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A method has been proposed to study heat transport in magnetically confinement plasmas, based on the transfer entropy (TE). In this work, we study this method by introducing perturbations in simulations made using a resistive Magneto-HydroDynamic model. The evolution of radial heat transport is monitored using the TE, and these results are used to compute an effective heat diffusivity. This effective diffusivity is then compared to estimates from other methods. The analysis is applied to several numerical simulations and in various radial ranges. It is shown that the transfer entropy is a suitable technique to analyze heat transport and evaluate an effective diffusivity in fusion plasmas. [ABSTRACT FROM AUTHOR]

This work focuses on the relationship between L-H (or L-I) transitions and MHD activity in the low magnetic shear TJ-II stellarator. It is shown that the presence of a low order rational surface in the plasma edge (gradient) region lowers the threshold density for H-mode access. MHD activity is systematically suppressed near the confinement transition. We apply a causality detection technique (based on the Transfer Entropy) to study the relation between magnetic oscillations and locally measured plasma rotation velocity (related to Zonal Flows). For this purpose, we study a large number of discharges in two magnetic configurations, corresponding to "fast" and "slow" transitions. With the "slow" transitions, the developing Zonal Flow prior to the transition is associated with the gradual reduction of magnetic oscillations. The transition itself is marked by a strong spike of "information transfer" from magnetic to velocity oscillations, suggesting that the magnetic drive may play a role in setting up the final sheared flow responsible for the H-mode transport barrier. Similar observations were made for the "fast" transitions. Thus, it is shown that magnetic oscillations associated with rational surfaces play an important and active role in confinement transitions, so that electromagnetic effects should be included in any complete transition model. [ABSTRACT FROM AUTHOR]

A partial collapse observed in magnetic axis swing experiments in the Large Helical Device (LHD) is analyzed with a nonlinear magnetohydrodynamic (MHD) simulation. Real time control of the background field in the operation is incorporated by means of a multi-scale numerical scheme in the simulation. The simulation result indicates that the changing background field accelerates the growth of an infernal-like mode and causes the partial collapse. [ABSTRACT FROM AUTHOR]

Linear and nonlinear magnetohydrodynamic (MHD) calculations have been performed to study the stability of tokamak discharges with reversed or negative central magnetic shear using the finite aspect ratio (FAR) suite of MHD codes [Charlton et al., J. Comput. Phys. 86, 270 (1990)]. The linear calculations confirm anew that radially localized resistive interchange modes can be unstable in the reversed or negative central magnetic shear region. The calculations further show that these resistive interchange modes are more unstable for toroidal mode numbers n higher than n=1. The nonlinear calculations do however demonstrate that toroidal mode number n=1, enhanced by the nonlinear couplings of the linearly more unstable higher n toroidal harmonics, dominates the nonlinearly saturated steady state. While the resistive interchange modes may account for the precursors detected experimentally, the saturated levels of magnetic fluctuations obtained in the nonlinear calculations do not appear large enough to cause the experimentally observed global collapse of such discharges. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

A set of reduced magnetohydrodynamic (MHD) equations to study linear stability in general toroidal configurations is presented. The equations are derived by applying the averaging method to an equilibrium represented in a straight-field-line coordinate system. They permit the calculation of the low-n stability of fully three-dimensional (3-D) equilibria for stellerator configurations with either a planar or a helical magnetic axis. Numerical solutions are shown to agree well with marginal stability boundaries given by the classical stellerator expansion when average stellarator equilibria with a planar magnetic axis are used as input. [ABSTRACT FROM AUTHOR]

Magnetohydrodynamic (MHD) stability and nonlinear evolution of the m=1 mode are studied in toroidal geometry for safety factor profiles having an inflection point at the q=1 surface. For ideally stable cases, linear growth rates of the resistive m=1 mode are decreased by any combination of the following variations: decreasing the aspect ratio, decreasing shear at the q=1 surface, increasing S, decreasing q0, and/or decreasing beta. Transitions from resistive kink to tearing mode to complete stability are accompanied by increasing localization as the mode is stabilized. The ideal stability of the m=1 mode for low-shear inflection-point profiles is broken at very low, but finite, beta by the appearance of a radially localized ideal interchange mode. As beta is increased, the m=1 mode becomes a global ideal internal kink. These ideal modes are stabilized by decreasing the aspect ratio and, to a lesser extent, by increasing shear at the q=1 surface. Nonlinear evolution of the m=1 mode is found to follow the Kadomtsev complete reconnection process or to be stable, depending on the linear stability of the mode. However, all nonlinear calculations were carried out at Lundquist number S=105 and hence contain substantial resistive kink contributions. Consequently, nonlinear evolution in the m=1 tearing mode regime is not examined. Even for cases in which ideal effects dominate the linear mode, Kadomtsev reconnection is observed. The nonlinear stability of linearly stable modes was also uniformly observed, even for several cases having large initial perturbations. Hence complete linear stabilization resulting from a combination of toroidal effects and low shear at the q=1 surface can suppress sawteeth, as described by the Kadomtsev reconnection process, in tokamaks having safety factor profiles with q0<1 at the magnetic axis; but, for the S values considered, nonlinear calculations of unstable modes result in complete Kadomtsev reconnection. [ABSTRACT FROM AUTHOR]

The linear stability and nonlinear evolution of the resistive m=1 mode in tokamaks is studied using a full set of resistive magnetohydrodynamic (MHD) equations in toroidal geometry. The modification of the linear and nonlinear properties of the mode by a combination of strong toroidal effects and low resistivity is the focus of this work. Linearly there is a transition from resistive kink to resistive tearing behavior as the aspect ratio and resistivity are reduced, and there is a corresponding modification of the nonlinear behavior, including a slowing of the island growth and development of a Rutherford regime, as the tearing regime is approached. In order to study the sensitivity of the stability and evolution to assumptions concerning the equation of state, two sets of full nonlinear resistive MHD equations (a pressure convection set and an incompressible set) are used. Both sets give more stable nonlinear behavior as the aspect ratio is reduced. The pressure convection set shows a transition from a Kadomtsev reconnection at large aspect ratio to a saturation at small aspect ratio. The incompressible set yields Kadomtsev reconnection for all aspect ratios, but with a significant lengthening of the reconnection time and development of a Rutherford regime at an aspect ratio approaching the transition from a resistive kink mode to a tearing mode. The pressure convection set gives an incomplete reconnection similar to that sometimes seen experimentally. The pressure convection set is, however, strictly justified only at high beta. [ABSTRACT FROM AUTHOR]

The multiple helicity nonlinear interaction of resistive tearing modes is compared for the tokamak and reversed field pinch configurations using the magnetohydrodynamic equations. Unlike the case of the tokamak disruption, for which this interaction is destabilizing when islands overlap, the nonlinear coupling of the dominant helicities is shown to be a stabilizing influence in the reversed field pinch. The behavior of the coupled instabilities in the two configurations can be understood as a consequence of the stability properties of the nonlinearly driven modes. In the case of the tokamak disruption, quasilinear effects linearly destabilize the dominant driven mode, which then feeds energy to the driving mode. For the reversed field pinch the driven modes remain stable, acting as a brake on the growth of the dominant instabilities. Furthermore, for the reversed field pinch configuration, numerical results indicate that nonlinear coupling of different helicities results in noticeably more rapid saturation of the dominant instabilities than was observed in single helicity studies. [ABSTRACT FROM AUTHOR]

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[sub *]. regime is presented. [ABSTRACT FROM AUTHOR]

Access to the magnetohydrodynamic (MHD) second stability regime has been achieved in the Advanced Toroidal Facility (ATF) torsatron [Fusion Technol. 10, 179 (1986) ]. Operation with a field error that reduced the plasma radius and edge rotational transform resulted in peaked pressure profiles and increased Shafranov shift that lowered the theoretical transition to ideal MHD second stability to β[sub o] ≈ 1.3%; the experimental β values (β[sub o] ≤ 3%) are well above this transition. The measured magnetic fluctuations decrease with increasing β, and the pressure profile broadens, consistent with the theoretical expectations for self-stabilization of resistive interchange modes. Initial results from experiments with the field error removed show that the pressure profile is now broader. These later discharges are characterized by a transition to improved ( × 2-3) confinement and a marked change in the edge density fluctuation spectrum, but the causal relationship of these changes is not yet clear. [ABSTRACT FROM AUTHOR]

Ideal linear magnetohydrodynamic (MHD) stability calculations demonstrate reasonable adherence at low aspect ratio (AR<2) to the Troyon scaling relationship for maximum beta, resulting in a broad regime of stable high-beta equilibria. For a specific low-aspect-ratio case (AR=5/3), a wide range of stable equilibria having volume-averaged beta, <β>, in excess of 20% is found. A systematic approach for estimating the maximum beta is used. First, the aspect ratio is reduced, for fixed shape and profiles, starting from the Troyon optimized case at AR=2.5; the plasma cross-section shape is then varied for fixed profiles at fixed AR=5/3; and finally, pressure and safety factor profiles are varied for fixed shape and aspect ratio. The calculations are carried out for low n (n=1–3), usually with a conducting wall at a radius of 1.5 times the plasma minor radius, for n=∞ ballooning modes, and for Mercier stability. Several additional ‘‘spot checks’’ on the effects of moving the conducting wall to infinity and of the stability of n=0 and n=4 and 5 modes indicate good stability properties for these, also. The calculations presented here demonstrate a straightforward extrapolation of the Troyon scaling formula to low aspect ratio, in spite of qualitative differences previously noted in low-aspect-ratio equilibria. [ABSTRACT FROM AUTHOR]

The stability of the ideal and resistive m=1 internal modes is investigated for tokamak equilibria having a variety of different q(r) profiles, including nonmonotonic q(r) with multiple q=1 surfaces. Detailed comparisons between analytic theory and numerical results from a linear toroidal magnetohydrodynamic code are presented. Particular attention is paid to the study of equilibria that are near marginal stability. [ABSTRACT FROM AUTHOR]