Tokamak magnetic islands in the presence of nonaxisymmetric perturbations

The effects of a small, externally imposed, nonaxisymmetric magnetic field perturbation on magnetic islands are studied analytically, assuming zero {beta}, tokamak ordering, and narrow islands. For the tearing stable case, the conditions under which the self-consistent plasma response is self-healing or amplifying are elucidated. For the tearing unstable case, the quasilinear theory of tearing modes is extended to a description of locked modes. 16 refs., 12 figs

Suppression of magnetic islands by rf-driven currents

The quasilinear theory for the saturation of nonlinear tearing modes is modified to include rf driven currents. It is shown that the presence of lower hybrid driven currents can strongly suppress the growth of magnetic islands

Nonlinear tearing instabilities in tokamaks with locally flattened current profiles

Nonlinear tearing stability is evaluated for current profiles which are linearly stabilized by flattening the current in the neighborhood of the rational surface. When marginally stable to the linear instability, these profiles remain unstable in the presence of a small but finite island. The growth of the island saturated only when the island reaches the width it would have attained in the absence of flattening. Implications are discused for proposed methods of tearing mode stabilization and for theories of the tokamak sawtooth oscillation. 19 refs., 1 fig

Numerical solution of three-dimensional magnetic differential equations

A computer code is described that solves differential equations of the form B . del f = h for a single-valued solution f, given a toroidal three-dimensional divergence-free field B and a single-valued function h. The code uses a new algorithm that Fourier decomposes a given function in a set of flux coordinates in which the field lines are straight. The algorithm automatically adjusts the required integration lengths to compensate for proximity to low order rational surfaces. Applying this algorithm to the Cartesian coordinates defines a transformation to magnetic coordinates, in which the magnetic differential equation can be accurately solved. Our method is illustrated by calculating the Pfirsch-Schlueter currents for a stellarator

Computation of magnetic coordinates and action-angle variables

We have developed a new algorithm for calculating magnetic surfaces and coordinates for a given three-dimensional magnetic field. The algorithm serves also to solve the equivalent problem of computing invariant tori and action-angle variables for a one-dimensional time-dependent numerically specified Hamiltonian (or a two-dimensional time-independent Hamiltonian). Our approach combines features of both iterative and trajectory following methods. This allows us to overcome the inefficiency of trajectory following methods near low order rational surfaces, while retaining some of the robustness of these methods. 26 refs., 8 figs., 1 tab

Reduction of Islands in Full-pressure Stellarator Equilibria

The control of magnetic islands is a crucial issue in designing Stellarators. Islands are associated with resonant radial magnetic fields at rational rotational-transform surfaces and can lead to chaos and poor plasma confinement. In this article, we show that variations in the resonant fields of a full-pressure stellarator equilibrium can be related to variations in the boundary via a coupling matrix, and inversion of this matrix determines a boundary modification for which the island content is significantly reduced. The numerical procedure is described and the results of island optimization are presented. Equilibria with islands are computed using the Princeton Iterative Equilibrium Solver, and resonant radial fields are calculated via construction of quadratic-flux-minimizing surfaces. A design candidate for the National Compact Stellarator Experiment [Phys. Plasmas 8, 2001], which has a large island, is used to illustrate the technique. Small variations in the boundary shape are used to reduce island size and to reverse the phase of a major island chain

A nonvariational code for calculating three-dimensional MHD (magnetohydrodynamic) equilibria

Details are presented of the PIES code, which uses a nonvariational algorithm for calculating fully three-dimensional MHD equilibria. The MHD equilibrium equations are directly iterated in special coordinates to find self-consistent currents and magnetic fields for given pressure and current profiles and for a given outermost magnetic surface. Three important advantages of this approach over previous methods are the ease with which net current profiles can be imposed, the explicit treatment of resonances, and the ability to handle magnetic islands and stochastic field lines. The convergence properties of the code are studied for several axisymmetric and nonaxisymmetric finite-..beta.. equilibria that have magnetic surfaces. 36 refs., 14 figs., 3 tabs

Physics Basis for High-Beta, Low-Aspect-Ratio Stellarator Experiments

High-beta, low-aspect-ratio (compact) stellarators are promising solutions to the problem of developing a magnetic plasma configuration for magnetic fusion power plants that can be sustained in steady-state without disrupting. These concepts combine features of stellarators and advanced tokamaks and have aspect ratios similar to those of tokamaks (2-4). They are based on computed plasma configurations that are shaped in three dimensions to provide desired stability and transport properties. Experiments are planned as part of a program to develop this concept. A beta = 4% quasi-axisymmetric plasma configuration has been evaluated for the National Compact Stellarator Experiment (NCSX). It has a substantial bootstrap current and is shaped to stabilize ballooning, external kink, vertical, and neoclassical tearing modes without feedback or close-fitting conductors. Quasi-omnigeneous plasma configurations stable to ballooning modes at beta = 4% have been evaluated for the Quasi-Omnigeneous Stellarator (QOS) experiment. These equilibria have relatively low bootstrap currents and are insensitive to changes in beta. Coil configurations have been calculated that reconstruct these plasma configurations, preserving their important physics properties. Theory- and experiment-based confinement analyses are used to evaluate the technical capabilities needed to reach target plasma conditions. The physics basis for these complementary experiments is described