[en] The rich information contained in the plasma response to external magnetic perturbations can be used to help design stellarator coils more effectively. We demonstrate the feasibility by first devel oping a simple, direct method to study perturbations in stellarators that do not break stellarator symmetry and periodicity. The method applies a small perturbation to the plasma boundary and evaluates the resulting perturbed free-boundary equilibrium to build up a sensitivity matrix for the important physics attributes of the underlying configuration. Using this sensitivity information, design methods for better stellarator coils are then developed. The procedure and a proof-of-principle application are given that (1) determine the spatial distributions of external normal magnetic field at the location of the unperturbed plasma boundary to which the plasma properties are most sen- sitive, (2) determine the distributions of external normal magnetic field that can be produced most efficiently by distant coils, (3) choose the ratios of the magnitudes of the the efficiently produced magnetic distributions so the sensitive plasma properties can be controlled. Using these methods, sets of modular coils are found for the National Compact Stellarator Experiment (NCSX) that are either smoother or can be located much farther from the plasma boundary than those of the present design.

[en] If quasi-axisymmetry is preserved, non-axisymmetric shaping can be used to design tokamaks that do not require current drive, are resilient to disruptions, and have robust plasma stability without feedback. Suggestions for addressing the critical issues of tokamaks can only be validated when presented with sufficient specificity that validating experiments can be designed. The purpose of this paper is provide that specificity for non-axisymmetric shaping. To our knowledge, no other suggestions for the solution of a number of tokamak issues, such as disruptions, have reached this level of specificity. Sequences of three-field-period quasi-axisymmetric plasmas are studied. These sequences address the questions: (1) What can be achieved at various levels of non-axisymmetric shaping? (2) What simplifications to the coils can be achieved by going to a larger aspect ratio? (3) What range of shaping can be achieved in a single experimental facility? The sequences of plasmas found in this study provide a set of interesting and potentially important configurations.

[en] The use of magnetic coordinates is ubiquitous in toroidal plasma physics, but the distortion in Fourier spectra produced by these coordinates is not well known. A spatial symmetry of the field is not always represented by a symmetry in the Fourier spectrum when magnetic coordinates are used because of the distortion of the toroidal angle. The practical importance of spectral distortion is illustrated with a tokamak example

[en] A nominally axisymmetric plasma configuration, such as a tokamak or a spherical torus, is highly sensitive to non-axisymmetric magnetic perturbations due to currents outside of the plasma. The high sensitivity means that the primary interest is in the response of the plasma to very small perturbations, |(rvec b)/(rvec B)| ∼ 10^-2 to 10^-4, which can be calculated using the theory of perturbed equilibria. The Ideal Perturbed Equilibrium Code (IPEC) is described and applied to the study of the plasma response in a spherical torus to such external perturbations.

[en] A magnetic evolution is ideal if it is consistent with the field being embedded in a perfectly conducting fluid. Faraday's law implies the evolution is ideal when the parallel component of the electric field is the derivative of a scalar potential, a condition that generically holds in any local region of space. Reconnection requires the non-existence of such a potential. In systems with two periodic directions, non-existence focuses reconnection onto the surfaces in which the magnetic field lines close on themselves, the rational surfaces. This rational surface effect does not arise in astrophysics but does appear in periodic simulation codes. Effects that could give astrophysical reconnection are discussed

[en] What is the minimal information that must be supplied on a constant pressure surface of a toroidal plasma to completely specify a local magnetohydrodyamic equilibrium? Clearly the shape of the surface must be specified, but other information such as the separation between neighboring surfaces must also be given. This paper explores the conditions required for three-dimensional equilibria and how local equilibrium constraints are related to global constraints. The resulting conditions provide useful checks on the accuracy of equilibrium solvers, particularly for solvers for three-dimensional equilibria, and allow local refinements in the accuracy of equilibria

[en] Classical transport theory in a spherical torus differs from that in a standard tokamak because in the spherical torus the gyroradius has a width comparable to that of a drift orbit, the banana width. In addition, the operating spherical torus experiments have gradient scales that are comparable to the gyroradius of the ions. Transport theories should use the full kinetic equation, which can be solved numerically using Monte Carlo methods. Such a code for the spherical torus could be based on Alan Glasser's unpublished ORBIT code, which solves the full orbit equations, plus a Monte Carlo equivalent of the collision operator. This paper derives an appropriate Monte Carlo collision operator for use in such a code

[en] Nonaxisymmetric shaping of magnetic fusion plasmas extends the design space of nominally axisymmetric configurations, such as the tokamak, and defines fundamentally nonaxisymmetric configurations, called stellarators. Shaping is the primary design freedom to ensure suitable plasma equilibria for fusion applications. In fusion plasmas, the plasma pressure and current distributions are largely self-determined, and the only other determinant of plasma equilibria is the plasma shape. Since most of the freedom of shaping is in nonaxisymmetric shaping, understanding is needed. No fundamental demarcation exists between axisymmetric and quasiaxisymmetric tokamaks, so nonaxisymmetric shaping can be used to address issues that must be addressed for tokamaks to be an attractive fusion system. Stellarators offer design freedom beyond that available from extending the design space of nominally axisymmetric concepts. Stellarator experiments have demonstrated many benefits of nonaxisymmetric shaping, but the primary benefit is that sufficient freedom exists to design around many problems of fusion plasmas.

[en] A new method for correcting magnetic field errors in the ITER tokamak is developed using the Ideal Perturbed Equilibrium Code (IPEC). The dominant external magnetic field for driving islands is shown to be localized to the outboard midplane for three ITER equilibria that represent the projected range of operational scenarios. The coupling matrices between the poloidal harmonics of the external magnetic perturbations and the resonant fields on the rational surfaces that drive islands are combined for different equilibria and used to determine an ordered list of the dominant errors in the external magnetic field. It is found that efficient and robust error field correction is possible with a fixed setting of the correction currents relative to the currents in the main coils across the range of ITER operating scenarios that was considered

[en] Poloidal symmetry breaking in toroidal plasmas causes a damping of poloidal rotation and toroidal symmetry breaking a damping of toroidal rotation. These torques are transmitted by the magnetic field to the outside world. An upper limit exists on the torque that can be transmitted by magnetic asymmetries. This limit is enforced by shielding asymmetries from the plasma, which can be an important effect for toroidal asymmetries. The torque interaction of plasmas with magnetic fields can be either through an anisotropic pressure or by the drive for magnetic islands. The physics of both types of interactions are considered and paradoxical effects are clarified.