F. Troyon

The KINX ideal MHD stability code for axisymmetric plasmas with separatrix

The paper presents the KINX code for computing linear ideal MHD growth rates and eigenvectors of axisymmetric plasmas surrounded by a vacuum layer and a conducting wall. Plasma equilibrium magnetic surfaces are assumed to be nested either in the whole plasma domain (separatrix at the plasma boundary is possible) or in the domains separated by an internal separatrix (doublet and divertor configurations). The computational domain is decomposed into subdomains with nested flux surfaces. In each subdomain finite hybrid elements are used on an equilibrium grid adapted to magnetic surfaces. Numerical destabilization is eliminated; this results in better convergence properties and makes possible efficient stability index calculation (delta W-code). An inverse vector iteration method and a vectorizable matrix solver are applied to the matrix eigenvalue problem. The stability studies of external kink modes for doublet and single null configurations are given as application examples of the KINX code. Another version of the code, KINX-W, computing resistive wall n = 0 mode growth rates, is also presented for single null, doublet and divertor plasma configurations.

Hera and other extensions of Erato

Abstract The MHD stability code ERATO has been modified in order to study helically symmetric equilibria. The resulting new code is called HERA. A new formulation to calculate the vacuum contribution has been added to the spectral codes ERATO and HERA. The finite hybrid element approach is equivalent to that in the plasma region. The stability problem including a conducting wall is now done in one step. The fast angular variation of high n modes has been eliminated by a change of variables. With this new quasi-mode representation it is possible to study unstable modes with nq values up to 1000 in the case of high β, high shear equilibria. It applies equally well to internal and external modes.

Numerical Study of the Ideal-MHD Stability Limits in Oblate Spheromaks

The ideal-MHD stability properties of a class of hollow oblate spheromaks are studied numerically with a spectral code. An internal kink instability is found whenever the safety factor on axis, qo, rises above one. Its growth rate is only a weak function of the pressure. By shaping the current profile such that, simultaneously, q0 = 1 and the Mercier criterion is satisfied, full stability against internal perturbations is obtained up to a maximum value of β, this value increasing with the aspect ratio. For a configuration without a central hole, the maximum β is 1.5% and for an aspect ratio of 2.34, which is the largest that has been studied, it reaches 40%. Without a conducting shell, all equilibria are unstable to free-boundary modes, the fastest-growing mode being that associated with a global tilting motion. These modes, in contrast to the internal modes, are stabilized as the aspect ratio decreases. In the limiting case of no hole, the force-free equilibrium is only unstable with respect to n = 1 displacement which can be stabilized by a conducting shell located at a distance from the plasma boundary of 30% of the plasma minor radius.

Recent results from the TCV Tokamak

During the first two years of operation, the TCV tokamak has produced a large variety of plasma shapes and magnetic configurations, with 1.0≤Btor≤1.46T,Ip≤800kA,k≤2.05, −0.7≤δ≤1. A new shape control algorithm, based on a finite element reconstruction of the plasma current in real time, has been implemented. Vertical growth rates up to 1000s−1 have been stabilized using the external coil system. Ohmic H-modes with Troyon factors (βtoraB/Ip) up to two and densities up to 2.25×1020m−3, corresponding to the Greenwald limit, have been obtained in diverted discharges. Limiter H-modes with line averaged electron densities up to 1.7×1020m−3 have been obtained in elongated D-shaped plasmas with 360 kA≤IP≤600 kA.

β limits in H -mode-like discharges

Reference CRPP-ARTICLE-1986-008doi:10.1016/0021-9991(86)90072-0View record in Web of Science Record created on 2008-04-16, modified on 2017-05-12

Low-n ideal MHD stability of tokamaks: Current and beta limits

The results of extensive investigations of the low-n ideal magnetohydrodynamic stability of the TCV, NET and DIII-D tokamaks are compared in order to identify the general qualitative effects of cross-sectional shaping on the low-n stability of elongated tokamaks. The results consistently indicate a breakdown of the simple stability picture for circular and moderately elongated cross-sections when the cross-section deviates strongly from circular. Simplified extrapolations of the standard stability picture to high elongation and triangularity and to low aspect ratio are unreliable; at high elongation, the scaling of both the current limit and the beta limit is strongly dependent on the cross-section shape. Several implications for next generation tokamaks can be drawn from the conclusions, and these are discussed briefly.

Ideal magnetohydrodynamic stability of high-beta, high-current tokamak equilibria

The ideal-MHD stability of a class of tokamak equilibria is analysed numerically by using a spectral code. This class is characterized by flat current distribution in the plasma core and vanishing current at the edge. Both circular and D-shaped plasmas are considered for varying current width, safety factor on axis, βp and aspect ratio. The introduction of a pressureless and current-free plasma layer at the edge stabilizes the residual kink instabilities caused by the non-vanishing current gradient at the surface. The optimum value of β is found to occur at low values of βp (0.25 to 0.4 times the aspect ratio) and reaches 6% for JET.

Current and Beta-Limitations for the Tcv Tokamak

Initial ideal MHD stability results for the Tokamak Configuration Variable (TCV) tokamak with variable elongation are presented. Two configurations have been studied: a racetrack shape and a D-shape at a fixed elongation of 2.5. Low beta studies indicate the existence of stable racetrack equilibria at currents up to an edge safety factor value of qs = 2, but the window of operation is limited in qo to narrow bands above each integer value. For the D-shape, qs = 3 gives the current limit at low beta, but the operating range in q0 is much wider than that for the racetrack. Beta optimization studies show that the maximum beta set by the n= 1 freeboundary stability limit decreases as the current increases, except for the lowest currents in the range studied. Although further optimization cannot be ruled out, considerable enhancement of the beta over that for an equivalent circular cross-section of the same major radius and aspect ratio can be obtained by elongation of the plasma cross-section.

Effect of plasma shape on confinement and MHD behaviour in TCV

Note: 38th Annual Meeting, APS Division of Plasma Physics, Denver, CO, USA, November 1996, Bull. Amer. Phys. Soc. 41(7), 1513 (1996) Reference CRPP-CONF-1996-037 Record created on 2008-05-13, modified on 2016-08-08

Influence of Triangularity and Plasma Profiles on Ideal Mhd Beta-Limits

The paper presents ideal MHD stability calculations to show the effect of triangularity δ on the beta limit for plasmas of the NET/ITER type with ellipticity κ = 2 and aspect ratio A = 3.7. Two different types of beta optimizations have been made to clarify the influence of the equilibrium profiles. In the first set of optimizations, current profiles that are flat in the central region are prescribed and the pressure profile is optimized. The resulting pressure profiles are broad, and triangularity has only a weak influence on the beta limit. In the second set, more peaked pressure distributions are prescribed and the current profile is optimized. For peaked pressure profiles, triangularity has a clear, positive effect on the beta limit, and for δ ≥ 0.4 the peaked pressure profiles give about the same beta limit as the broad profiles. For cross-sections of small triangularity, peaking of the pressure profile is clearly unfavourable, and reasonably high beta values can be reached only if the current profile has strong gradients in the central region or if the central safety factor is significantly above unity. This is required for stability of Mercier and ballooning modes. The beta limit is found to be rather weakly dependent on the plasma current for safety factors at the plasma edge in the range of 2.2–5.