherence of three waves establishes the existence of three-wave coupling. Lissajous-curves of those waves manifest that their phases are locked, which again confirms that they are nonlinearly coupled to each other. Moreover, coupled modes triggered by supersonic molecular beam injection are investigated. The phase evolution of them is given by the Lissajous-curve. Further details of phase-flip and phase-slip are presented and discussed.
Nonlinear couplings of various Alfvén modes driven by energetic particles in HL-2 A are addressed by employing the Fourier bicoherence and Lissajous-curve technique. Long-lived modes and high-frequency coherent modes are presented. Then the squared bicoherence of three waves establishes the existence of three-wave coupling. Lissajous-curves of those waves manifest that their phases are locked, which again confirms that they are nonlinearly coupled to each other. Moreover, coupled modes triggered by supersonic molecular beam injection are investigated. The phase evolution of them is given by the Lissajous-curve. Further details of phase-flip and phase-slip are presented and discussed.
Nonlinear couplings of various Alfvén modes driven by energetic particles in HL-2 A are addressed by employing the Fourier bicoherence and Lissajous-curve technique. Long-lived modes and high-frequency coherent modes are presented. Then the squared bicoherence of three waves establishes the existence of three-wave coupling. Lissajous-curves of those waves manifest that their phases are locked, which again confirms that they are nonlinearly coupled to each other. Moreover, coupled modes triggered by supersonic molecular beam injection are investigated. The phase evolution of them is given by the Lissajous-curve. Further details of phase-flip and phase-slip are presented and discussed.
引文
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[26] Chen W et al 2016 Nucl. Fusion 56 036018
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[28] Hou Y M et al 2018 Nucl. Fusion 58 096028
[29] Bierwage A et al 2017 Nucl. Fusion 57 016036
[2] Gorelenkov N N et al 2014 Nucl. Fusion 54 125001
[3] Wong K L et al 1991 Phys. Rev. Lett. 66 1874
[4] Heidbrink W W et al 1991 Nucl. Fusion 31 1635
[5] Breizman B N and Sharapov S E 2011 Plasma Phys. Control.Fusion 53 054001
[6] Chen L et al 1998 Plasma Phys. Control. Fusion 40 1823
[7] Chen L and Zonca F 2007 Nucl. Fusion 47 S727
[8] Vlad G et al 2009 Nucl. Fusion 49 075024
[9] Kuramoto Y 1978 Prog. Theor. Phys. Suppl. 64 346
[10] Acebrón J A et al 2005 Rev. Mod. Phys. 77 137
[11] Guo Z B and Diamond P H 2015 Phys. Rev. Lett. 114 145002
[12] Crocker N A et al 2006 Phys. Rev. Lett. 97 045002
[13] Crocker N A et al 2009 Phys. Plasmas 16 042513
[14] Fredrickson E D et al 2003 Phys. Plasmas 10 2852
[15] Fredrickson E D et al 2006 Phys. Plasmas 13 056109
[16] PodestàM et al 2011 Nucl. Fusion 51 063035
[17] Chen W et al 2014 Europhys. Lett. 107 25001
[18] Chen W et al 2017 Nucl. Fusion 57 114003
[19] Chen W et al 2018 Nucl. Fusion 58 056004
[20] Shi P W et al 2017 Phys. Plasmas 24 042509
[21] Ido T et al 2016 Phys. Rev. Lett. 116 015002
[22] Lesur M et al 2016 Phys. Rev. Lett. 116 015003
[23] Wang H et al 2018 Phys. Rev. Lett. 120 175001
[24] Kim Y C and Powers E J 1979 IEEE Trans. Plasma Sci. 7 120
[25] Xu D F 1995 College Physics 14 7(in Chinese)
[26] Chen W et al 2016 Nucl. Fusion 56 036018
[27] Chen W et al 2014 Nucl. Fusion 54 104002
[28] Hou Y M et al 2018 Nucl. Fusion 58 096028
[29] Bierwage A et al 2017 Nucl. Fusion 57 016036