Tokamak error fields and locked modes

The effects of externally applied, resonant magnetic field perturbations on tokamak plasmas are discussed. An analytical model assuming tokamak ordering and narrow islands clarifies the conditions under which error fields are amplified or diminished by self- consistent effects. A strong amplification of error fields near marginal tearing stability is found to broaden the range of parameters over which deleterious tearing effects are seen. Three- dimensional numerical solutions indicate that saturated tearing mode island widths can be sensitive to the presence of small nonaxisymmetric perturbations. It is argued that the theoretical conclusions are consistent with observations in error compensation experiments, and are also consistent with observations of enhanced growth for locked modes. 19 refs., 17 figs

Three-dimensional tokamak equilibria in the presence of resonant field errors

Numerical solutions are described for three-dimensional MHD equilibria in the presence of resonant magnetic field perturbations. The effects of a realistic spectrum of resonant field errors are calculated for a range of current profiles. It is found that field errors of the magnitude existing in present day devices, and contemplated for future devices, can produce a set of magnetic islands occupying a significant fraction of the plasma cross-section

Siting Transmission Lines in a Changed Milieu: Evolving Notions of the "Public Interest" In Balancing State and Regional Considerations

This Article discusses how state public utility law presents a barrier to the siting of new high voltage transmission lines to serve renewable resources, and how states could approach its evolution in order to preserve a role for state regulators in a new energy economy in which renewable energy will play a significant role. The traditional approach to determining the "public interest" in siting transmission lines is well on its way to obsolescence. Two developments over the past fifteen years have begun to challenge this paradigm. First, policies at the federal level and in many states have encouraged increased competition in generation, contributing to de-monopolization of the bulk power side of the industry. Second, the increased emphasis on environmental, energy independence, and other public policy objectives, has resulted in a dramatically increased demand for renewable energy, particularly given heightened attention to climate change. Given that wind power -- the most economically viable renewable resource on a bulk power basis -- is feasible predominantly in locations far removed from, load centers, the demand for new multistate transmission facilities has been brought clearly into focus. After an introduction in Part I, Part II describes the existing arrangements in several resource rich Western states for siting new transmission lines, and the coexistence of those arrangements with a conventional understanding of the public interest in determining need and addressing environmental concerns under traditional state transmission siting laws. Part III discusses transmission issues related to the competitive wholesale market and increased attention to climate change and highlights how federal law has expanded to accommodate some of these concerns. Part IV emphasizes the need for a new definition of the public interest which might better reflect these new market circumstances and opportunities, and highlights the two main barriers to this: 1) legislative and/or regulatory inertia and 2) an outdated cost-allocation model. The public interest under most state siting statutes is sufficiently capacious to give regulators some flexibility to evolve, but in other instances legislative action may be needed. In addition, the state cost-of-service ratemaking model must evolve to a more regional approach to allocating the costs of new transmission

Heliac parameter study

Helical axis stellarators (heliacs) with zero net current are found to possess very good stability properties. Helically symmetric or straight heliacs with bean-shaped cross sections have a first region of stability that reaches to (..beta..) of 30% or more. Those with circular cross sections have second region of stability to Mercier modes. In addition we report on the stability properties of these plasma configurations as functions of pressure profile, helical aspect ratio, and helical period length

Comparison between resistive and collisionless double tearing modes for nearby resonant surfaces

The linear instability and nonlinear dynamics of collisional (resistive) and collisionless (due to electron inertia) double tearing modes (DTMs) are compared with the use of a reduced cylindrical model of a tokamak plasma. We focus on cases where two q = 2 resonant surfaces are located a small distance apart. It is found that regardless of the magnetic reconnection mechanism, resistivity or electron inertia, the fastest growing linear eigenmodes may have high poloidal mode numbers m ~ 10. The spectrum of unstable modes tends to be broader in the collisionless case. In the nonlinear regime, it is shown that in both cases fast growing high-m DTMs lead to an annular collapse involving small magnetic island structures. In addition, collisionless DTMs exhibit multiple reconnection cycles due to reversibility of collisionless reconnection and strong ExB flows. Collisionless reconnection leads to a saturated stable state, while in the collisional case resistive decay keeps the system weakly dynamic by driving it back towards the unstable equilibrium maintained by a source term.Comment: 15 pages, 9 figure

Free-boundary Full-pressure Island Healing in a Stellarator: Coil-healing

The lack of axisymmetry in stellarators guarantees that in general magnetic islands and chaotic magnetic field lines will exist. As particle transport is strongly tied to the magnetic field lines, magnetic islands and chaotic field lines result in poor plasma confinement. For stellarators to be feasible candidates for fusion power stations it is essential that, to a good approximation, the magnetic field lines lie on nested flux-surfaces, and the suppression of magnetic islands is a critical issue for stellarator coil design, particularly for small aspect ratio devices. A procedure for modifying stellarator coil designs to eliminate magnetic islands in free-boundary full-pressure magnetohydrodynamic equilibria is presented. Islands may be removed from coil-plasma free-boundary equilibria by making small changes to the coil geometry and also by variation of trim coil currents. A plasma and coil design relevant to the National Compact Stellarator Experiment is used to illustrate the technique

Magnetic Field Line Tracing Calculations for Conceptual PFC Design in the National Compact Stellarator Experiment

The National Compact Stellarator Experiment (NCSX) is a three-field period compact stellarator presently in the construction phase at Princeton, NJ. The design parameters of the device are major radius R=1.4m, average minor radius <a> = 0.32m, 1.2 {le} toroidal field (B{sub t}) {le} 1.7 T, and auxiliary input power up to 12 MW with neutral beams and radio-frequency heating. The NCSX average aspect ratio <R/a> of 4.4 lies well below present stellarator experiments and designs, enabling the investigation of high {beta} physics in a compact stellarator geometry. Also the NCSX design choice for a quasi-axisymmetric configuration aims toward the achievement of tokamak-like transport. In this paper, we report on the magnetic field line tracing calculations used to evaluate conceptual plasma facing component (PFC) designs. In contrast to tokamaks, axisymmetric target plates are not required to intercept the majority of the heat flux in stellarators, owing to the nature of the 3-D magnetic field footprint. The divertor plate design investigated in this study covers approximately one half of the toroidal extent in each period. Typical Poincare plots in Figure 1 illustrate the plasma cross-section at several toroidal angles for a computed NCSX high-beta equilibrium. The plates used for these calculations are centered in each period about the elongated cross-section shown in Figure 1a, extending to +/- {pi}/6 in each direction. Two methods for tracing the edge field line topology were used in this study. The first entails use of the VMEC/MFBE-2001 packages, whereas the second entails use of the PIES code with a post-processor by Michael Drevlak; the same field line integration routine was used to evaluate the equilibria for this comparison. Both inputs were generated based on the {beta}=4%, =iota=0.5 equilibrium computed from the final NCSX coil set. We first compare these two methods for a specific plate geometry, and conclude with a comparison of the strike characteristics for two different target plate poloidal lengths using the latter method. The details of the magnetic topology differ when computed with VMEC/MFBE as compared with an iterated PIES solution. This difference is illustrated in Figure 2. The presence of islands in the PIES solution effectively reduces the radius of the last closed magnetic surface (LCMS) by about 8 cm. As expected, this difference in the edge topology translates to a difference in field line terminations