K. E. Weimer

APPLICATION OF THE ENERGY PRINCIPLE TO ASTRON-TYPE AND OTHER AXISYMMETRIC DEVICES.

The stability of Astron-type devices is investigated on the basis of a model in which the electrons in the E-layer are assumed rigid.

Stability Limitations for Stellarators with Sharp Surfaces

Application of the magnetohydrodynamic energy principle to a stellarator equilibrium where the plasma pressure is constant inside a bounding magnetic surface shows that the configuration is unstable to a nearly rigid shift of the plasma column.

Use of the stellarator expansion to investigate plasma equilibrium in stellarators

A numerical code utilizing a large‐aspect‐ratio, small ‐helical‐distortion expansion is developed and used to investigate the effect of plasma currents on stellarator equilibrium. Application is made to several existing and proposed stellarators. The modification of the equilibrium properties with pressure is strongly dependent on the vacuum‐field configuration. The modular stellarator model which is investigated gives somewhat discouraging results because a large rotational transform, and hence large coil deformation, is needed to achieve high‐beta equilibria.

Toroidal effects on magnetohydrodynamic modes in tokamaks

In order to investigate the effect of toroidal curvature on magnetohydrodynamic modes in tokamak configurations, stability criteria are derived by means of an expansion in the inverse aspect ratio. For a low‐pressure system, βθ ∼ 1, with a nearly constant safety factor, q = qa(0) + …, the well known stability criterion for kink modes, relating qa to the ratio a / b of the plasma radius to that of a conducting wall, is determined in second order. Here, it is shown that toroidal effects modify this criterion favorably in fourth order when the vacuum region does not extend too far. Typically, it is found that improvement is achieved when b / a is less than 1.25 to 1.5. Interchange and ballooning effects are incorporated in the stability criteria.

Inertial and Resistive Effects in Toroidal Systems

Nearly steady‐state toroidal configurations are examined analytically and numerically in a resistive, low‐pressure fluid model. An optimal ordering of the physical parameters is introduced in such a way that the problem separates into two distinct time scales, diffusive and acoustic. The dispersion relation, for small oscillations on the acoustic time scale, reduces to a fifth‐order algebraic equation coupling rotation, acoustic oscillations, and geodesic modes. In the supersonic regime, two oscillatory, low‐frequency modes are unstable, and the rotational and geodesic modes are damped. In the subsonic regime, the rotational mode is always growing, the geodesic modes are damped, and the acoustic modes may or may not be unstable, depending on the parameters. Good agreement is found between the analytic predictions and the results of numerical simulation.

Optimization techniques for modular stellarator coils

Introduction of a non-sinusoidal deformation can enhance the efficacy of modular coils for generating magnetic fields with a built-in rotational transform. Techniques are developed that provide an understanding of how specific deformations affect the harmonic content of the magnetic field and thus the properties of the vacuum configuration. A procedure is provided for optimizing a modular-coil configuration with respect to the equivalent current, which provides a useful measure of the product of the rotational transform and the cross-sectional area. Application is made to systems with l = 2. It is shown that the configuration properties can be enhanced by introducing a modulation of the curve defining the centres of the coils or by having an additional elliptical shaping of the coils.

Equilibrium and stability for systems with small curvature

Expansion techniques are used to obtain analytic expressions for the stability criterion of toroidal hydromagnetic equilibria with l = 2 or l = 3 multipolar fields. The first case shows that care must be taken in using stability criteria in which the coupling of the Fourier modes of the perturbation is not correctly treated. The latter demonstrates the restrictions which the equilibrium criteria can impose on the system if the rotational transform vanishes somewhere in the system.

Localized magnetohydrodynamic instabilities in Tokamaks with non-circular cross sections

Evaluation of the Mercier stability criterion indicates that localized modes should impose few constraints on the possibility of using Tokamaks with non-circular cross sections. The importance of the details of the geometry in the vacuum region is noted.

CRITICAL PRESSURE FOR EQUILIBRIUM IN A TOROIDAL SYSTEM

The outward shift of a plasma column in a toroidal system is calculated using the ideal hydromagnetic equations for a stellarator model. At a critical value of the plasma pressure this outward shift becomes infinite. This is the pressure for which the equivalent straight system is marginally stable against the type of displacement induced by the toroidal curvature. The very close relationship between equilibrium and stability problems is thus illustrated.

Equilibrium and stability of a sharp-surface stellarator with a longitudinal current

Earlier results on stellarators with sharp plasma surfaces are extended to include the case with a current parallel to the magnetic field. A previous theorem that equilibrium shift becomes infinite and changes sign at marginal stability is generalized. A configuration with constant rotational transform outside the plasma is shown to have properties favourable to stabilization of the kink mode.