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  • 1
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 6 (1999), S. 3878-3889 
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Locked (i.e., nonrotating) dynamo modes give rise to a serious edge loading problem during the operation of high current reversed field pinches. Rotating dynamo modes generally have a far more benign effect. A simple analytic model is developed in order to investigate the slowing down effect of electromagnetic torques due to eddy currents excited in the vacuum vessel on the rotation of dynamo modes in both the Madison Symmetric Torus (MST) [Fusion Technol. 19, 131 (1991)] and the Reversed Field Experiment (RFX) [Fusion Eng. Des. 25, 335 (1995)]. This model strongly suggests that vacuum vessel eddy currents are the primary cause of the observed lack of mode rotation in RFX. The eddy currents in MST are found to be too weak to cause a similar problem. The crucial difference between RFX and MST is the presence of a thin, highly resistive vacuum vessel in the former device. The MST vacuum vessel is thick and highly conducting. Various locked mode alleviation methods are discussed. © 1999 American Institute of Physics.
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  • 2
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 5 (1998), S. 2340-2354 
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A formalism is developed for optimizing the design of feedback coils placed around a tokamak plasma in order to control the resistive shell mode. It is found that feedback schemes for controlling the resistive shell mode fail whenever the distortion of the mode structure by the currents circulating in the feedback coils becomes too strong, in which case the mode escapes through the gaps between the coils, or through the centers of the coils. The main aim of the optimization process is to reduce this distortion by minimizing the coupling of different Fourier harmonics due to the feedback currents. It is possible to define a quantity α0 which parametrizes the strength of the coupling. Feedback fails for α0≥1. The optimization procedure consists of minimizing α0 subject to practical constraints. If there are very many evenly spaced feedback coils surrounding the plasma in the poloidal direction then the optimization can be performed analytically. Otherwise, the optimization must be performed numerically. The optimal configuration is to have many, large, overlapping coils in the poloidal direction. © 1998 American Institute of Physics.
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  • 3
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 6 (1999), S. 3536-3547 
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A reactor relevant reversed field pinch (RFP) must be capable of operating successfully when surrounded by a close-fitting resistive shell whose L/R time is much shorter than the pulse length. Resonant modes are largely unaffected by the shell resistivity, provided that the plasma rotation is maintained against the breaking effect of nonaxisymmetric eddy currents induced in the shell. This may require an auxiliary momentum source, such as a neutral beam injector. Nonresonant modes are largely unaffected by plasma rotation, and are expected to manifest themselves as nonrotating resistive shell modes growing on the L/R time of the shell. A general RFP equilibrium is subject to many simultaneously unstable resistive shell modes; the only viable control mechanism for such modes in a RFP reactor is active feedback. It is demonstrated than an N-fold toroidally symmetric arrangement of feedback coils, combined with a strictly linear feedback algorithm, is capable of simultaneously stabilizing all intrinsically unstable resistive shell modes over a wide range of different RFP equilibria. The number of coils in the toroidal direction N, at any given poloidal angle, must be greater than, or equal to, the range of toroidal mode numbers of the unstable resistive shell modes. However, this range is largely determined by the aspect-ratio of the device. The optimum coil configuration corresponds to one in which each feedback coil slightly overlaps its immediate neighbors in the toroidal direction. The critical current which must be driven around each feedback coils is, at most, a few percent of the equilibrium toroidal plasma current. The feedback scheme is robust to small deviations from pure N-fold toroidal symmetry or a pure linear response of the feedback circuits. © 1999 American Institute of Physics.
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  • 4
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 1 (1994), S. 3337-3355 
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The influence of a general static external magnetic perturbation on the stability of resistive modes in a tokamak plasma is examined. There are three main parts to this investigation. First, the vacuum perturbation is expanded as a set of well-behaved toroidal ring functions, and is, thereafter, specified by the coefficients of this expansion. Second, a dispersion relation is derived for resistive plasma instabilities in the presence of a general external perturbation, and finally, this dispersion relation is solved for the amplitudes of the tearing and twisting modes driven in the plasma by a specific perturbation. It is found that the amplitudes of driven tearing and twisting modes are negligible until a certain critical perturbation strength is exceeded. Only tearing modes are driven in low-β plasmas with εβp(very-much-less-than)1. However, twisting modes may also be driven if εβp(approximately-greater-than)1. For error-field perturbations made up of a large number of different poloidal and toroidal harmonics the critical strength to drive locked modes has a "staircase'' variation with edge-q, characterized by strong discontinuities as coupled rational surfaces enter or leave the plasma. For single harmonic perturbations, the variation with edge-q is far smoother. Both types of behavior have been observed experimentally. The critical perturbation strength is found to decrease strongly close to an ideal external kink stability boundary. This is also in agreement with experimental observations.
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  • 5
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 4 (1997), S. 2997-3000 
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A feedback system, which essentially makes a resistive wall appear ideally conducting, is discussed. Such a system applied to a resistive wall surrounding a plasma will stabilize certain modes which would be unstable in the absence of the feedback system. The system discussed is similar to the "intelligent shell" by Bishop [Plasma Phys. Controlled Fusion 31, 1179 (1989)]; it utilizes a number of autonomous subsystems, each covering only a fraction of the resistive wall. A model example discussed suggests that only relatively few autonomous subsystems are needed and that the requirements of the electronics appear modest. © 1997 American Institute of Physics.
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  • 6
    Electronic Resource
    Electronic Resource
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 4 (1992), S. 413-416 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The question of the influence of nonaxisymmetric field perturbations on tokamaks is investigated. Recent experiments in the COMPASS-C tokamak [in Proceedings of the 15th Symposium on Fusion Technology, Utrecht (North-Holland, Amsterdam, 1989), Vol. 1, p. 361] with externally applied helical fields reveal that magnetic islands do not appear until the applied field exceeds a certain value, when plasma rotation and confinement are affected. A new resistive magnetohydrodynamic model including plasma rotation now provides an explanation of this threshold, and is quantitatively consistent with experimental results in Ohmic plasmas. The results indicate the tolerable error fields in future tokamaks. The effects of perturbations with various poloidal and toroidal mode numbers have been studied.
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  • 7
    Electronic Resource
    Electronic Resource
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 3 (1991), S. 644-673 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The penetration of a helical magnetic perturbation into a rotating tokamak plasma is investigated. In the linear regime, it is found that unless the frequency of the imposed perturbation matches closely to one of the natural mode frequencies, reconnection at the rational surface is suppressed by a large factor. In order to deal with the problem in the nonlinear regime a theory of propagating, constant-ψ magnetic islands is developed. This theory is valid provided the island width greatly exceeds any microscopic scale length (but still remains small compared with the minor radius), and the magnetic Reynolds number of the plasma is sufficiently large. An island width evolution equation is obtained which, in addition to the usual Rutherford term, contains a stabilizing term due ultimately to the inertia of the plasma flow pattern set up around the propagating island. A complete solution is presented for the case where the island and its associated flow pattern are steady. In the nonlinear regime, a fairly sharp threshold is predicted for the magnitude of the applied perturbation. Below this threshold, the induced islands are rotationally suppressed and partially dragged along by the rotating plasma, and above it the islands are virtually fully reconnected and "locked'' at the applied frequency of the perturbation. Numerical results from an initial value code are presented, which show good agreement with the analytic predictions. Finally, it is demonstrated that these theories can be used to interpret data recently obtained from the COMPASS-C device [Controlled Fusion and Plasma Heating 1990 (EPS, Geneva, 1990), Vol. 1, p. 379]. In particular, a positive explanation is given of why in some cases an applied quasistatic resonant magnetic perturbation can stabilize magnetohydrodynamic modes, but in others leads to a disruption.
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  • 8
    Electronic Resource
    Electronic Resource
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 2 (1990), S. 2636-2642 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The set of semicollisional layer equations derived by Fitzpatrick [Phys. Fluids B 1, 2381 (1989)] is used to investigate the effect of trapped particles on the linear stability of long wavelength resistive modes in a large-aspect-ratio tokamak. At O(1) shear, destabilization by trapped particles is found to significantly modify previous cylindrical results for the drift-tearing mode. At low shear, a fairly weak trapped particle-driven interchange (g mode) instability is found, in addition to the usual drift-tearing mode instability, which, in this limit, is virtually unaffected by trapped particles.
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  • 9
    Electronic Resource
    Electronic Resource
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 4 (1992), S. 2098-2103 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Otherwise stable discharges can become nonlinearly unstable to disruptive locked modes when subjected to a resonant m=2, n=1 error field from irregular poloidal field coils, as in DIII-D [Nucl. Fusion 31, 875 (1991)], or from resonant magnetic perturbation coils as in COMPASS-C [Proceedings of the 18th European Conference on Controlled Fusion and Plasma Physics, Berlin (EPS, Petit-Lancy, Switzerland, 1991), Vol. 15C, Part II, p. 61]. Experiments in Ohmically heated deuterium discharges with q≈3.5, n¯ ≈ 2 × 1019 m−3 and BT ≈ 1.2 T show that a much larger relative error field (Br21/BT ≈ 1 × 10−3) is required to produce a locked mode in the small, rapidly rotating plasma of COMPASS-C (R0 = 0.56 m, f≈13 kHz) than in the medium-sized plasmas of DIII-D (R0 = 1.67 m, f≈1.6 kHz), where the critical relative error field is Br21/BT ≈ 2 × 10−4. This dependence of the threshold for instability is explained by a nonlinear tearing theory of the interaction of resonant magnetic perturbations with rotating plasmas that predicts the critical error field scales as (fR0/BT)4/3n¯2/3. Extrapolating from existing devices, the predicted critical field for locked modes in Ohmic discharges on the International Thermonuclear Experimental Reactor (ITER) [Nucl. Fusion 30, 1183 (1990)] (f=0.17 kHz, R0 = 6.0 m, BT = 4.9 T, n¯ = 2 × 1019 m−3) is Br21/BT ≈ 2 × 10−5. Such error fields could be produced by shifts and/or tilts of only one of the larger poloidal field coils of as little as 0.6 cm with respect to the toroidal field. A means to increase the rotation frequency would obviate the sensitivity to error fields and increase allowable tolerances on coil construction.
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  • 10
    Electronic Resource
    Electronic Resource
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 1 (1989), S. 2381-2396 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The semicollisional layer equations governing the linear stability of small mode number tearing modes in a low beta, large aspect ratio, tokamak equilibrium are derived from an expansion of the gyrokinetic equation. In this analysis only the cases where the ion Larmor radius is either much less than, or much greater than, the layer width are considered. Both the electrons and the ions are assumed to lie in the banana collisionality regime. One interesting feature of the derived layer equations, in the limit of small ion Larmor radius, is a substantial reduction in the effective collisionality of the system due to neoclassical ion dynamics. Next, using a shooting code, a dispersion relation is obtained from the layer equations in the limits of small ion Larmor radius and a vanishingly small fraction of trapped particles. As expected, strong semicollisional stabilization of the mode is found, but, in addition, a somewhat weaker destabilizing effect is obtained in the transition region between the collisional and semicollisional regimes.
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