摘要
高比压等离子体中的微观漂移不稳定性是等离子体理论研究中的前沿课题之一,它对于理解等离子体的基本行为,对于先进磁约束聚变研究和空间物理研究都有着重要的意义。本文发展了剪切平板位形中适合任意比压的微观漂移不稳定性的动理学特征模积分方程,并对离子温度梯度(ITG)模进行了深入的研究。特征模方程包含了静电势扰动和磁场的垂直扰动和平行扰动,并且考虑了等离子体压力平衡所要求的磁场梯度的效应。模型中不仅包含了离子温度梯度,电子温度梯度(ETG),质量流平行速度剪切(PVS),垂直速度剪切(E×B剪切)和平行电流等因素,而且完整地包含了有限拉莫尔半径效应,波-粒子相互作用,粒子的热传递效应等电子和离子的低频动理学行为。对ITG模的研究表明典型参数下的ITG模并不能象小比压模型结果中所描述的那样被有限比压稳定,因为比压对模的稳定能力会随着频率的减小和比压的增大而减弱。高比压下的不稳定模对离子温度梯度和角向波长的变化的响应减弱。平行速度剪切对模的解稳定作用也在有限比压下被削弱,平行电流只是在中等比压时表现出弱的稳定作用,但磁剪切和垂直速度剪切仍然能稳定高比压下的不稳定模,而且弱的磁剪切会增强垂直速度剪切的作用。剪切方向相反( V 0 'VE'<0)的平行剪切流和垂直剪切流共存有利于降低不稳定性,但同时改变各自的符号不会改变模的色散关系。研究还表明具有撕裂模结构的高一阶ITG模只在低比压和弱磁剪切下占优势。本文还研究了温度比和等离子体比压在稳定ITG模的过程中的相互作用。结果发现Te/Ti通常总是不稳定因素,而电子比压总是稳定因素,而离子比压的作用非常弱。非等温等离子体中比压的各种作用可以看成这三种机制互相影响的结果。由于完整地包含了离子和电子的动理学行为,本文的模型方程也可以研究ETG模,漂移阿尔芬模等不稳定模态,并且为在同一的框架内研究低频漂移不稳定性提供了平台。
Study of microscopic drift instabilities in highβ(plasma pressure/magnetic pressure) plasmas is one of advanced topics in plasma theory studies,for it is of great important in understanding the basic plasma behaviors and researching on advanced magnetic confinement fusion and space physics. In this dissertation, a set of integral equations is developed to study drift instabilities in arbitraryβplasmas with a sheared slab magnetic configuration model. Both components of the perturbed vector potential, A~/ / and A~⊥, are considered in the equations, as well as the perturbation of the electrostatic potentialφ~ . The ? B drift effects are taken into account to maintain pressure equilibrium for highβplasmas. Such factors as the ion temperature gradient (ITG), electron temperature gradient (ETG), mass flow parallel velocity shear (PVS), parallel current and perpendicular flow shear (E×B shear) are included in this model. Full kinetic effects, including finite Larmor radius effect, particle-wave interaction, transit effect, are considered both for ions and electrons. At the typical parameters, the ITG modes are found to be unstable in the highβregime since theβeffects cannot effectively change the frequency and the particle-wave interaction in the lower frequency regime. The unstable mode is not sensitive to the ion temperature gradient parameter and the poloidal wavelength. The destabilizing effect of the PVS is also weakened by finiteβ. However, the magnetic shear and the E×B shear can stabilize the unstable mode, even at a highβvalue, and the E×B shear effect is strengthened as the magnetic shear decreases. The parallel sheared flow and perpendicular sheared flow with V 0 'VE'<0 benefit the instability suppression while the eigen-frequency does not change when the signs of flow shears are simultaneously reversed. It is also concluded that the next order ITG eigenmode with tearing parity dominants only in the lowβand weak magnetic shear regime. The investigation on theβeffect in anisothermal plasmas reveals that the Te/Ti is usually destabilizing, the direct effect ofβe is always stabilizing, and the direct effect ofβi is weak. The combination and interaction of these effects dominant theβeffect on the anisothermal ITG mode. The eigenmode equation in this dissertation can also be used to study the ETG mode, the drift Alfven waves, and so on. So it provides a unique frame to study the low frequency drift instabilities.
引文
【1】 Kadomtsev B. B. Tokamak Plasma: A Complex Physical System. Bristol and Philadelphia: IOP Publishing Ltd., 1992
【2】 Burrell K. H. Summary of experimental progress and suggestions for future work. Plasma Phys. Control. Fusion, 1994, 36: A291
【3】 石秉仁. 磁约束聚变原理于实践. 北京: 原子能出版社,1999. 265~277
【4】 Wagner F., Becker G., Behringer K., et al. Regime of improved confinement and high-beta in neutral beam heated divertor discharges of the ASDEX tokamak. Phys. Rev. Lett. 1982, 49: 1408
【5】 Greenfield C. M., Balet B. and Burrell, K. H., et al. Investigations of VH-mode in DIII-D and JET. Plasma Phys. Control. Fusion, 1993, 35: B263
【6】 Jackson G. L., Winter J., Taylor T. S., et al. Regime of very high confinement in the boronized DIII-D tokamak. Phys. Rev. Lett, 1991, 67:3098
【7】 Deliyanakis N, O'Brien D. P., Balet B., et al. The VH-mode in JET. Plasma Phys. Control. Fusion, 1994, 36:1159
【8】 Strait E.J., Lao L.L., Mauel M.E., et al. Enhanced confinement and stability in DIII-D discharges with reversed magnetic shear. Phys. Rev. Lett., 1995, 11: 4421.
【9】 Koide Y., KiKuchi M., Mori M., et al. Internal transport barrier on q=3 surface and poloidal plasma spin up in JT-60U high β p discharges. Phys. Rev. Lett., 1994, 72:3662.
【10】 Levinton F.M., Zarnstroff M. C., Batha S. H. et al. Improved confinement with reversed megnetic shear in TFTR Phys. Rev. Lett., 1995, 75:4417.
【11】 Burrell K. H. Effects of E×B velocity shear and magnetic shear on turbulence and transport in magnetic devices. Phys. Plasmas, 1997, 4:1499
【12】 Hahm T. S. and Burrell K. H. Flow Shear-induced fluctuation suppression in finite aspect ratio shaped tokamak plasma. Phys. Plasmas, 1995, 2:1648
【13】 Biglari H., Diamond P. H. and Terry P. W. Influence of sheared poloidal rotation on edge turbulence. Phys. Fluids B, 1990, 2:1
【14】 Shaing K. C., Crume E. C. Jr., and Houlberg W. A. Bifurcation of poloidal rotation and suppression of turbulent fluctuations: a model for the L-H transition in tokamaks. Phys. Fluids B, 1990,2: 1492
【15】 Itoh K. and Itoh S.-I. The role of the electric field in confinement. Plasma Phys. Control. Fusion, 1996, 38: 1
【16】 Ware A. S., Terry P. W., Diamond P. H., et a.l Transport reduction via shear flow modification of the cross phase. Plasma Phys. Control. Fusion, 1996, 38:1343
【17】 Wagner F. New subjects of the H-mode. Plasma Phys. Control. Fusion, 1994, 36: A319
【18】 Parkins W. Krumhansl J. and Starr C. Insurmountable engineering problems seen as ruling out ‘Fusion Power to the People’ in 21st century. Phys. Today, May 1997: 9; Schmitt J. A., Davison R. D. Holt R. D. et al. Development of fusion power seen as essential to world’s energy future; critics Respond. ibid: 11
【19】 Sessler A. M., Stix T. H. and Rosenbluth M. N. Build the international thermonuclear experimental reactror? Phys. Today, June 1996:21
【20】 ITER web station (www.iter.org)
【21】 Peng, Y.-K. M. and Strickler D. J. Features of spherical torus plasmas. Nucl. Fusion, 1986, 26:769
【22】 Sykes, A. The spherical tokamak program at Culham. Nucl. Fusion 1999, 39:1271
【23】 Ono M., Bell M. G., Bell R. E., et al. Overview of the initial NSTX experimental results. Nucl. Fusion 2001, 41, 1435
【24】 Cunningham G. and the MAST team. Progress on MAST. in the joint meeting of the 2nd IAEA technical committee meeting and the 7th international spherical torus workshop, Sao Jose dos Campos, SP, Brazil, 1-3 Augst 2001
【25】 He Yexi and the SUNIST team. Research program of spherical tokamak in China. Ibid.
【26】 Balescu R. Transport Processes in Plasmas: Vol. 1 & 2 , North-Holland: Amsterdam, 1988.
【27】 Liewer P. C. Measurements of microturbulence in tokamaks and comparisons with theories of turbulence and anomalous transport. Nucl. Fusion, 1985, 25:543.
【28】 Tang W. M. Microinstability theory in tokamaks. Nucl. Fusion, 1978, 18: 1089.
【29】 Horton W. Drift waves and transport, Rev. Mod. Phys., 1999, 71:735
【30】 Sagdeev R. Z., Galeev A. A. Nonlinear Plasma Theory, New York: Plenum Press, 1970
【31】 Hasegawa A. and Mima K. Stationary spectrum of strong turbulence in magnetised nonuniform plasma. Phys. Rev. Lett., 1977, 39:205
【32】 Hirshman S. P. and Movig K. Turbulent destabilization and saturation of the universal drift mode in a sheared magnetic field. Phys. Rev. Lett., 1979, 43:648
【33】 Diamond P. H. and Rosenbluth M. N. Theory of the renormalized dielectric for electrostatic drift wave turbulence in Tokamaks. Phys. Fluids, 1981, 24: 1641
【34】 Similon P. L. and Diamond P. H. Nonlinear interaction of toroidicity-induced drift modes. Phys. Fluids, 1984, 27:916
【35】 Waltz R. E. and Dominguez R. R. Drift-wave turbulence with wave-wave and wave-particle nonlinear effects in a sheared slab. Phys. Fluids, 1983, 26: 3338
【36】 Terry P. W. and Horton W. Drift wave turbulence in a low-order k space. Phys. Fluids, 1983, 26: 106
【37】 Xu X. Q. and Rosenbluth M. N. Numerical simulation of ion-temperature-gradient-driven modes. Phys. Fluids B, 1991, 3: 627
【38】 Hong B. G., Romanelli R., and Ottaviani M., Coherent structures in η i-mode turbulence Phys. Fluids B, 1991, 3: 615
【39】 Waltz R. E., Kerbel G. D., Milovich J., et al. Toroidal gyro-Landau fluid model turbulence simulations in a nonlinear ballooning mode representation with radial modes. Phys. Plasmas, 1994, 2: 2408
【40】 Hammett G. W., Beer M. A., Dorland W., et al. Developments in the gyrofluid approach to Tokamak turbulence simulations. Plasma Phys. Controlled Fusion 1993, 35: 973
【41】 Lee W. W. and Santoro R. A. Gyrokinetic simulation of isotope effects in tokamak plasmas. Phys. Plasmas 1997, 4:169
【42】 Lin Z., Hahm T. S., Lee W. W., et al. Turbulent transport reduction by zonal flows: Massively parallel simulations. Science 1998, 281:1835
【43】 Chen L. and Cheng C. Z. Absolute dissipative drift-wave instabilities in Tokamaks. Phys. Fluids, 1980, 20: 901
【44】 Connor J. W., Hastie R. J., and Taylor J. B. Shear, periodicity, and plasma ballooning modes. Phys. Rev. Lett., 1978, 40: 396
【45】 Mikhailovskii A. B. in Reviews of Plasma Physics (Leontovich M. A. Ed.), Vol. 3 New York: Consultants Bureau, 1967. 159
【46】 Krall N.A., Rosenbluth M. N. Phys. Fluids 1963,6:254.
【47】 Pearlstein L. D., Berk H. L. Universal eigenmode in a strongly sheared magnetic field. Phys. Rev. Lett., 1969,23:220.
【48】 Rosenbluth M. N. and Catto P. J. An improved calculation of critical magnetic shear in an inhomogeneous plasma. Nucl. Fusion, 1975, 15:573
【49】 Chen Liu, Guzdar P. N., Hsu, J. Y. et al. . Theory of drift and trapped-electron instabilities. Nucl. Fusion, suppl., vol.1, 1979, 19:763.
【50】 Winske D. and Gary S. P. Magnetic gradient effects on the universal drift instability. Phys. Fluids, 1979, 22:665
【51】 Hastings D. E., McCune J. E. The high- beta universal drift mode, Phys. Fluids, 1982, 25:509.
【52】 Gladd N. T. and Liu C. S. Current-driven drift modes in sheared magnetic field, Phys. Fluids, 1979, 22: 1289
【53】 Coppi B., Lampis G. and Pegoraro F., Anomalous transport model in high density regimes of confined plasmas. Phys. Lett. A, 1976, 59:118
【54】 Nishi-Kawa K, Numerical analysis of current-driven collisional drift instability in a sheared magnetic field. J. Phys. Soc. Japan, 1979, 46:357
【55】 Inoue S., Itoh K., and Yoshikawa S. Non-local drift instability of current-carrying plasma with temperature inhomogeneities. Nucl. Fusion, 1978, 18:755
【56】 Antonsen T. M. Jr., Barton Lane. Kinetic equations for low frequency instabilities in inhomogeneous plasmas. Phys. Fluids, 1980, 23:1205
【57】 Tang W. M., Connor J. W. and Hastie R. J. Kinetic-ballooning-mode theory in general geometry. Nucl Fusion, 1980, 20:1439
【58】 Rewoldt G., Tang W. M., Chance M. S. Electromagnetic kinetic toroidal eigenmodes for general magnetohydrodynamic equilibria. Phys. Fluids, 1982, 25:480
【59】 Horton W., Sedlak J. E., Choi Duk-In et al. Kinetic theory of the electromagnetic drift modes driven by pressure gradients. Phys. Fluids, 1985, 28:3050.
【60】 B. Coppi, M.N. Rosenbluth, and R. Z. Sagdeev, Instabilities due to temperature gradients in complex magnetic field configuration. Phys. Fluids 1967, 10: 582
【61】 Tang W. M. Rewoldt G. and Frieman E. A. Integral equation analysis of drift wave eigenmodes in a sheared slab geometry. Phys. Fluids, 1980 12:2454
【62】 Linsker R. Integral-equation formulation for drift eigenmodes in cylindrically symmetric systems. Phys. Fluids, 1981 24:1485
【63】 Hahm T. S. and Tang W. M. Properties of ion temperature gradient drift instabilities in H-mode plasmas. Phys. Fluids B, 1989, 1: 1185
【64】 Dong J. Q., Guzdar P. N., and Lee Y. C., Finite beta effects on ion temperature gradient driven modes. Phys. Fluids 1987, 30: 2694
【65】 Pu Y._K. and Migliuolo S. Finite beta stabilization of the kinetic ion mixing mode. Phys. Fluids 1985, 28:1722
【66】 F. Romanelli, Ion temperature-gradient-driven modes and anomalous ion transport in tokamaks. Phys. Fluids B, 1989, 1:1018
【67】 Dong J. Q., Horton W., and Kim J. Y., Toroidal kinetic η i-mode study in high-temperature plasmas. Phys. Fluids B, 1992, 4:1867
【68】 Kim J. Y., Horton W. and Dong J. Q., Electromagnetic effect on the toroidal ion temperature gradient mode. Phys. Fluids B, 1993, 5: 4030
【69】 Jarmen A., Anderson P., and Weiland J. Fully toroidal ion temperature gradient driven drift modes. Nucl. Fusion 1987, 27: 941
【70】 Weiland J. and Hirose A. Electromagnetic and kinetic effects on the ion temperature gradient mode. Nucl. Fusion, 1992, 32: 151
【71】 Hong B. G., Horton W., and Choi D. I. Plasma Pressure gradient-driven modes in finite beta toroidal plasmas. Phys. Controlled Fusion, 1989, 31:1291
【72】 Rewoldt G., Tang W.M. Toroidal microinstability studies of high-temperature tokamaks. Phys. Fluids B, 1990, 2: 318
【73】 Waltz R. E., Pfeiffer W., Dominguez R.R. Electrostatic drift waves in tokamaks: a numerical study of instability and transport. Nucl. Fusion, 1980, 20: 43
【74】 Dong J. Q., Zhang Y. Z., Mahajan S. M. et al. Study of microinstabilities in toroidal plasmas with negative magnetic shear. Phys. Plasmas 3, 3065 (1996)
【75】 Dong J. Q. Mahajan S. M and Horton W. Coupling of η i and trapped electron modes in plasmas with negative magnetic shear. Phys. Plasmas, 1997, 4 : 755
【76】 Ganguli G., Lee Y. C., and Palmadesso P. J. Kinetic theory for electrostatic waves due to transverse velocity shears. Phys. Fluids, 1988, 31:823
【77】 Dong J. Q., Horton W. Kinetic quasitoroidal ion temperature gradient instability in the presence of sheared flows. Phys.Fluids B, 1993, 5: 1581.
【78】 Artun M., Tang W.M. Gyrokinetic analysis of ion temperature gradient modes in the presence of sheared flows. Phys.Fluids B, 1992, 4: 1102
【79】 Dong J.Q., Horton W., Bengtson R.D. and Li G.X. Momentum-energy transport from turbulence driven by parallel flow shear. Phys.Plasmas, 1994, 1: 3250
【80】 Hamaguchi S., Horton W. Effects of sheared flow on ion-temperature-gradient-driven turbulent transport. Phys. Fluids B, 1992, 4: 319.
【81】 傅新宇. 磁化等离子体的微观不稳定性和湍流输运:[博士学位论文]. 北京:清华大学工程物理系,1997
【82】 Rajendran K., Dong J. Q. and Mahajan S. M. Effects of negative magnetic shear on toroidicity induced eigenmode instability in tokamaks. Phys. Plasmas, 1997, 4: 908
【83】 Dong J. Q., Zhang Y. Z. and Mahajan S. M. Studies of instability and transport in sheared-slab plasmas with very weak magnetic shear. Phys. Plasmas, 1997, 4:3334
【84】 Fu X. Y., Dong J. Q. Horton W. et al Turbulent particle transport in tokamak plasmas with impurities. Phys. Plasmas, 1997, 4:
【85】 Tang W. M., White R.B., Guzdar P.N. Impurity effects on ion-drift-wave eigenmodes in a sheared magnetic field. Phys.Fluids, 1980, 23: 167
【86】 R.R.Dominguez R. R., Staebler G.M., Impurity effects on drift wave stability and impurity transport. Nucl.Fusion, 1993, 31: 51
【87】 Hirose A. Phys. Plasmas,2000,7:433
【88】 J. V. M. Reynders, Finite-beta modification of the ion-temperature-gradient-driven instability in a sheared slab geometry. Phys. Plasmas 1, 1953 (1994)
【89】 Dong J. Q., Chen L. and Zonca F. Study of kinetic shear Alfven modes driven by ion temperature gradient in tokamak plasmas. Nucl Fusion, 1999, 39:1041
【90】 Lee Y. C., Dong J. Q., Guzdar P. N. et al. Collisionless electron temperature gradient instability. Phys. Fluids 30, 1331 (1987)
【91】 Kim J. Y. and Horton W. Electromagnetic effect on the toroidal electron temperature gradient mode. Phys. Fluids B, 1991, 3:3194
【92】 Idomura Y., Wakatani M., and Tokuda S. Gyrokinetic theory of slab electron temperature gradient mode in negative shear tokamaks. Phys. Plasmas, 2000, 7:2456
【93】 Dong J. Q., Sanuki H., and Itoh K. Gyrokinetic study of the electron temperature gradient instability in plasmas with slightly hollow density profiles. Phys. Plasmas, 2001, 8:3635
【94】 Singh R., Tangri V., Nordman H. et al. Fluid description of electron temperature gradient driven drift modes, Phys. Plasmas, 2001, 8:4340
【95】 B. W. Stallard, C. M. Greenfield, G. M. Staebler et al Electron heat transport in improved confinement discharges in DIII-D. Phys Plasmas, 1999, 6:1978
【96】 Rewoldt G. Microinstability properties of small-aspect-ratio tokamaks. Phys. Plasmas 1996, 3:1667
【97】 Fredrickson E. D., Gorelenkov N., Cheng C. Z. et al. Observation of compressional Alfven modes during neutral-beam heating on the National Spherical Torus Experiment. Phys. Rev. Lett., 2001, 87: 145001
【98】 Bourdelle C., Bell R. E., Dorland W., et al. Microstabilities analysis of experimental NSTX plasmas, in the joint meeting of the 2nd IAEA technical committee meeting and the 7th international spherical torus workshop, Sao Jose dos Campos, SP, Brazil, 1-3 Augst 2001
【99】 Beer M., Fu G., Gorelenkov N., et al Theoretical Research for NSTX, PPPL Report.
【100】 Li J. and Scheffei J. Kinetic high-beta equilibria in a plasma slab. Phys. Fluids B, 1991, 3:2506
【101】 D’Angelo N. Phys. Fluids, 1965, 8:1748
【102】 Dobrowolny M. Phys. Fluids, 1972, 15: 2263
【103】 Catto P. J., Rosenbluth M. N. and Liu C. S. Parallel velocity shear instabilities in an inhomogeneous plasmas with a sheared magnetic filed. Phys. Fluids, 1973, 16:1917
