电流调制稳定线性撕裂模的数值模拟研究
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摘要
撕裂模是托卡马克运行过程中最危险的磁流体不稳定性之一,它可以改变磁场的拓扑结构破坏等离子体平衡,严重时可能导致托卡马克放电终止,造成严重后果。为保证托卡马克正常运行,必须抑制这种不稳定性。到目前为止实验上已经采用了很多方法抑制撕裂模,但是这些方法在技术上都有一定的难度。一种简单易行的办法是通过加入随时间振荡的调制电流抑制撕裂模。在等离子体平衡电流的基础上加入随时间振荡的调制电流,有理面的位置会随时间振荡。如果有理面位置的振幅足够大且振荡频率高于撕裂模的线性增长率,撕裂模可以被有效抑制。通过振荡有理面抑制撕裂模所需要的低杂波电流驱动的功率和通常的通过电子回旋波电流驱动抑制撕裂模所需的功率相差不多。随着托卡马克参数的提高,新经典效应对电流调制稳定撕裂模的效率有着不可忽略的作用。新经典电阻效应降低了等离子体内部电流扩散时间,使调制电流更易于穿透到等离子体内部。在振荡环电压的作用下,等离子体以调制的Ware-pinch速度随时间径向振荡。这些新经典效应提高了电流调制稳定撕裂模的效率。
Tearing mode, which is one of the most dangerous magnetohydrodynamic in-stabilities in tokamak, can change the topology of the magnetic field, destroy the equilibrium of plasma, and in extreme cases the tearing mode can terminate the plasma discharge and lead to grave consequences. Therefore, to ensure the normal operation of a tokamak,the tearing mode must be stabilized effectively. Various methods have been used to stabilize the tearing mode, but these methods have some technical difficulties. An alternative way to control the tearing mode is to make the resonant surface oscillate with time by modulating the plasma current. With a modulation current which oscillates with time added on the equilibrium current, the radial position of the resonant surface can be oscillated. Tearing modes can be stabilized, if the frequency of the oscillation is higher than the clas-sical growth rate of the tearing mode, and the amplitude of the resonant surface oscillation is large enough. The power needed for the lower hybrid current drive to oscillate the resonant surface and suppress the tearing mode is comparable to the conventional method of tearing mode suppression by the electron cyclotron wave current drive. As the parameters of tokamak improved, the neoclassical effects play important roles on the stabilization of tearing modes by current modulation. Neoclassical effects enhance the resistivity and reduce the resistive diffusion time of the modulation current. Therefore, the oscillating current can penetrate deeper into the plasma. With an oscillating loop voltage, the plasma oscillates radially in the Ware-pinch velocity. These neoclassical effects improve the efficiency of tearing mode stabilization by the current modulation.
Tearing mode, which is one of the most dangerous magnetohydrodynamic in-stabilities in tokamak, can change the topology of the magnetic field, destroy the equilibrium of plasma, and in extreme cases the tearing mode can terminate the plasma discharge and lead to grave consequences. Therefore, to ensure the normal operation of a tokamak,the tearing mode must be stabilized effectively. Various methods have been used to stabilize the tearing mode, but these methods have some technical difficulties. An alternative way to control the tearing mode is to make the resonant surface oscillate with time by modulating the plasma current. With a modulation current which oscillates with time added on the equilibrium current, the radial position of the resonant surface can be oscillated. Tearing modes can be stabilized, if the frequency of the oscillation is higher than the clas-sical growth rate of the tearing mode, and the amplitude of the resonant surface oscillation is large enough. The power needed for the lower hybrid current drive to oscillate the resonant surface and suppress the tearing mode is comparable to the conventional method of tearing mode suppression by the electron cyclotron wave current drive. As the parameters of tokamak improved, the neoclassical effects play important roles on the stabilization of tearing modes by current modulation. Neoclassical effects enhance the resistivity and reduce the resistive diffusion time of the modulation current. Therefore, the oscillating current can penetrate deeper into the plasma. With an oscillating loop voltage, the plasma oscillates radially in the Ware-pinch velocity. These neoclassical effects improve the efficiency of tearing mode stabilization by the current modulation.
引文
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[2]Mao J, Phillips P, Gentle K, et al. Modulated toroidal current suppression of MHD activity on the HT-7 superconducting tokamak. Nucl. Fusion,2001,41(11):1645.
[3]Nguyen C N, Bateman G, Kritz A H. Simulation of saturated tearing modes in tokamaks. Physics of Plasmas,2004, 11(7):3460-3471.
[4]White R B, Rutherford P H, Colestock P, et al. Sawtooth Stabilization by Energetic Trapped Particles. Phys. Rev. Lett.,1988,60:2038-2041.
[5]Sauter O, Westerhof E, Mayoral M L, et al. Control of Neoclassical Tearing Modes by Sawtooth Control. Phys. Rev. Lett.,2002,88:105001.
[6]Morris A W. MHD instability control, disruptions, and error fields in tokamaks. Plasma Physics and Controlled Fusion,1992,34(13):1871.
[7]White R B, Monticello D A, Rosenbluth M N. Simulation of Large Magnetic Islands:A Possible Mechanism for a Major Tokamak Disruption. Phys. Rev. Lett.,1977,39:1618-1621.
[8]Carreras B A, Rosenbluth M N, Hicks H R. Nonlinear Destabilization of Tearing Modes. Phys. Rev. Lett.,1981,46:1131-1134.
[9]Furth H P, Rutherford P H, Selberg H. Tearing mode in the cylindrical tokamak. Physics of Fluids, 1973,16(7):1054-1063.
[10]Yu Q, Giinter S, Scott B D. Numerical modeling of linear drift-tearing mode stability. Physics of Plasmas,2003,10(3):797-810.
[11]郑永真,石秉仁.HL-1装置的低q放电实验.核聚变与等离子体物理,10(2)：67-77.
[12]Westerhof E, Lazaros A, Farshi E, et al. Tearing mode stabilization by electron cyclotron resonance heating demonstrated in the TEXTOR tokamak and the implication for ITER. Nucl. Fusion,2007, 47(2):85.
[13]Reiman A H. Suppression of magnetic islands by rf driven currents. Phys. Fluids,1983, 26(5):1338-1340.
[14]Hender T C, Cowley S C. Toroidal effects on m=2 feedback. Phys. Fluids B:Plasma Phys.,1989, 1(11):2194-2200.
[15]Cowley S C, Kulsrud R M, Hahm T S. Linear stability of tearing modes. Physics of Fluids,1986, 29(10):3230-3244.
[16]Rutherford P H. Nonlinear growth of the tearing mode. Physics of Fluids,1973,16(11):1903-1908.
[17]Drake J F, Lee Y C. Nonlinear Evolution of Collisionless and Semicollisional Tearing Modes. Phys. Rev. Lett.,1977,39:453-456.
[18]Esarey E, Freidberg J P, Molvig K, et al. Stabilization of the Tearing Mode in Low-Density Tokamak Plasmas by Turbulent Electron Diffusion. Phys. Rev. Lett.,1983,50:583-580.
[19]Izzo R, Monticello D A, Park W, et. al. Effects of toroidicity on resistive tearing modes. Physics of Fluids,1983,26(8):2240-2246.
[20]Furth II P, Killeen J, Rosenbluth M N. Finite-Resistivity Instabilities of a Sheet Pinch. Physics of Fluids,1963,6(4):459-484.
[21]J W. Tokamaks(Oxford Engineering Science Series 48). Oxford:Oxford University Press,1997.
[22]White R B. Theory of Tokamak Plasmas. Netherlands:Elsevier Science Publishing Company, Inc., 1989.
[23]Glasser A H, Furth H P, Rutherford P H. Stabilization of Resistive Kink Modes in the Tokamak. Phys. Rev. Lett.,1977,38:234-237.
[24]Giruzzi G, Zabiego M, Gianakon T, et al. Dynamical modelling of tearing mode stabilization by RF current drive. Nucl. Fusion,1999,39(1):107.
[25]Classen I G J, Westerhof E, Domier C W, et al. Effect of Heating on the Suppression of Tearing Modes in Tokumaks. Phys. Rev. Lett.,2007,98:035001.
[26]Petty C, Haye R L, Luce T, et al. Complete suppression of the m= 2/n=1 neoclassical tearing mode using electron cyclotron current drive in DⅢ-D. Nucl. Fusion,2004,44(2):243.
[27]Thyagaraja A, Hazcltine R D, Aydemir A Y. Stabilization of the m= 1 tearing mode by resonance detuning. Phys. Fluids B:Plasma Phys.,1992,4(9):2733-2736.
[28]Mao J, Phillips P, Gentle K, et al. Modulated toroidal current suppression of MHD activity on the HT-7 superconducting tokamak. Nucl. Fusion,2001,41(11):1645.
[29]Nagasaki K, Isayama A, Ide S. Stabilization effect of early ECCD on a neoclassical tearing mode in the JT-60U tokamak. Nucl. Fusion,2003,43(10):L7.
[30]Hayashi N, Ozeki T, Hamamatsu K, et al. ECCD power necessary for the neoclassical tearing mode stabilization in ITER. Nucl. Fusion,2004,44(4):477.
[31]Coda S, Goodman T P, Henderson M A, et al. High-power ECH and fully non-inductive operation with ECCD in the TCV tokamak. Plasma Phys. Controlled Fusion,2000,42(12B):B311.
[32]Park W, Monticello D A, White R B. Reconnection rates of magnetic fields including the effects of viscosity. Physics of Fluids,1984,27(1):137-149.
[33]Callen J D, Shaing K C. A pressure-gradient-driven tokamak "resistive magnetohydrodynamic" instability in the banana-plateau collisionality regime. Physics of Fluids,1985,28(6):1845-1858.
[34]Hirshman S, Sigmar D. Neoclassical transport of impurities in tokamak plasmas. Nuclear Fusion, 1981,21(9):1079.
[35]Callen J D, Cole A J, Hegna C C. Toroidal flow and radial particle flux in tokamak plasmas. Physics of Plasmas,2009,16(8):082504.
[36]Braginskii S. TRANSPORT PROCESSES IN A PLASMA. Reviews of Plasma Physics,1965.205.
[37]Kadomtsev B, Pogutse O. Trapped particles in toroidal magnetic systems. Nuclear Fusion,1971, 11(1):67.
[38]Rutherford P H, Kovrizhnikh L M, Rosenbluth M N, et al. Effect of Longitudinal Electric Field on Toroidal Diffusion. Phys. Rev. Lett.,1970,25:1090-1093.
[39]Ramos J J. General expression of the gyroviscous force. Physics of Plasmas,2005,12(11):112301.
[40]Connor J, Grimm R, Hastie R, et al. The conductivity of a toroidal plasma. Nuclear Fusion,1973, 13(2):211
[41]Qu W, Callen J. Nonlinear growth of a single neoclassical MHD tearing mode in a tokamak. Technical report, Wisconsin Univ., Madison (USA). Dept. of Nuclear Engineering,1985.
[42]Wang S. Finite bootstrap current density and finite neoclassical reduction of electrical conductivity at the magnetic axis of a tokamak. Physics of Plasmas,1998,5(9):3319-3324.
[43]Oarrera R, Hazeltine R D, Kotschenrenther M. Island bootstrap current modification of the non-linear dynamics of the tearing mode. Physics of Fluids,1986,29(4):899-902.
[44]McGuire K M, Robinson D C. Major Disruptions in the TOSCA Tokamak. Phys. Rev. Lett.,1980, 44:1666-1669.
[45]Strait E J. Stability of high beta tokamak plasmas@f|. Phys. Plasmas,1994,1 (5):1415-1431.
[46]Hazeltine R D, Strauss H R. Tokamak Heat Transport Due to Tearing Modes. Phys. Rev. Lett., 1976,37:102-104.
[47]Ikeda K. Progress in the ITER Physics Basis. Nucl. Fusion,2007,47(6).
[48]Sauter (), Haye R J L, Chang Z, et al. Beta limits in long-pulse tokamak discharges. Phys. Plasmas, 1997,4(5):1654-1664.
[49]Fitzpatrick R. Helical temperature perturbations associated with tearing modes in tokamak plas-mas. Phys. Plasmas,1995,2(3):825-838.
[50]Daybelge U. Electrical Conductivity in Toroidal Plasma with Trapped Particles. Phys. Rev. Lett., 1971,27:916-919.
[51]Kadomtsev B, Pogutse O. Trapped particles in toroidal magnetic systems. Nuclear Fusion,1971, 11(1):67.
[52]Ware A A. Pinch Effect for Trapped Particles in a Tokamak. Phys. Rev. Lett.,1970,25:15-17.
[53]Yang X, Wang S, Yang W. Stabilization of tearing modes by oscillating the resonant surface. Physics of Plasmas,2012,19(7):072503.
[2]Mao J, Phillips P, Gentle K, et al. Modulated toroidal current suppression of MHD activity on the HT-7 superconducting tokamak. Nucl. Fusion,2001,41(11):1645.
[3]Nguyen C N, Bateman G, Kritz A H. Simulation of saturated tearing modes in tokamaks. Physics of Plasmas,2004, 11(7):3460-3471.
[4]White R B, Rutherford P H, Colestock P, et al. Sawtooth Stabilization by Energetic Trapped Particles. Phys. Rev. Lett.,1988,60:2038-2041.
[5]Sauter O, Westerhof E, Mayoral M L, et al. Control of Neoclassical Tearing Modes by Sawtooth Control. Phys. Rev. Lett.,2002,88:105001.
[6]Morris A W. MHD instability control, disruptions, and error fields in tokamaks. Plasma Physics and Controlled Fusion,1992,34(13):1871.
[7]White R B, Monticello D A, Rosenbluth M N. Simulation of Large Magnetic Islands:A Possible Mechanism for a Major Tokamak Disruption. Phys. Rev. Lett.,1977,39:1618-1621.
[8]Carreras B A, Rosenbluth M N, Hicks H R. Nonlinear Destabilization of Tearing Modes. Phys. Rev. Lett.,1981,46:1131-1134.
[9]Furth H P, Rutherford P H, Selberg H. Tearing mode in the cylindrical tokamak. Physics of Fluids, 1973,16(7):1054-1063.
[10]Yu Q, Giinter S, Scott B D. Numerical modeling of linear drift-tearing mode stability. Physics of Plasmas,2003,10(3):797-810.
[11]郑永真,石秉仁.HL-1装置的低q放电实验.核聚变与等离子体物理,10(2)：67-77.
[12]Westerhof E, Lazaros A, Farshi E, et al. Tearing mode stabilization by electron cyclotron resonance heating demonstrated in the TEXTOR tokamak and the implication for ITER. Nucl. Fusion,2007, 47(2):85.
[13]Reiman A H. Suppression of magnetic islands by rf driven currents. Phys. Fluids,1983, 26(5):1338-1340.
[14]Hender T C, Cowley S C. Toroidal effects on m=2 feedback. Phys. Fluids B:Plasma Phys.,1989, 1(11):2194-2200.
[15]Cowley S C, Kulsrud R M, Hahm T S. Linear stability of tearing modes. Physics of Fluids,1986, 29(10):3230-3244.
[16]Rutherford P H. Nonlinear growth of the tearing mode. Physics of Fluids,1973,16(11):1903-1908.
[17]Drake J F, Lee Y C. Nonlinear Evolution of Collisionless and Semicollisional Tearing Modes. Phys. Rev. Lett.,1977,39:453-456.
[18]Esarey E, Freidberg J P, Molvig K, et al. Stabilization of the Tearing Mode in Low-Density Tokamak Plasmas by Turbulent Electron Diffusion. Phys. Rev. Lett.,1983,50:583-580.
[19]Izzo R, Monticello D A, Park W, et. al. Effects of toroidicity on resistive tearing modes. Physics of Fluids,1983,26(8):2240-2246.
[20]Furth II P, Killeen J, Rosenbluth M N. Finite-Resistivity Instabilities of a Sheet Pinch. Physics of Fluids,1963,6(4):459-484.
[21]J W. Tokamaks(Oxford Engineering Science Series 48). Oxford:Oxford University Press,1997.
[22]White R B. Theory of Tokamak Plasmas. Netherlands:Elsevier Science Publishing Company, Inc., 1989.
[23]Glasser A H, Furth H P, Rutherford P H. Stabilization of Resistive Kink Modes in the Tokamak. Phys. Rev. Lett.,1977,38:234-237.
[24]Giruzzi G, Zabiego M, Gianakon T, et al. Dynamical modelling of tearing mode stabilization by RF current drive. Nucl. Fusion,1999,39(1):107.
[25]Classen I G J, Westerhof E, Domier C W, et al. Effect of Heating on the Suppression of Tearing Modes in Tokumaks. Phys. Rev. Lett.,2007,98:035001.
[26]Petty C, Haye R L, Luce T, et al. Complete suppression of the m= 2/n=1 neoclassical tearing mode using electron cyclotron current drive in DⅢ-D. Nucl. Fusion,2004,44(2):243.
[27]Thyagaraja A, Hazcltine R D, Aydemir A Y. Stabilization of the m= 1 tearing mode by resonance detuning. Phys. Fluids B:Plasma Phys.,1992,4(9):2733-2736.
[28]Mao J, Phillips P, Gentle K, et al. Modulated toroidal current suppression of MHD activity on the HT-7 superconducting tokamak. Nucl. Fusion,2001,41(11):1645.
[29]Nagasaki K, Isayama A, Ide S. Stabilization effect of early ECCD on a neoclassical tearing mode in the JT-60U tokamak. Nucl. Fusion,2003,43(10):L7.
[30]Hayashi N, Ozeki T, Hamamatsu K, et al. ECCD power necessary for the neoclassical tearing mode stabilization in ITER. Nucl. Fusion,2004,44(4):477.
[31]Coda S, Goodman T P, Henderson M A, et al. High-power ECH and fully non-inductive operation with ECCD in the TCV tokamak. Plasma Phys. Controlled Fusion,2000,42(12B):B311.
[32]Park W, Monticello D A, White R B. Reconnection rates of magnetic fields including the effects of viscosity. Physics of Fluids,1984,27(1):137-149.
[33]Callen J D, Shaing K C. A pressure-gradient-driven tokamak "resistive magnetohydrodynamic" instability in the banana-plateau collisionality regime. Physics of Fluids,1985,28(6):1845-1858.
[34]Hirshman S, Sigmar D. Neoclassical transport of impurities in tokamak plasmas. Nuclear Fusion, 1981,21(9):1079.
[35]Callen J D, Cole A J, Hegna C C. Toroidal flow and radial particle flux in tokamak plasmas. Physics of Plasmas,2009,16(8):082504.
[36]Braginskii S. TRANSPORT PROCESSES IN A PLASMA. Reviews of Plasma Physics,1965.205.
[37]Kadomtsev B, Pogutse O. Trapped particles in toroidal magnetic systems. Nuclear Fusion,1971, 11(1):67.
[38]Rutherford P H, Kovrizhnikh L M, Rosenbluth M N, et al. Effect of Longitudinal Electric Field on Toroidal Diffusion. Phys. Rev. Lett.,1970,25:1090-1093.
[39]Ramos J J. General expression of the gyroviscous force. Physics of Plasmas,2005,12(11):112301.
[40]Connor J, Grimm R, Hastie R, et al. The conductivity of a toroidal plasma. Nuclear Fusion,1973, 13(2):211
[41]Qu W, Callen J. Nonlinear growth of a single neoclassical MHD tearing mode in a tokamak. Technical report, Wisconsin Univ., Madison (USA). Dept. of Nuclear Engineering,1985.
[42]Wang S. Finite bootstrap current density and finite neoclassical reduction of electrical conductivity at the magnetic axis of a tokamak. Physics of Plasmas,1998,5(9):3319-3324.
[43]Oarrera R, Hazeltine R D, Kotschenrenther M. Island bootstrap current modification of the non-linear dynamics of the tearing mode. Physics of Fluids,1986,29(4):899-902.
[44]McGuire K M, Robinson D C. Major Disruptions in the TOSCA Tokamak. Phys. Rev. Lett.,1980, 44:1666-1669.
[45]Strait E J. Stability of high beta tokamak plasmas@f|. Phys. Plasmas,1994,1 (5):1415-1431.
[46]Hazeltine R D, Strauss H R. Tokamak Heat Transport Due to Tearing Modes. Phys. Rev. Lett., 1976,37:102-104.
[47]Ikeda K. Progress in the ITER Physics Basis. Nucl. Fusion,2007,47(6).
[48]Sauter (), Haye R J L, Chang Z, et al. Beta limits in long-pulse tokamak discharges. Phys. Plasmas, 1997,4(5):1654-1664.
[49]Fitzpatrick R. Helical temperature perturbations associated with tearing modes in tokamak plas-mas. Phys. Plasmas,1995,2(3):825-838.
[50]Daybelge U. Electrical Conductivity in Toroidal Plasma with Trapped Particles. Phys. Rev. Lett., 1971,27:916-919.
[51]Kadomtsev B, Pogutse O. Trapped particles in toroidal magnetic systems. Nuclear Fusion,1971, 11(1):67.
[52]Ware A A. Pinch Effect for Trapped Particles in a Tokamak. Phys. Rev. Lett.,1970,25:15-17.
[53]Yang X, Wang S, Yang W. Stabilization of tearing modes by oscillating the resonant surface. Physics of Plasmas,2012,19(7):072503.
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