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C. G. Gimblett - One of the best experts on this subject based on the ideXlab platform.
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Magnetohydrodynamic Stability at a Separatrix: Part II
arXiv: Plasma Physics, 2009Co-Authors: A. J. Webster, C. G. GimblettAbstract:In the first part to this paper[1] it was shown how a simple Magnetohydrodynamic model could be used to determine the Stability of a Tokamak plasma’s edge to a Peeling (External Kink) mode. Stability was found to be determined by the value of � ′ , a normalised measure of the discontinuity in the radial derivative of the radial perturbation to the magnetic field at the plasma-vacuum interface. Here we calculate � ′ , but in a way that avoids the numerical divergences that can arise near a separatrice’s X-point. This is accomplished by showing how the method of conformal transformations may be generalised to allow their application to systems with a non-zero boundary condition, and using the technique to obtain analytic expressions for both the vacuum energy and � ′ . A conformal transformation is used again to obtain an equilibrium vacuum field surrounding a plasma with a separatrix. This allows the subsequent evaluation of the vacuum energy and � ′ . For a plasma-vacuum boundary that approximates a separatrix, the growth rate normalised by the Aflven frequency A is then found to have ln(/A) = − 1 ln(q ′ /q). Consequences for Peeling mode Stability are discussed.
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Magnetohydrodynamic Stability of a toroidal plasma's separatrix.
Physical review letters, 2009Co-Authors: A. J. Webster, C. G. GimblettAbstract:Large tokamaks capable of fusion power production such as ITER, should avoid large edge localized modes (ELMs), thought to be triggered by an ideal Magnetohydrodynamic inStability due to current at the plasma's separatrix boundary. Unlike analytical work in a cylindrical approximation, numerical work finds the modes are stable. The plasma's separatrix might stabilize modes, but makes analytical and numerical work difficult. We generalize a cylindrical model to toroidal separatrix geometry, finding one parameter Delta' determines Stability. The conformal transformation method is generalized to allow nonzero derivatives of a function on a boundary, and calculation of the equilibrium vacuum field allows Delta' to be found analytically. As a boundary more closely approximates a separatrix, we find the energy principle indicates inStability, but the growth rate asymptotes to zero.
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An analytic study of the Magnetohydrodynamic Stability of inverse shear profiles
Physics of Plasmas, 1996Co-Authors: C. G. Gimblett, R J Hastie, T. C. HenderAbstract: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.
R L Miller - One of the best experts on this subject based on the ideXlab platform.
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ideal Magnetohydrodynamic Stability of the tokamak high confinement mode edge region
Physics of Plasmas, 1999Co-Authors: H. R. Wilson, S J Fielding, A. R. Field, John R. Ferron, J. W. Connor, R L Miller, A D TurnbullAbstract:The ideal Magnetohydrodynamic (MHD) Stability of the tokamak edge is analyzed, with particular emphasis on radially localized instabilities; it is proposed that these are responsible for edge pressure gradient limits and edge localized modes (ELMS). Data and Stability calculations from DIII-D [to appear in Proceedings of the 16th International Conference on Fusion Energy, Yokohama (International Atomic Energy Agency, Vienna, 1998), Paper No. IAEA-F1-CN-69/EX8/1] tokamak equilibria indicate that two types of inStability are important: the ballooning mode (driven by pressure gradient) and the peeling mode (driven by current density). The characteristics of these instabilities, and their coupling, are described based on a circular cross-section, large aspect ratio model of the tokamak equilibrium. In addition, preliminary results are presented from an edge MHD Stability code which is being developed to analyze general geometry tokamak equilibria; an interpretation of the density threshold to access the high-...
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Magnetohydrodynamic Stability of tokamak edge plasmas
Physics of Plasmas, 1998Co-Authors: J. W. Connor, H. R. Wilson, R J Hastie, R L MillerAbstract:A new formalism for analyzing the Magnetohydrodynamic Stability of a limiter tokamak edge plasma is developed. Two radially localized, high toroidal mode number n instabilities are studied in detail: a peeling mode and an edge ballooning mode. The peeling mode, driven by edge current density and stabilized by edge pressure gradient, has features which are consistent with several properties of tokamak behavior in the high confinement “H”-mode of operation, and edge localized modes (or ELMs) in particular. The edge ballooning mode, driven by the pressure gradient, is identified; this penetrates ∼n1/3 rational surfaces into the plasma (rather than ∼n1/2, expected from conventional ballooning mode theory). Furthermore, there exists a coupling between these two modes and this coupling provides a picture of the ELM cycle.
S. N. Bhattacharyya - One of the best experts on this subject based on the ideXlab platform.
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Effect of the flow continuum on Magnetohydrodynamic Stability
Physics of Plasmas, 1997Co-Authors: S. N. Bhattacharyya, Amitava BhattacharjeeAbstract:The flow resonance is concealed when the linearized equation of motion in Magnetohydrodynamics is written in terms of the Lagrangian displacement vector. Its contribution to the dispersion equation of a rotating cylindrical plasma column, surrounded by a thin resistive wall, is clarified by a simple model calculation, relevant for axisymmetric modes, in the Eulerian representation. Under certain assumptions the flow resonance is shown to damp the resistive wall mode, with the damping proportional to the square of the gradient of vorticity at the resonant surface. It is shown that a flow resonance can stabilize a slightly elliptical plasma, surrounded by a thin resistive wall, against axisymmetric modes.
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Ideal Magnetohydrodynamic Stability in the presence of a resistive wall
Physics of Plasmas, 1995Co-Authors: S. N. BhattacharyyaAbstract:Using the Galerkin method, the equations governing the linear Stability of an ideal plasma in the presence of a thin resistive wall is reduced to a standard matrix eigenvalue problem. This can be used to compute the entire spectrum of normal modes. Stability is shown to be governed by an energy principle. As an application, the Galerkin formulation is used to study the Stability of an elliptical cross‐section straight tokamak, surrounded by a thin resistive wall, to rigid vertical displacements. The Galerkin formulation is also generalized to include equilibrium mass flow of the plasma and allow for arbitrary thickness of the resistive wall. Stability is again shown to be governed by an energy principle.
W.a. Cooper - One of the best experts on this subject based on the ideXlab platform.
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Fluid Magnetohydrodynamic Stability in a Heliotron with anisotropic fast particle species
Plasma Physics and Controlled Fusion, 2007Co-Authors: W.a. Cooper, Jonathan Graves, Martin Jucker, K.y. Watanabe, Y. Narushima, T. YamaguchiAbstract:The local and global fluid Magnetohydrodynamic Stability properties of anisotropic pressure plasmas are investigated with the Kruskal-Oberman and rigid hot particle Johnson et al energy principles. A Heliotron configuration that models the Large Helical Device with finite pressure anisotropy driven by neutral beams at beta = 4% shows that the Kruskal-Oberman model predicts Stability when beta(h)/beta similar to 1/3 provided that the hot particle pressure profile is sufficiently peaked. The rigid hot particle model, on the other hand, is stable to local and global modes for broad and peaked profiles. For central deposition, the marginal pressure profiles are somewhat broader for p(parallel to) > p(perpendicular to) than for p(perpendicular to)> p(parallel to). Global n = 3 modes produce stricter Stability criteria than n = 1,2 and 4 modes. Off-axis hot particle deposition yields more unstable conditions with respect to global and local modes than on-axis deposition. The mode structures localize near the plasma periphery according to the Kruskal-Oberman model and near the plasma core according to the Johnson et al model. This observation could help resolve the appropriate model to apply to the experimental conditions in Heliotron devices.
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Ideal Magnetohydrodynamic Stability of the NCSX
Fusion Science and Technology, 2007Co-Authors: M. Isaev, W.a. Cooper, M. H. Redi, M. I. Mikhailov, Raul Sanchez, A. A. Subbotin, S.p. Hirshman, D. A. MonticelloAbstract:The ideal Magnetohydrodynamic (MHD) Stability of the National Compact Stellarator Experiment (NCSX) is extensively analyzed using the most advanced three-dimensional MHD codes. It is shown that the NCSX is stable to finite-n MHD modes, including the vertical mode, external kink modes and ballooning modes. However, high-n external kink modes that peak near the plasma edge are found to be weakly unstable. A global calculation shows that finite-n ballooning modes are significantly more stable than the local infinite-n modes.
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Magnetohydrodynamic Stability of free-boundary quasi-axisymmetric stellarator equilibria with finite bootstrap current
Fusion Science and Technology, 2004Co-Authors: W.a. Cooper, K.y. Watanabe, Y. Narushima, S. Ferrando I Margalet, S.j. Allfrey, J. Kisslinger, H. Wobig, S. Okamura, Chihiro Suzuki, Kozo YamazakiAbstract:The impact of the bootstrap current is investigated on the equilibrium properties of a two-period quasi-axisymmetric stellarator reactor with free boundary and on the corresponding ideal Magnetohydrodynamic Stability properties. Although the magnetic field strength B spectrum is dominated by a m/n = 1/0 component, the discrete filamentary coils trigger some small-amplitude symmetry-breaking components that can disturb,the quasi-symmetry of B. Finite beta causes the plasma column to shift outward in the absence of bootstrap current. With a self-consistent bootstrap current in the 1/v regime, the plasma becomes more elongated and more distorted in the horizontally elongated up-down symmetric cross section. At beta similar or equal to 3.25%, the plasma can be restored to its near-vacuum shape with the application of a vertical field with coil currents 20% of those of the modular coils, but at the expense of a significant mirror component in the B-field spectrum. The bootstrap current causes the rotational transform iota profile to increase above the critical resonant value (iota(c) = 1/2 for beta greater than or equal to 1.1%) and combines with the Pfirsch-Schluter current to destabilize a m/n = 2/1 external kink mode for beta greater than or equal to 1.8%.
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Robustness and flexibility in compact quasiaxial stellarators: Global ideal Magnetohydrodynamic Stability and energetic particle transport
Physics of Plasmas, 2000Co-Authors: M. H. Redi, W.a. Cooper, M. C. Zarnstorff, Ahmed Diallo, C. Nührenberg, Neil Pomphrey, A. H. Reiman, Ncsx-teamAbstract:Concerns about the flexibility and robustness of a compact quasiaxial stellarator design are addressed by studying the effects of varied pressure and rotational transform profiles on expected performance. For thirty, related, fully three-dimensional configurations the global, ideal Magnetohydrodynamic (MHD) Stability and energetic particle transport are evaluated. It is found that tokamak intuition is relevant to understanding the Magnetohydrodynamic Stability, with pressure gradient driving terms and shear stabilization controlling both the periodicity preserving, N=0, and the nonperiodicity preserving, N=1, unstable kink modes. Global kink modes are generated by steeply peaked pressure profiles near the half radius and edge localized kink modes are found for plasmas with steep pressure profiles at the edge as well as with edge rotational transform above 0.5. Energetic particle transport is not strongly dependent on these changes of pressure and current (or rotational transform) profiles, although a weak inverse dependence on pressure peaking through the corresponding Shafranov shift is found. While good transport and MHD Stability are not anticorrelated in these equilibria, Stability only results from a delicate balance of the pressure and shear stabilization forces. A range of interesting MHD behaviors is found for this large set of equilibria, exhibiting similar particle transport properties. (C) 2000 American Institute of Physics. [S1070-664X(00)03606-5].
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Local ideal Magnetohydrodynamic Stability of a quasihelically symmetric stellarator
Physics of Plasmas, 1996Co-Authors: Joseph Talmadge, W.a. CooperAbstract:The ideal Magnetohydrodynamic Stability with respect to localized ballooning modes and the Mercier criterion of a quasihelically symmetric stellarator configuration is investigated. Configurations with an enhanced magnetic mirror and a deeper magnetic well that can be achieved by energizing a set of auxiliary coils have also been analyzed. In all cases, the Mercier criterion imposes a slightly stricter β limit than the ballooning modes. Using relatively broad pressure profiles, the Mercier criterion yields β=0.4% for the standard configuration, β=0.3% for the high mirror configuration and β=1.3% for the deep well configuration. The comparable ballooning limits are β=0.7%, β=0.6%, and β=1.66% for the standard, high mirror, and deep well configurations, respectively. With a more peaked pressure profile, ballooning instabilities near the center of the plasma and Mercier modes near the edge of the plasma limit the performance of the standard configuration at β≂0.8%.
J. W. Connor - One of the best experts on this subject based on the ideXlab platform.
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ideal Magnetohydrodynamic Stability of the tokamak high confinement mode edge region
Physics of Plasmas, 1999Co-Authors: H. R. Wilson, S J Fielding, A. R. Field, John R. Ferron, J. W. Connor, R L Miller, A D TurnbullAbstract:The ideal Magnetohydrodynamic (MHD) Stability of the tokamak edge is analyzed, with particular emphasis on radially localized instabilities; it is proposed that these are responsible for edge pressure gradient limits and edge localized modes (ELMS). Data and Stability calculations from DIII-D [to appear in Proceedings of the 16th International Conference on Fusion Energy, Yokohama (International Atomic Energy Agency, Vienna, 1998), Paper No. IAEA-F1-CN-69/EX8/1] tokamak equilibria indicate that two types of inStability are important: the ballooning mode (driven by pressure gradient) and the peeling mode (driven by current density). The characteristics of these instabilities, and their coupling, are described based on a circular cross-section, large aspect ratio model of the tokamak equilibrium. In addition, preliminary results are presented from an edge MHD Stability code which is being developed to analyze general geometry tokamak equilibria; an interpretation of the density threshold to access the high-...
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Magnetohydrodynamic Stability of tokamak edge plasmas
Physics of Plasmas, 1998Co-Authors: J. W. Connor, H. R. Wilson, R J Hastie, R L MillerAbstract:A new formalism for analyzing the Magnetohydrodynamic Stability of a limiter tokamak edge plasma is developed. Two radially localized, high toroidal mode number n instabilities are studied in detail: a peeling mode and an edge ballooning mode. The peeling mode, driven by edge current density and stabilized by edge pressure gradient, has features which are consistent with several properties of tokamak behavior in the high confinement “H”-mode of operation, and edge localized modes (or ELMs) in particular. The edge ballooning mode, driven by the pressure gradient, is identified; this penetrates ∼n1/3 rational surfaces into the plasma (rather than ∼n1/2, expected from conventional ballooning mode theory). Furthermore, there exists a coupling between these two modes and this coupling provides a picture of the ELM cycle.