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  • 1
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 3 (1996), S. 3369-3374 
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: This paper reports on the ideal magnetohydrodynamic (MHD) stability of tokamak field profiles that have a non-monotonic safety factor q(r). An analytic criterion is obtained for these "inverse shear'' profiles by expanding in inverse aspect ratio and assuming that the minimum in q is slightly less than the m/n value of the mode under examination (m and n being the principal poloidal and toroidal mode numbers of the instability). Three terms are identified as controlling the stability of this "double kink''; two of them are stabilizing and due, respectively, to field line bending and the interaction of average favorable curvature with the pressure gradient. The possibility of instability comes from the third term which is due to toroidal coupling and is ballooning in character. The analytic results are compared with those from a fully toroidal stability code.
    Type of Medium: Electronic Resource
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  • 2
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The operational limits observed in spherical tokamaks, notably the small tight aspect ratio tokamak (START) device [A. Sykes et al., Nucl. Fusion 32, 694 (1992)], are consistent with those found in conventional aspect ratio tokamaks. In particular the highest β achieved (∼40%) is consistent with an ideal magneto-hydro-dynamic (MHD) Troyon type limit, the upper limit on density is well described by the Greenwald density (πa2n¯e/Ip∼1) and the normalized current (Ip/aBt) is limited such that q95(approximately-greater-than)2. Stability calculations indicate scope for increasing both normalized β and normalized current beyond the values so far achieved, although wall stabilization is generally needed for low-n modes. In double null configurations current terminating disruptions occur at each of the operational boundaries, though the current quench tends to be slow at the density limit and disruptions at high β may be due to the low q. In early limiter START discharges, before the divertor coils were installed, disruptions rarely occurred. Instead internal reconnection events which have all the characteristics of a disruption except the current quench occurred. These various disruptive behaviors are explained in terms of a model in which helicity is conserved during the disruption. Due to the low toroidal field beam ions in START, and α particles in a ST power plant, are super-Alfvénic. This gives the possibility for toroidal Alfvén eigenmodes (TAEs) to occur and such modes are frequently observed in START neutral beam injection (NBI) discharges, but seem to be benign. The features of these observed TAEs are shown to be in agreement with MHD calculations.
    Type of Medium: Electronic Resource
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  • 3
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Experiments designed for generating internal transport barriers in the plasmas of the Joint European Torus [JET, P. H. Rebut et al., Proceedings of the 10th International Conference, Plasma Physics and Controlled Nuclear Fusion, London (International Atomic Energy Agency, Vienna, 1985), Vol. I, p. 11] reveal cascades of Alfvén perturbations with predominantly upward frequency sweeping. These experiments are characterized by a hollow plasma current profile, created by lower hybrid heating and current drive before the main heating power phase. The cascades are driven by ions accelerated with ion cyclotron resonance heating (ICRH). Each cascade consists of many modes with different toroidal mode numbers and different frequencies. The toroidal mode numbers vary from n=1 to n=6. The frequency starts from 20 to 90 kHz and increases up to the frequency range of toroidal Alfvén eigenmodes. In the framework of ideal magnetohydrodynamics (MHD) model, a close correlation is found between the time evolution of the Alfvén cascades and the evolution of the Alfvén continuum frequency at the point of zero magnetic shear. This correlation facilitates the study of the time evolution of both the Alfvén continuum and the safety factor, q(r), at the point of zero magnetic shear and makes it possible to use Alfvén spectroscopy for studying q(r). Modeling shows that the Alfvén cascade occurs when the Alfvén continuum frequency has a maximum at the zero shear point. Interpretation of the Alfvén cascades is given in terms of a novel-type of energetic particle mode localized at the point where q(r) has a minimum. This interpretation explains the key experimental observations: simultaneous generation of many modes, preferred direction of frequency sweeping, and the absence of strong continuum damping. © 2002 American Institute of Physics.
    Type of Medium: Electronic Resource
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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.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 31 (1988), S. 577-590 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The separation of the cylindrical tearing mode stability problem into a resistive resonant layer calculation and an external marginal ideal magnetohydrodynamic (MHD) calculation (Δ' calculation) is generalized to axisymmetric toroidal geometry. The general structure of this separation is analyzed and the marginal ideal MHD information (the toroidal generalization of Δ') required to discuss stability is isolated. This can then, in principle, be combined with relevant resonant layer calculations to determine tearing mode growth rates in realistic situations. Two examples are given: the first is an analytic treatment of toroidally coupled (m=1, n=1) and (m=2, n=1) tearing modes in a large aspect ratio torus; the second, a numerical treatment of the toroidal coupling of three tearing modes through finite pressure effects in a large aspect ratio torus. In addition, the use of a coupling integral approach for determining the stability of coupled tearing modes is discussed. Finally, the possibility of using initial value resistive MHD codes in realistic toroidal geometry to determine the necessary information from the ideal MHD marginal solution is discussed.
    Type of Medium: Electronic Resource
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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.
    Type of Medium: Electronic Resource
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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.
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 31 (1988), S. 1202-1216 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The nonlinear evolution of the internal kink mode is studied in toroidal geometry for noncircular cross-section tokamak plasmas. The study is focused on very low-shear and hollow q profiles, with q(ρ)≥1 for which the internal kink is unstable in the latter case, even at β=0. The nonlinear evolution is dominated by ideal magnetohydrodynamics (MHD), and the instability saturates, giving a quasihelical shift to the magnetic axis. The nonlinear saturation is caused by increased field line bending. Time scales of 103 τHp and axis shifts of 20% are reached when changes in q on the order of 3×10−3 from the marginal profile are produced.
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 28 (1985), S. 1116-1125 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A linear and nonlinear kinetic theory of resistive ballooning modes that includes diamagnetic drifts and finite Larmor radius effects is presented. The linear stability of resistive ballooning modes is examined analytically and numerically. A renormalized resistive ballooning equation is derived, and the saturation level of the instabilities is analytically calculated. Finally, a calculation of the electron thermal conductivity for the large ω@B| regime is presented.
    Type of Medium: Electronic Resource
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  • 10
    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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