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The Mercier criterion is a well-known stability criterion for tokamaks. It is derived from a 2 × 2 matrix eigenvalue problem arising from the expansion of resonant solutions about a singular surface where m−nq=0, with m and n being the poloidal and toroidal mode numbers, respectively, and q being the safety factor. The stability criterion is that the eigenvalues must be real, otherwise, the solution oscillates, violating the Newcomb crossing criterion. Because of the non-axisymmetry of stellarators, different toroidal as well as poloidal harmonics couple to each other. It follows that each singular surface can have multiple resonant harmonics, with multiplicity M≥1. The corresponding matrix eigenvalue problem involves a 2M×2M matrix, resulting in M pairs of positive and negative eigenvalues. The generalized stability criterion is that all eigenvalues must be real. While the original Mercier criterion can be expressed in terms of quadratures of equilibrium quantities over the singular surface, which can be evaluated anywhere, the generalized Mercier criterion can only be evaluated on rational q surfaces with a given set of resonant harmonics.

High fidelity kinetic plasma equilibrium reconstructions are an essential requirement for accurate stability and disruption prediction analyses to support continuous operation of high beta tokamak plasmas. The present kinetic equilibrium reconstructions of plasmas in the KSTAR device include plasma density and temperature profiles from Thomson scattering and ion temperature from charge exchange spectroscopy diagnostics, and allowance for fast particle pressure. In addition, up to 25 channels of motional Stark effect (MSE) diagnostic data are used to constrain the magnetic field pitch angle profile in the plasma to produce a reliable computation of the safety factor, q, profile. H-mode plasmas exhibit clear pedestal characteristics in the reconstructed pressure profile compared to internal transport barrier or L-mode plasmas. The plasma configuration and vertical position of inner strike points are validated by CCD and infrared camera images. Ideal and resistive MHD stability analyses using the DCON and resistive DCON codes utilize these kinetic equilibrium reconstructions to compare to experimental plasma stability. Equilibria with sufficiently low convergence error can provide reliable computation of ideal and resistive magnetohydrodynamic (MHD) stability analysis.

The method of solving the linear resistive plasma response, based on the asymptotic matching approach, is developed for full toroidal tokamaks by upgrading the resistive DCON code [A. H. Glasser, Z. R. Wang, and J.-K. Park, Phys. Plasmas 23, 112506 (2016)]. The derived matching matrix, asymptotically matching the outer and inner regions, indicates that the applied three dimension (3-D) magnetic perturbations contribute additional small solutions at each resonant surface due to the toroidal coupling of poloidal modes. In contrast, the resonant harmonic only affects the corresponding resonant surface in the cylindrical plasma. The solution of the ideal outer region is critical to the asymptotic matching and is challenging in toroidal geometry due to the singular power series solution at the resonant surfaces. Thus, a systematic verification of the outer region Δ ′ matrix is made by reproducing the well-known analytical Δ ′ result in Furth et al. [Phys. Fluids 16, 1054–1063 (1073)] and by making a quantitative benchmark with the PEST3 code [A. Pletzer and R. L. Dewar, J. Plasma Phys. 45, 427–451 (1991)]. Finally, the reconstructed numerical solution of the resistive plasma response from the toroidal matching matrix is presented. Compared with the ideal plasma response, the global structure of the response can be affected by the small finite island at the resonant surfaces.

In the following work, we demonstrate the efficacy of a Riccati δW ideal MHD stability analysis that bypasses the numerically intractable integration of the Newcomb equation. By transforming the linear Newcomb equation into a quadratic Riccati equation, an accurate and equivalent δW analysis is performed that is shown to enjoy some numerical advantages. We demonstrate that the Riccati approach is better conditioned than its Newcomb counterpart at the magnetic axis, and we apply dynamical systems insights to examine its behavior at singular points. We further discuss the constraints involved in solving for the extremal admissible perturbations of a δW analysis.

This document is the product of a stellarator community workshop, organized by the National Stellarator Coordinating Committee and referred to as Stellcon, that was held in Cambridge, Massachusetts in February 2016, hosted by MIT. The workshop was widely advertised, and was attended by 40 scientists from 12 different institutions including national labs, universities and private industry, as well as a representative from the Department of Energy. The final section of this document describes areas of community wide consensus that were developed as a result of the discussions held at that workshop. Areas where further study would be helpful to generate a consensus path forward for the US stellarator program are also discussed. The program outlined in this document is directly responsive to many of the strategic priorities of FES as articulated in “Fusion Energy Sciences: A Ten-Year Perspective (2015–2025)” [1]. The natural disruption immunity of the stellarator directly addresses “Elimination of transient events that can be deleterious to toroidal fusion plasma confinement devices” an area of critical importance for the US fusion energy sciences enterprise over the next decade. Another critical area of research “Strengthening our partnerships with international research facilities,” is being significantly advanced on the W7-X stellarator in Germany and serves as a test-bed for development of successful international collaboration on ITER. This report also outlines how materials science as it relates to plasma and fusion sciences, another critical research area, can be carried out effectively in a stellarator. Additionally, significant advances along two of the Research Directions outlined in the report; “Burning Plasma Science: Foundations—Next-generation research capabilities”, and “Burning Plasma Science: Long pulse—Sustainment of Long-Pulse Plasma Equilibria” are proposed.

A recent publication presents a detailed prescription for constructing global eigenfunctions and complex growth rates for resistive instabilities in axisymmetric toroidal systems, using the method of matched asymptotic expansions. At each singular surface in the plasma, the small-x asymptotic solutions of the ideal MHD outer-region equations are matched to the large-x asymptotic solutions of the resistive inner-region equations, with x being the distance from the singular surface. The success of this method depends upon accurate asymptotic solutions of the resistive inner region equations. Extensive studies have shown that there are not only regimes of excellent agreement with straight-through methods, without asymptotic matching, but also regimes of strong disagreement. In an effort to find the cause of this discrepancy, we present here a different method of constructing asymptotic solutions of the inner region equations and we study the convergence properties of the new and old solutions.

The Direct Fusion Drive (DFD), a compact, anuetronic fusion engine, will enable more challenging exploration missions in the solar system. The engine proposed here uses a deuterium–helium-3 reaction to produce fusion energy by employing a novel field-reversed configuration (FRC) for magnetic confinement. The FRC has a simple linear solenoid coil geometry yet generates higher plasma pressure, hence higher fusion power density, for a given magnetic field strength than other magnetic-confinement plasma devices. Waste heat generated from the plasma׳s Bremsstrahlung and synchrotron radiation is recycled to maintain the fusion temperature. The charged reaction products, augmented by additional propellant, are exhausted through a magnetic nozzle. A 1 MW DFD is presented in the context of a mission to deploy the James Webb Space Telescope (6200 kg) from GPS orbit to a Sun–Earth L2 halo orbit in 37 days using just 353 kg of propellant and about half a kilogram of 3He. The engine is designed to produce 40 N of thrust with an exhaust velocity of 56.5 km/s and has a specific power of 0.18 kW/kg.

Background: Life expectancy (LE) is a major marker of individual survival. It also serves as a guide to highlight both the progress and the gaps in total social and societal health. Comparative LE in concert with measures of gender-specific experience, indices of empowerment and societal happiness and development offer a comparative tool to examine trends and similarities of societal progress as seen through the lens of cross-national experience. Methods: To determine the gender gaps in LE (GGLE) trends, we performed a longitudinal analysis, covering a period of 49 years (1960–2008). To examine the association of GGLE with development indices, we used the 2007 GGLE data, the newest happiness data mostly drawn from 2006; the 2006 Human Development Index (HDI) data and the 2006 Gender Empowerment Measure (GEM) data. Results: It revealed that most of the Organization for Economic Co-operation and Development (OECD) countries had a GGLE trend that occurred in an inverted U-curve fashion. We divided them into three subgroups based on the peak years of respective GGLE. The earlier the peak year, the happier the countries, the higher the HDI and the smaller the current GGLE are. Association analysis indicates that Happiness, HDI and GEM are all negatively associated with GGLE. Conclusion: This pattern suggests that GGLE undergoes three phases of growth, peak and stability and decline. Japan will soon be seeing its GGLE gradually shrinking in the foreseeable future. The continuing increases in Happiness, HDI and GEM are associated with a decrease in GGLE, which should be carefully taken into consideration.

The truncation of large physical domains to concentrate computational resources is necessary or desirable in simulating many natural and man-made plasma phenomena. Three open boundary condition (BC) methods for such domain truncation of dissipative magnetohydrodynamics (MHD) problems are described and compared here. A novel technique, lacuna-based open boundary conditions (LOBC), is presented for applying open BC to dissipative MHD and other hyperbolic and mixed hyperbolic-parabolic systems of partial differential equations. LOBC, based on manipulating Calderon-type near-boundary sources, essentially damp hyperbolic effects in an exterior region attached to the simulation domain and apply BC appropriate for the remaining parabolic effects (if present) at the exterior region boundary. Another technique, approximate Riemann BC (ARBC), is adapted from finite volume and discontinuous Galerkin methods. In ARBC, the value of incoming flux is specified using a local, characteristic-based method. A third commonly-used open BC, zero-normal derivative BC (ZND BC), is presented for comparison. These open BC are tested in several gas dynamics and dissipative MHD problems. LOBC are found to give stable, low-reflection solutions even in the presence of strong parabolic behavior, while ARBC are stable only when hyperbolic behavior is dominant. Pros and cons of the techniques are discussed and put into context within the body of open BC research to date.

Major developments on the Mega Amp Spherical Tokamak (MAST) have enabled important advances in support of ITER and the physics basis of a spherical tokamak (ST) based component test facility (CTF), as well as providing new insight into underlying tokamak physics. For example, L–H transition studies benefit from high spatial and temporal resolution measurements of pedestal profile evolution (temperature, density and radial electric field) and in support of pedestal stability studies the edge current density profile has been inferred from motional Stark effect measurements. The influence of the q-profile and E × B flow shear on transport has been studied in MAST and equilibrium flow shear has been included in gyro-kinetic codes, improving comparisons with the experimental data. H-modes exhibit a weaker q and stronger collisionality dependence of heat diffusivity than implied by IPB98(y,2) scaling, which may have important implications for the design of an ST-based CTF. ELM mitigation, an important issue for ITER, has been demonstrated by applying resonant magnetic perturbations (RMPs) using both internal and external coils, but full stabilization of type-I ELMs has not been observed. Modelling shows the importance of including the plasma response to the RMP fields. MAST plasmas with q > 1 and weak central magnetic shear regularly exhibit a long-lived saturated ideal internal mode. Measured plasma braking in the presence of this mode compares well with neo-classical toroidal viscosity theory. In support of basic physics understanding, high resolution Thomson scattering measurements are providing new insight into sawtooth crash dynamics and neo-classical tearing mode critical island widths. Retarding field analyser measurements show elevated ion temperatures in the scrape-off layer of L-mode plasmas and, in the presence of type-I ELMs, ions with energy greater than 500 eV are detected 20 cm outside the separatrix. Disruption mitigation by massive gas injection has reduced divertor heat loads by up to 70%.

We describe kinetic electromagnetic particle-in-cell simulation of a field reversed configuration with rotating magnetic fields (RMF). The energy-conserving algorithm calculates RMF penetration, gas breakdown and field reversal for the odd-parity RMF, PFRC device. An advanced simulation technique is being developed that preserves charged particle orbits for large time steps. These techniques are being developed to model future devices.

Active feedback control of ideal MHD stability in a tokamak requires rapid plasma stability analysis. Toward this end, we reformulate the δW stability method with a Hamilton-Jacobi theory, elucidating analytical and numerical features of the generic tokamak ideal MHD stability problem. The plasma response matrix is demonstrated to be the solution of an ideal MHD matrix Riccati differential equation. Since Riccati equations are prevalent in the control theory literature, such a shift in perspective brings to bear a range of numerical methods that are well-suited to the robust, fast solution of control problems. We discuss the usefulness of Riccati techniques in solving the stiff ordinary differential equations often encountered in ideal MHD stability analyses—for example, in tokamak edge and stellarator physics. We demonstrate the applicability of such methods to an existing 2D ideal MHD stability code—DCON [A. H. Glasser, Phys. Plasmas 23, 072505 (2016)]—enabling its parallel operation in near real-time, with wall-clock time ≪1s. Such speed may help enable active feedback ideal MHD stability control, especially in tokamak plasmas whose ideal MHD equilibria evolve with inductive timescale τ≳ 1s—as in ITER.

Study Objective To estimate the safety and efficacy of the HydroThermAblator (HTA) system for performance of endometrial ablation in the medical office setting using local anesthesia and minimal oral sedation and to compare results obtained in patients with submucous myomas with those in patients with normal endometrial cavities. Design Retrospective cohort analysis of 246 HTA procedures (Canadian Task Force classification II-2). Setting Medical offices of a suburban community medical center that is part of a large health maintenance organization. Patients Two hundred forty-six women aged 28 to 63 years (mean [SD], 45.1 [6.0] years) with abnormal uterine bleeding unresponsive to conservative management, including 104 patients (42.3%) with submucous myomas. Type 0 or type I myomas were present in at least 86 patients with submucous myomas (82.7%) and ranged from 1 to 4 cm in greatest diameter. In the other 18 patients, submucous myomas were not classified by type. Patients were evaluated at 2 to 70 months after the procedure (median follow-up, 31.0 months). Three patients were lost to follow-up, and 12 patients underwent hysterectomy for indications other than abnormal bleeding and were excluded from the analysis. Thus, 231 patients were included in the analysis. Interventions Endometrial ablation was performed using the HTA system with paracervical or intracervical block after oral premedication with ibuprophen, diazepam, and acetominophen or hydrocodone and intramuscular ketorolac. No intravenous or intramuscular narcotics were used. The anesthesia regimen was the same in patients with submucous myomas as in those with normal cavities, and the procedure was performed in exactly the same manner. All procedures were performed in the medical office procedure room by 7 board-certified gynecologists; most procedures were performed by the authors. Measurements and Main Results Of the 231 patients included in the analysis, 121 (53.4%) reported postablation amenorrhea, 62 (26.8%) reported light menses or spotting, 21 (9.1%) reported normal menses, 15 (6.5%) reported menorrhagia, and 12 (5.2%) underwent hysterectomy because of bleeding. In the 136 patients with normal cavities, amenorrhea was achieved in 84 patients (61.8%), oligomenorrhea in 35 (25.7%), and eumenorrhea in 12 (8.8%). Four patients (2.9%) continued to have menorrhagia requiring medical treatment. In the 95 patients with submucous myomas, amenorrhea was reported by 37 patients (38.9%), oligomenorrhea by 27 (28.4%), eumenorrhea by 9 (9.5%), and menorrhagia by 11 (11.6%). In 11 patients (11.6%), hysterectomy was performed because of menorrhagia. All patients who underwent hysterectomy had multiple myomas, and 9 (81.8%) also had adenomyosis. The failure rate, defined as patients with menorrhagia or undergoing hysterectomy because of bleeding, was 11.7% overall. The failure rate in patients with submucous myomas and normal cavities was 23.2% and 3.7%, respectively (relative risk, 6.3; 95% confidence interval, 2.5–16.0). While the failure rate in the group with myomas was statistically significantly higher than in the group without myomas, the failure rate in the myoma group was still comparable to that achieved using electrosurgical resection and ablation of similar types of myomas as reported in the literature. The amenorrhea rate achieved in the myoma group (38.9%) was also comparable to that achieved in US Food and Drug Administration pivotal trials in patients with normal cavities treated using all of the nonhysteroscopic global ablation devices as well those treated using rollerball endometrial ablation. The rate of hysterectomy because of bleeding was 5.2% overall. The hysterectomy rate in patients with submucous myomas and normal cavities was 11.6% and 0.7%, respectively. Only 1 procedure was discontinued (at 8 minutes) because of pain. Four patients had postoperative endometritis, with 2 requiring hospitalization for intravenous antibiotic therapy. Two false passages were created while dilating the cervix, with subsequent inability to perform the procedure. Conclusions Hydrothermablation performed in the medical office using local anesthesia seems to be a safe, effective, and cost-saving procedure for treatment of abnormal uterine bleeding in women with both normal and myomatous uteri. Although the success rate in patients with normal cavities was higher than that achieved in patients with submucous myomas, hysterectomy because of abnormal bleeding related to myomas was avoided in 88.4% of the group with myomas.

A public health perspective based on social justice and a population health point of view emphasizes pharmacy policy innovations regarding safety and costs. Such policies that effectively reduce costs include controlling profits, establishing profit targets, extending prescription providers, revising prescription classification schemes, emphasizing generic medications, and establishing formularies. Public education and universal programs may reduce costs, but co-pays and "cost-sharing" do not. Switching medications to over-the-counter (OTC) status, pill splitting, and importing medication from abroad are poor substitutes for authentic public health pharmacy policy. Where policy changes yield savings, public health insists that these savings should be used to increase access and improve population health. In the future, pharmacy policies may emphasize public health accountability more than individual liberty because of potential cost savings to society. Fear of litigation, as an informal mechanism of focusing manufacturer's attention on safety, is inefficient; public health pharmacy policy regarding safety looks toward a more active regulatory role on the part of government. A case study of direct-to-consumer advertising illustrates the complexity of public health pharmacy policy.

The National Spherical Torus Experiment (NSTX) offers an operational space characterized by high-beta (βt= 39%, βN> 7,) and low aspect ratio (A> 1.27) to leverage the plasma parameter dependences of RWM stabilization and plasma rotation damping physics giving greater confidence for extrapolation to ITER. Significant new capability for RWM research has been added to the device with the commissioning of a set of six non-axisymmetric magnetic field coils, allowing generation of fields with dominant toroidal mode number,n, of 1–3. These coils have been used to study the dependence of resonant field amplification on applied field frequency and RWM stabilization physics by reducing the toroidal rotation profile below its steady-state value through non-resonant magnetic braking. Modification of plasma rotation profiles shows that rotation outsideq= 2.5 is not required for passive RWM stability and there is large variation in the RWM critical rotation at theq= 2 surface, both of which are consistent with distributed dissipation models.

Sustainability in the context of China is an immediate and massive concept. A society of 1.3 billion has economic growth of 9-10% and a dramatic rise in life expectancy. It has rapidly-accumulating material wealth, major lifestyle changes and growing inequalities. It is putting great pressure on natural resources such as water and air quality. The Chinese Government's new 5-year plan uses the term 'sustainable development' as an important social goal for the first time. Sustainability requires a global effort and Sino-European partnerships are important.

The National Spherical Torus Experiment (NSTX) has demonstrated the advantages of low aspect ratio geometry in accessing high toroidal and normalized plasma beta, and βN ≡ 10 8〈βt〉 aB0/Ip. Experiments have reached βt = 39% and βN = 7.2 through boundary and profile optimization. High βN plasmas can exceed the ideal no-wall stability limit, βNno-wall, for periods much greater than the wall eddy current decay time. Resistive wall mode (RWM) physics is studied to understand mode stabilization in these plasmas. The toroidal mode spectrum of unstable RWMs has been measured with mode number n up to 3. The critical rotation frequency of Bondeson-Chu, Ωcrit = ωA/(4q2), describes well the RWM stability of NSTX plasmas when applied over the entire rotation profile and in conjunction with the ideal stability criterion. Rotation damping and global rotation collapse observed in plasmas exceeding βNno-wall differs from the damping observed during tearing mode activity and can be described qualitatively by drag due to neoclassical toroidal viscosity in the helically perturbed field of an ideal displacement. Resonant field amplification of an applied n = 1 field perturbation has been measured and increases with increasing βN. Equilibria are reconstructed including measured ion and electron pressure, toroidal rotation and flux isotherm constraint in plasmas with core rotation ω/ωA up to 0.48. Peak pressure shifts of 18% of the minor radius from the magnetic axis have been reconstructed.

The major objective of the National Spherical Torus Experiment (NSTX) is to understand basic toroidal confinement physics at low aspect ratio and high βT in order to advance the spherical torus (ST) concept. In order to do this, NSTX utilizes up to 7.5 MW of neutral beam injection, up to 6 MW of high harmonic fast waves (HHFWs), and it operates with plasma currents up to 1.5 MA and elongations of up to 2.6 at a toroidal field up to 0.45 T. New facility, and diagnostic and modelling capabilities developed over the past two years have enabled the NSTX research team to make significant progress towards establishing this physics basis for future ST devices. Improvements in plasma control have led to more routine operation at high elongation and high βT (up to ~40%) lasting for many energy confinement times. βT can be limited by either internal or external modes. The installation of an active error field (EF) correction coil pair has expanded the operating regime at low density and has allowed for initial resonant EF amplification experiments. The determination of the confinement and transport properties of NSTX plasmas has benefitted greatly from the implementation of higher spatial resolution kinetic diagnostics. The parametric variation of confinement is similar to that at conventional aspect ratio but with values enhanced relative to those determined from conventional aspect ratio scalings and with a BT dependence. The transport is highly dependent on details of both the flow and magnetic shear. Core turbulence was measured for the first time in an ST through correlation reflectometry. Non-inductive start-up has been explored using PF-only and transient co-axial helicity injection techniques, resulting in up to 140 kA of toroidal current generated by the latter technique. Calculated bootstrap and beam-driven currents have sustained up to 60% of the flat-top plasma current in NBI discharges. Studies of HHFW absorption have indicated parametric decay of the wave and associated edge thermal ion heating. Energetic particle modes, most notably toroidal Alfven eigenmodes and fishbone-like modes result in fast particle losses, and these instabilities may affect fast ion confinement on devices such as ITER. Finally, a variety of techniques has been developed for fuelling and power and particle control.

The Medicine and Public Health Initiative (MPHI) was created jointly 10 years ago by the American Medical Association and the American Public Health Association to bridge the nearly century-wide gulf between the respective disciplines. We review the history of MPHI and its growing significance in light of recent terrorism events. We report on current MPHI activities by examining three bellwether states-California, Florida, and Texas-as well as international sites. Upon its inception, MPHI was rapidly embraced and nationally disseminated. Sustainability 10 years later in the post-911 world requires renewed commitment by all collaborators. In order to meet the numerous health challenges facing our nation, from terrorism to chronic disease, and for MPHI to be successful, medicine and public health must work in tandem.

Study objective To assess the efficacy of performing myomectomies through 3- to 6-cm incisions for the removal of myomas up to 14 cm in diameter. Design A retrospective analysis of 139 myomectomies performed at our center from January 1995 through December 2003 (Canadian Task Force classification II-3). Setting A suburban medical center, part of a large prepaid health maintenance organization. Patients One hundred thirty-nine women. Interventions Myomectomies were performed through 3- to 6-cm suprapubic cruciate incisions using atraumatic elastic retractors with or without laparoscopic assist. Myomas were morcellated with a scalpel before being enucleated. The uterus was repaired in a classic three-layered closure in all cases. All procedures were performed in the ambulatory surgery unit of our hospital, which is part of the main operating room. Measurements and main results The median age of the patients in this series was 30.0 years (range 23–56 years). The median weight of the myomas removed was 275.0 g (range of 30–975 g). One hundred thirty-seven (98.5%) of 139 patients were discharged in 23 hours or less, with 24 patients leaving within 4 hours and 61 within 8 hours. The median length of stay was 6.0 hours, with two patients remaining hospitalized for 48 hours. The median operating time was 110 minutes (range 44–260 min). Estimated blood loss ranged from 50 to 2000 mL, with a median of 300 mL. Three hysterectomies were performed: one as an emergency for hemorrhage and two for recurrent myomas. Three patients developed wound seromas, and one developed a wound infection. Conclusions Minilaparotomy myomectomy is a safe, effective minimally invasive alternative to laparoscopic myomectomy. Early discharge and return to normal activities is comparable to laparoscopy and is far more cost effective. It affords the ability to palpate the uterus and close the myometrial defect easily with a standard three-layered closure making it particularly suitable for gynecologists with limited laparoscopic suturing skills.

To estimate the ectopic pregnancy rate at Kaiser Permanente, Northern California, during 1997-2000.Computerized data systems covering inpatient, outpatient, and pharmacy records were reviewed for evidence of ectopic pregnancies during the study period. Denominator data were calculated from computerized utilization and membership data for the same period.We identified 2,617 ectopic pregnancies that occurred between 1997 and 2000 among 126,451 reported pregnancies for an annual rate of 20.70 per 1,000 reported pregnancies and 1.03 per 1,000 women 15-44 years old. There was no evidence of a trend over time in these data. The rate increased with increasing age. Approximately 35% of these women were medically treated, and we observed an increase over time in the proportion of women who were medically treated.Using computerized data systems in a large integrated health delivery system, we found that the rate of ectopic pregnancy in 1997-2000 was similar to the national rate in 1990-1992, when national data were last available. These data suggest that the ectopic pregnancy rate is not increasing, although differences in the study populations need to be kept in mind. Medical treatment seems to be increasing over time.

An overview of the research capabilities and the future plans on the MA-class National Spherical Torus Experiment (NSTX) at Princeton is presented. NSTX research is exploring the scientific benefits of modifying the field line structure from that in more conventional aspect ratio devices, such as the tokamak. The relevant scientific issues pursued on NSTX include energy confinement, MHD stability at high beta, non-inductive sustainment, solenoid-free start-up, and power and particle handling. In support of the NSTX research goal, research tools are being developed by the NSTX team. In the context of the fusion energy development path being formulated in the US, an ST-based Component Test Facility (CTF) and, ultimately a high beta Demo device based on the ST, are being considered. For these, it is essential to develop high performance (high beta and high confinement), steady-state (non-inductively driven) ST operational scenarios and an efficient solenoid-free start-up concept. We will also briefly describe the Next-Step-ST (NSST) device being designed to address these issues in fusion-relevant plasma conditions.

The SEL (Spectral ELement) macroscopic modeling code for magnetically confined plasma combines adaptive spectral element spatial discretization and nonlinearly implicit time stepping via Newton's method on massively parallel computers. Static condensation is implemented to construct the Shur complement of the Jacobian matrix, which greatly accelerates the linear system solution and distinguishes itself from conventional Newton–Krylov schemes. Grid alignment with the evolving magnetic field, implemented with a variational principle, is a key component of grid adaptation in SEL, and is critical to toroidal plasma applications. Results of 2D magnetic reconnection are shown to illustrate the accuracy and efficiency of the parallel algorithms built on the Portable, Extensible Toolkits for Scientific Computing (PETSC) framework.

Steady-state operation of the advanced tokamak reactor relies on maintaining plasma stability with respect to the resistive wall mode ~RWM!. Active magnetic feedback and plasma rotation are the two methods proposed and demonstrated for this purpose. A comprehensive modeling effort including both magnetic feedback and plasma rotation is needed for understanding the physical mechanisms of the stabilization and to project to future devices. For plasma with low rotation, a complete solution for the feedback issue is obtained by assuming the plasma obeys ideal magnetohydrodynamics ~MHDs! and utilizing a normal mode approach ~NMA! @M. S. Chu et al., Nucl. Fusion 43, 441 ~2003!#. It is found that poloidal sensors are more effective than radial sensors and coils inside of the vacuum vessel more effective than outside. For plasmas with non-negligible rotation, a comprehensive linear nonideal MHD code, the MARS-F has been found to be suitable. MARS-F @Y. Q. Liu et al., Phys. Plasmas 7, 3681 ~2000!# has been benchmarked in the ideal MHD limit against the NMA. The effect of rotation stabilization of the plasma depends on the plasma dissipation model. Broad qualitative features of the experiment are reproduced. Rotation reduces the feedback gain required for RWM stabilization. Reduction is significant when rotation is near the critical rotation speed needed for stabilization. The International Thermonuclear Experimental Reactor ~ITER! @R. Aymar et al., Plasma Phys. Controlled Fusion 44, 519 ~2002!# ~scenario IV for advanced tokamak operation! may be feedback stabilized with babove the no wall limit and up to an increment of ;50% towards the ideal limit. Rotation further improves the stability.

A conforming representation composed of 2D finite elements and finite Fourier series is applied to 3D nonlinear non-ideal magnetohydrodynamics using a semi-implicit time-advance. The self-adjoint semi-implicit operator and variational approach to spatial discretization are synergistic and enable simulation in the extremely stiff conditions found in high temperature plasmas without sacrificing the geometric flexibility needed for modeling laboratory experiments. Growth rates for resistive tearing modes with experimentally relevant Lundquist number are computed accurately with time-steps that are large with respect to the global Alfven time and moderate spatial resolution when the finite elements have basis functions of polynomial degree (p) two or larger. An error diffusion method controls the generation of magnetic divergence error. Convergence studies show that this approach is effective for continuous basis functions with p ≥ 2, where the number of test functions for the divergence control terms is less than the number of degrees of freedom in the expansion for vector fields. Anisotropic thermal conduction at realistic ratios of parallel to perpendicular conductivity (χ||/χ⊥) is computed accurately with p ≥ 3 without mesh alignment. A simulation of tearingmode evolution for a shaped toroidal tokamak equilibrium demonstrates the effectiveness of the algorithm in nonlinear conditions, and its results are used to verify the accuracy of the numerical anisotropic thermal conduction in 3D magnetic topologies.

Ion dynamics in a field-reversed configuration are explored for a highly elongated device, with emphasis placed on ions having positive canonical angular momentum. Due to angular invariance, the equations of motion are that of a two degree-of-freedom system with spatial variables ρ and ζ. As a result of separation of time scales of motion caused by large elongation, there is a conserved adiabatic invariant, Jρ, which breaks down during the crossing of the phase-space separatrix. For integrable motion, which conserves Jρ, an approximate one-dimensional effective potential was obtained by averaging over the fast radial motion. This averaged potential has the shape of either a double or single symmetric well centered about ζ=0. The condition for the approach to the separatrix and therefore the breakdown of the adiabatic invariance of Jρ is derived and studied under variation of Jρ and conserved angular momentum, πφ. Since repeated violation of Jρ results in chaotic motion, this condition can be used to predi...

A major research goal of the national spherical torus experiment is establishing long-pulse, high beta, high confinement operation and its physics basis. This research has been enabled by facility capabilities developed during 2001 and 2002, including neutral beam (up to 7?MW) and high harmonic fast wave (HHFW) heating (up to 6?MW), toroidal fields up to 6?kG, plasma currents up to 1.5?MA, flexible shape control, and wall preparation techniques. These capabilities have enabled the generation of plasmas with of up to 35%. Normalized beta values often exceed the no-wall limit, and studies suggest that passive wall mode stabilization enables this for H mode plasmas with broad pressure profiles. The viability of long, high bootstrap current fraction operations has been established for ELMing H mode plasmas with toroidal beta values in excess of 15% and sustained for several current relaxation times. Improvements in wall conditioning and fuelling are likely contributing to a reduction in H mode power thresholds. Electron thermal conduction is the dominant thermal loss channel in auxiliary heated plasmas examined thus far. HHFW effectively heats electrons, and its acceleration of fast beam ions has been observed. Evidence for HHFW current drive is obtained by comparision of the loop voltage evolution in plasmas with matched density and temperature profiles but varying phases of launched HHFW waves. Studies of emissions from electron Bernstein waves indicate a density scale length dependence of their transmission across the upper hybrid resonance near the plasma edge that is consistent with theoretical predictions. A peak heat flux to the divertor targets of 10?MW?m?2 has been measured in the H mode, with large asymmetries being observed in the power deposition between the inner and outer strike points. Non-inductive plasma startup studies have focused on coaxial helicity injection. With this technique, toroidal currents up to 400?kA have been driven, and studies to assess flux closure and coupling to other current drive techniques have begun.

Research on the spherical torus (or spherical tokamak) (ST) is being pursued to explore the scientific benefits of modifying the field line structure from that in more moderate aspect ratio devices, such as the conventional tokamak. The ST experiments are being conducted in various US research facilities including the MA-class National Spherical Torus Experiment (NSTX) at Princeton, and three medium sized ST research facilities: PEGASUS at University of Wisconsin, HIT-II at University of Washington, and CDX-U at Princeton. In the context of the fusion energy development path being formulated in the US, an ST-based Component Test Facility (CTF) and, ultimately a Demo device, are being discussed. For these, it is essential to develop high performance, steady-state operational scenarios. The relevant scientific issues are energy confinement, MHD stability at high beta (?), non-inductive sustainment, Ohmic-solenoid-free start-up, and power and particle handling. In the confinement area, the NSTX experiments have shown that the confinement can be up to 50% better than the ITER-98-pby2 H-mode scaling, consistent with the requirements for an ST-based CTF and Demo. In NSTX, CTF-relevant average toroidal beta values ?T of up to 35% with a near unity central ?T have been obtained. NSTX will be exploring advanced regimes where ?T up to 40% can be sustained through active stabilization of resistive wall modes. To date, the most successful technique for non-inductive sustainment in NSTX is the high beta poloidal regime, where discharges with a high non-inductive fraction (~60% bootstrap current+NBI current drive) were sustained over the resistive skin time. Research on radio-frequency (RF) based heating and current drive utilizing high harmonic fast wave and electron Bernstein wave is also pursued on NSTX, PEGASUS, and CDX-U. For non-inductive start-up, the coaxial helicity injection, developed in HIT/HIT-II, has been adopted on NSTX to test the method up to Ip ~ 500?kA. In parallel, start-up using a RF current drive and only external poloidal field coils are being developed on NSTX. The area of power and particle handling is expected to be challenging because of the higher power density expected in the ST relative to that in conventional aspect-ratio tokamaks. Due to its promise for power and particle handling, liquid lithium is being studied in CDX-U as a potential plasma-facing surface for a fusion reactor.

Study Objective To assess the safety and efficacy of the HydroThermAblator (HTA) system to treat patients with menorrhagia and submucous myomas up to 4 cm in diameter. Design Retrospective, multicenter, cohort study (Canadian Task Force classification II-2). Setting Two medical centers from a large, prepaid, multispecialty health maintenance organization. Patients Twenty-two women. Intervention HTA endometrial ablation. Measurements and Main Results The HTA circulates free-flowing, heated (90° C) saline in the uterine cavity for 10 minutes under direct hysteroscopic control. All procedures were performed in the office under local anesthesia after premedication with oral anxiolytic and analgesic agents. At least 1 year after treatment (average follow-up 15.4 mo, range 12–20 mo), women were contacted regarding their menstrual history. Success was defined as no additional medical or surgical intervention. Amenorrhea was defined as no bleeding, eumenorrhea as normal periods, and oligomenorrhea as less than a normal period. Twelve patients (54%) reported complete amenorrhea; 7 were premenopausal (41% amenorrhea rate) and 5 were postmenopausal (100% amenorrhea rate). Five (23%) reported oligomenorrhea and three (14%) eumenorrhea, and were very satisfied with the result. The overall success rate was 91%. Of two failures (9%), one woman had a repeat HTA 13 months later for menorrhagia. The other had a repeat HTA for persistent spotting and sustained a false passage and small perforation before the procedure began. She elected to have a vaginal hysterectomy 1 month later. Although the results are not statistically significant, patients were extremely satisfied with the outcomes, and no serious complications were related to the device or its use for this indication. Conclusion HTA is probably safe and effective in treating women with menorrhagia and submucous myomas up to 4 cm in diameter. It offers advantages over hysterectomy and electrosurgical resection since it is an office-based procedure, and significant advantages over other global ablation technologies that, by their design, are unable to treat significantly distorted uterine cavities.

Feedback stabilization of the resistive wall mode (RWM) of a plasma in a general feedback configuration is formulated in terms of the normal modes of the plasma-resistive wall system. The growth/damping rates and the eigenfunctions of the normal modes are determined by an extended energy principle for the plasma during its open (feedback) loop operation. A set of equations are derived for the time evolution of these normal modes with currents in the feedback coils. The dynamics of the feedback system is completed by the prescription of the feedback logic. The feasibility of the feedback is evaluated by using the Nyquist diagram method or by solving the characteristic equations. The elements of the characteristic equations are formed from the growth and damping rates of the normal modes, the sensor matrix of the perturbation fluxes detected by the sensor loops, the excitation matrix of the energy input to the normal modes by the external feedback coils, and the feedback logic. (The RWM is also predicted to be excited by an external error field to a large amplitude when it is close to marginal stability.) This formulation has been implemented numerically and applied to the DIII-D tokamak. It is found that feedback with poloidal sensors is much more effective than feedback with radial sensors. Using radial sensors, increasing the number of feedback coils from a central band on the outboard side to include an upper and a lower band can substantially increase the effectiveness of the feedback system. The strength of the RWM that can be stabilized is increased from γτw = 1 to 30 (γ is the growth rate of the RWM in the absence of feedback and τw is the resistive wall time constant) Using poloidal sensors, just one central band of feedback coils is sufficient for the stabilization of the RWM with γτw = 30.

This paper describes the modelling of the feedback control and rotational stabilization of the resistive wall mode (RWM) in tokamaks. A normal mode theory for the feedback stabilization of the RWM has been developed for an ideal plasma with no toroidal rotation. This theory has been numerically implemented for general tokamak geometry and applied to the DIII-D tokamak. A general formulation is further developed for the feedback stabilization of a tokamak with toroidal rotation and plasma dissipation. It has been used to understand the role of the external resonant field in affecting the plasma stability and compared with the resonant field amplification phenomenon observed in DIII-D. The effectiveness of a differentially rotating resistive wall in stabilizing the RWM has also been studied numerically. It is found that for a non-circular tokamak, a wide range of flow patterns are all effective. The structure of the RWM predicted from ideal MHD theory has been compared with signals from various diagnostics. It is also projected that based on DIII-D results scaled up to the ITER-FEAT, 33 MW of 1 MeV negative neutral beam injection will be able to sustain plasma rotation sufficient to stabilize the RWM without relying on feedback.

The National Spherical Torus Experiment (NSTX) is currently being upgraded to operate at twice the toroidal field and plasma current (up to 1 T and 2 MA), with a second, more tangentially aimed neutral beam (NB) for current and rotation control, allowing for pulse lengths up to 5 s. Recent NSTX physics analyses have addressed topics that will allow NSTX-Upgrade to achieve the research goals critical to a Fusion Nuclear Science Facility. These include producing stable, 100% non-inductive operation in high-performance plasmas, assessing plasma–material interface (PMI) solutions to handle the high heat loads expected in the next-step devices and exploring the unique spherical torus (ST) parameter regimes to advance predictive capability. Non-inductive operation and current profile control in NSTX-U will be facilitated by co-axial helicity injection (CHI) as well as radio frequency (RF) and NB heating. CHI studies using NIMROD indicate that the reconnection process is consistent with the 2D Sweet–Parker theory. Full-wave AORSA simulations show that RF power losses in the scrape-off layer (SOL) increase significantly for both NSTX and NSTX-U when the launched waves propagate in the SOL. Toroidal Alfven eigenmode avalanches and higher frequency Alfven eigenmodes can affect NB-driven current through energy loss and redistribution of fast ions. The inclusion of rotation and kinetic resonances, which depend on collisionality, is necessary for predicting experimental stability thresholds of fast growing ideal wall and resistive wall modes. Neutral beams and neoclassical toroidal viscosity generated from applied 3D fields can be used as actuators to produce rotation profiles optimized for global stability. DEGAS-2 has been used to study the dependence of gas penetration on SOL temperatures and densities for the MGI system being implemented on the Upgrade for disruption mitigation. PMI studies have focused on the effect of ELMs and 3D fields on plasma detachment and heat flux handling. Simulations indicate that snowflake and impurity seeded radiative divertors are candidates for heat flux mitigation in NSTX-U. Studies of lithium evaporation on graphite surfaces indicate that lithium increases oxygen surface concentrations on graphite, and deuterium–oxygen affinity, which increases deuterium pumping and reduces recycling. In situ and test-stand experiments of lithiated graphite and molybdenum indicate temperature-enhanced sputtering, although that test-stand studies also show the potential for heat flux reduction through lithium vapour shielding. Non-linear gyro kinetic simulations have indicated that ion transport can be enhanced by a shear-flow instability, and that non-local effects are necessary to explain the observed rapid changes in plasma turbulence. Predictive simulations have shown agreement between a microtearing-based reduced transport model and the measured electron temperatures in a microtearing unstable regime. Two Alfven eigenmode-driven fast ion transport models have been developed and successfully benchmarked against NSTX data. Upgrade construction is moving on schedule with initial physics research operation of NSTX-U planned for mid-2015.

The method for accelerating ions and electrons in the field-reversed configuration using odd-parity rotating magnetic fields (RMFs) in the ion-cyclotron range-of-frequencies (ICRF) is studied. The approach is based on long, accurate numerical integration of Hamilton’s equations for single-particle orbits. Rapid ion heating to thermonuclear conditions occurs in

Research on the stability of spherical torus plasmas at and above the no-wall beta limit is being addressed on the National Spherical Torus Experiment [M. Ono et al., Nucl. Fusion 40, 557 (2000)], that has produced low aspect ratio plasmas, R/a∼1.27 at plasma current exceeding 1.4 MA with high energy confinement (TauE/TauE_ITER89P>2). Toroidal and normalized beta have exceeded 25% and 4.3, respectively, in q∼7 plasmas. The beta limit is observed to increase and then saturate with increasing li. The stability factor βN/li has reached 6, limited by sudden beta collapses. Increased pressure peaking leads to a decrease in βN. Ideal stability analysis of equilibria reconstructed with EFIT [L. L. Lao et al., Nucl. Fusion 25, 1611 (1985)] shows that the plasmas are at the no-wall beta limit for the n=1 kink/ballooning mode. Low aspect ratio and high edge q theoretically alter the plasma stability and mode structure compared to standard tokamak configurations. Below the no-wall limit, stability calculations show the perturbed radial field is maximized near the center column and mode stability is not highly effected by a nearby conducting wall due to the short poloidal wavelength in this region. In contrast, as beta reaches and exceeds the no-wall limit, the mode becomes strongly ballooning with long poloidal wavelength at large major radius and is highly wall stabilized. In this way, wall stabilization is more effective at higher beta in low aspect ratio geometry. The resistive wall mode has been observed in plasmas exceeding the ideal no-wall beta limit and leads to rapid toroidal rotation damping across the plasma core.

The trajectories of ions confined in a field-reversed configuration (FRC) equilibrium magnetic geometry and heated with a small-amplitude, odd-parity rotating magnetic field (RMF) have been studied with a Hamiltonian computer code. When the RMF frequency is in the ion-cyclotron range, explosive heating occurs. Higher-energy ions are found to have betatron-type orbits, preferentially localized near the FRC's midplane. These results are relevant to a compact magnetic-fusion-reactor design.

PURPOSE. Cataract surgery is one of the most successful procedures in medicine, and outcome is typically measured by a single factor – improvement in visual acuity. Health-related functional outcome testing, which quantifies the patient's self-reported perception of impairment, can be integrated with objective clinical findings. Based on the patient's self-assessed lifestyle impairment, the physician and patient together can make an informed decision on the treatment that is most likely to benefit the patient. METHOD. A functional outcome test (the Houston Vision Assessment Test – HVAT, copyrighted 1990, 1992) was evaluated in a cataract population of 149 patients from seven study centers. Test results were correlated with objective ophthalmic endpoints. The HVAT divides an estimated total impairment into subcomponents of Visual Impairment (correctable by cataract surgery) and non-visual Physical Impairments (co-morbidities not affected by cataract surgery). RESULTS. In this prospective study, the average...

Purpose Cataract surgery is one of the most successful procedures in medicine, and outcome is typically measured by a single factor - improvement in visual acuity. Health-related functional outcome testing, which quantifies the patient's self-reported perception of impairment, can be integrated with objective clinical findings. Based on the patient's self-assessed lifestyle impairment, the physician and patient together can make an informed decision on the treatment that is most likely to benefit the patient. Method A functional outcome test (the Houston Vision Assessment Test - HVAT, copyrighted 1990, 1992) was evaluated in a cataract population of 149 patients from seven study centers. Test results were correlated with objective ophthalmic endpoints. The HVAT divides an estimated total impairment into subcomponents of Visual Impairment (correctable by cataract surgery) and non-visual Physical Impairments (co-morbidities not affected by cataract surgery). Results In this prospective study, the average Visual Impairment score improved by 19 points (65%) following cataract extraction (the mean HVAT Visual Impairment score was 29 points before surgery and 10 points at 5 months post-surgery, a change of 65%). Physical Impairment remained unchanged by surgery. Visual acuity was a poor predictor of Visual Impairment. Conclusions The HVAT has 11 simple questions. It may be self-administered and is available on the Internet: http://www.DHAC.com. The physician may err if his decision in favor of cataract surgery is based only on visual acuity. The HVAT has the potential to guide the decision-making process between patient and physician.

Lonnie J. King, dvm, ms, mpa, dacvpm; Larry R. Anderson, dvm, md; Carina G. Blackmore, dvm, phd; Michael J. Blackwell, dvm, mph; Elizabeth A. Lautner, dvm, ms; Leonard C. Marcus, vmd, md; Travis E. Meyer, bs; Thomas P. Monath, md; James E. Nave, dvm; Joerg Ohle; Marguerite Pappaioanou, dvm, mpvm, phd, dacvpm; Justin Sobota, ms, dvm; William S. Stokes, dvm, daclam; Ronald M. Davis, md; Jay H. Glasser, phd; Roger K. Mahr, dvm

NIMROD is a code development project designed to study long-wavelength, low-frequency, nonlinear phenomena in toroidal plasmas with realistic geometry and dynamics. The numerical challenges of solving the fluid equations for a fusion plasma are discussed and our discretization scheme is presented. Simulations of a resistive tearing mode show that time steps much greater than the Alfven time are possible without loss of accuracy. Validation tests of a resistive interchange mode in a shaped equilibrium, a ballooning mode and nonlinear activity in reversed-field pinches are described.

Adherently growing mouse fibroblasts were cultivated for days in highly conductive culture media between micro-fabricated electrodes under strong ac-electric fields. Miniature electrodes have improved heat dissipation which allows the use of media with conductivity of more than 1 S/m at field strengths of up to 100 kV/m. Cell division rates, cell motility, cell viability and physiological parameters such as vesiculation were monitored and the actin and β-tubuline structures of cyto-skeleton were imaged by laser scanning fluorescence. The specific effects of polarisation could be differentiated from unspecific effects such as heating. We estimated the real field strength acting on cells. In the kHz-range, field application was clearly limited by membrane dielectric breakdown while temperature increases were less than 3°C. In the MHz-range, much stronger fields could be applied and heating became the limiting factor. Above an induced trans-membrane potential of 130–150 mV cells no longer proliferated under prolonged field application. In the MHz-range (above 5 MHz) cells could be exposed to surprisingly high field strengths (40 kV/m) for days. Therefore, there is a frequency window (up to several 100 MHz) which can be used for cell positioning, manipulation and characterisation techniques without significant loading of cells.

Electrosurgical vaporization, first performed by urologists in prostate surgery, is useful during operative hysteroscopy for endometrial ablation and myomectomy. From June 1995 through May 1996, 9 surgeons performed 44 endometrial ablations and hysteroscopic myomectomies using the vaporization electrode. Our experience with this technique thus far has been very favorable. The procedure is less expensive than laser ablation and is easier to teach than wire loop resection. It is also less tedious than wire loop resection since myoma chips that often obstruct the operator's view are eliminated. Long-term efficacy of this technique remains to be proved.

We present a method for determining the linear resistive magnetohydrodynamic (MHD) stability of an axisymmetric toroidal plasma, based on the method of matched asymptotic expansions. The plasma is partitioned into a set of ideal MHD outer regions, connected through resistive MHD inner regions about singular layers where q=m/n, with m and n toroidal mode numbers, respectively, and q the safety factor. The outer regions satisfy the ideal MHD equations with zero-frequency, which are identical to the Euler-Lagrange equations for minimizing the potential energy δW. The solutions to these equations go to infinity at the singular surfaces. The inner regions satisfy the equations of motion of resistive MHD with a finite eigenvalue, resolving the singularity. Both outer and inner regions are solved numerically by newly developed singular Galerkin methods, using specialized basis functions. These solutions are matched asymptotically, providing a complex dispersion relation which is solved for global eigenvalues and...

Most numerical simulations of the tokamak scrapeoff layer use a mapping to flux coordinates and a piecewise equidistributed grid in those coordinates to resolve multiple length scales and anisotropy. We have developed an alternative numerical method using simple cylindrical coordinates with a complex adaptive grid scheme, based on an unstructured grid of triangles which move adaptively, aligning themselves with the magnetic field and concentrating in regions of sharp gradients.