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A neoclassically optimized compact stellarator with simple coils has been designed. The magnetic field of the new stellarator is generated by only four planar coils including two interlocking coils of elliptical shape and two circular poloidal field coils. The interlocking coil topology is the same as that of the Columbia Non-neutral Torus (CNT) [Pedersen et al., Phys. Rev. Lett. 88, 205002 (2002)]. The new configuration was obtained by minimizing the effective helical ripple directly via the shape of the two interlocking coils. The optimized compact stellarator has very low effective ripple in the plasma core, implying excellent neoclassical confinement. This is confirmed by the results of the drift-kinetic code SFINCS [Landreman et al., Phys. Plasmas 21, 042503 (2014)], showing that the particle diffusion coefficient of the new configuration is one order of magnitude lower than CNT's.

An optimization study of Quasi-Axisymmetric (QA) stellarators with varied elongation has been carried out using the optimization code STELLOPT. The starting point of our optimization is a previously obtained QA stellarator with three field periods and an aspect ratio of 6. A series of QA stellarators are obtained at zero plasma beta with the varied elongation value ranging from 2.5 to 3.7. A good quasi-symmetry is kept when the elongation value is reduced from the original value of 3.7. The rotational transform profile and aspect ratio are kept fixed. The plasma volume is ether kept fixed or varied linearly with elongation. Furthermore, finite beta QA stellarators are considered. The corresponding bootstrap currents are calculated using the kinetic code SFINCS. A series of kink-stable QA stellarators are obtained via optimization with varied plasma beta up to 5% and self-consistent bootstrap current. This work demonstrates that good QA stellarators with finite beta and varied elongation exist that are stable to external kink modes.

The National Compact Stellarator Experiment (NCSX) was designed to test a compact, quasiaxisymmetric stellarator configuration. Flexibility and accurate realization of its complex 3D geometry were key requirements affecting the design and construction. While the project was terminated before completing construction, there were significant engineering accomplishments in design, fabrication, and assembly. The design of the stellarator core device was completed. All of the modular coils, toroidal field coils, and vacuum vessel sectors were fabricated. Critical assembly steps were demonstrated. Engineering advances were made in the application of CAD modeling, structural analysis, and accurate fabrication of complex-shaped components and subassemblies. The engineering accomplishments of the project are summarized

The National Compact Stellarator Experiment (NCSX) will study the physics of low-aspect ratio, high-β, quasi-axisymmetric stellarators. To achieve the scientific goals of the NCSX mission, the devi...

As part of an early PPPL pilot plant study an engineering exercise was undertaken to straighten the stellarator modular coil (MC) back legs to provide greater access to plasma components. Saddle coils were located within separate enclosures and configured to reconstitute changes in the magnetic fields caused by straightening the MC back legs. A follow on lab directed research study looked to further improve stellarator maintenance by considering higher aspect ratio plasmas along with improving the MC defining metrics by adding engineering maintenance requirements to the physics code used in defining the modular coil winding configuration. The physics design code (COILOPT) was upgraded to provide coil solutions with straightened MC back legs and to receive inputs of engineering constraints on the MC surface geometry and winding centers. Several improvements and extensions of COILOPT++ were made which include: the ability to target coil penalties and freeze coil geometry for individual coils; adding torsion constraints on the geometry of the space curve defining the MC winding; allowing freedom to straighten MC back legs over asymmetric distances above and below the outboard midplane; the inclusion of nested saddles with enforced minimum coil-to-coil separation distances and adding the ability to accept coil winding surface geometry from Pro- E. These changes along with a number of other features have substantially improved our ability to achieve better self-consistency between engineering maintenance requirements and plasma surface reconstructions with targeted physics. Using the new COILOPT++ code, a first pass design of an improved maintenance stellarator device has been developed. The code details and the ensuing device design will be presented.

It is demonstrated that there exists a plausible evolution of the discharge from the vacuum state to the desired high beta state with the self-consistent bootstrap current profile. The discharge evolution preserves stability and has adequate quasi axisymmetry along this trajectory. The study takes advantage of the quasi-axisymmetric nature of the device to model the evolution of flux and energy in two dimensions. The plasma confinement is modeled to be consistent with empirical scaling. The ohmic circuit, the plasma density, and the timing of the neutral beam heating control the poloidal flux evolution. The resulting pressure and current density profiles are then used in a three-dimensional optimization to find the desired sequence of equilibria. In order to obtain this sequence, active control of the helical and poloidal fields is required. These results are consistent with the planned power systems for the magnets.

The Columbia Nonneutral Torus is a new stellarator experiment being built at Columbia University, New York, to study the confinement of nonneutral and electron-positron plasmas. It will be a two-period, ultralow aspect ratio classical stellarator configuration created from four circular coils. The theory of the confinement and transport of pure electron plasmas on magnetic surfaces is reviewed. The guiding principles behind the experimental design are presented, together with the actual experimental design configuration.

An exploration of stellarator configuration space z for quasi-axisymmetric stellarator (QAS) designs is discussed, using methods which provide a more global view of that space. To this end, a “differential evolution” search algorithm has been implemented in an existing stellarator optimizer, which is much less prone to become trapped in local, suboptimal minima of the cost function χ than the local search methods used previously. This search algorithm is complemented by mapping studies of χ over z aimed at gaining insight into the results of the automated searches. It is found that a wide range of the attractive QAS configurations previously found fall into a small number of classes, with each class corresponding to a basin of χ(z). Maps are developed on which these earlier stellarators can be placed, the relations among them seen, and understanding gained into the physics differences between them. It is also found that, while still large, the region of z space containing practically realizable QAS config...

Compact optimized stellarators offer novel solutions for confining high-beta plasmas and developing magnetic confinement fusion. The three-dimensional plasma shape can be designed to enhance the magnetohydrodynamic (MHD) stability without feedback or nearby conducting structures and provide drift-orbit confinement similar to tokamaks. These configurations offer the possibility of combining the steady-state low-recirculating power, external control, and disruption resilience of previous stellarators with the low aspect ratio, high beta limit, and good confinement of advanced tokamaks. Quasi-axisymmetric equilibria have been developed for the proposed National Compact Stellarator Experiment (NCSX) with average aspect ratio 4-4.4 and average elongation similar to 1.8. Even with bootstrap-current consistent profiles, they are passively stable to the ballooning, kink, vertical, Mercier, and neoclassical-tearing modes for beta > 4%, without the need for external feedback or conducting walls. The bootstrap current generates only 1/4 of the magnetic rotational transform at beta = 4% (the rest is from the coils); thus the equilibrium is much less non-linear and is more controllable than similar advanced tokamaks. The enhanced stability is a result of 'reversed' global shear, the spatial distribution of local shear, and the large fraction of externally generated transform. Transport simulations show adequate fast-ion confinement and thermal neoclassical transport similar to equivalent tokamaks. Modular coils have been designed which reproduce the physics properties, provide good flux surfaces, and allow flexible variation of the plasma shape to control the predicted MHD stability and transport properties.

A new global optimization technique for designing stellarator coils has been developed and applied to the design of coils for the National Compact Stellarator Experiment. Using this technique coil sets were found with fewer coils and lower current densities than those obtained with traditional methods. A new coil design procedure which uses a genetic algorithm as the core optimization method is described and the resulting advanced coil designs presented.

Experimental devices for the study of the physics of high beta (β 4%), low aspect ratio (A 4.5) stellarator plasmas require coils that will produce plasmas satisfying a set of physics goals, provide experimental flexibility and be practical to construct. In the course of designing a flexible coil set for the National Compact Stellarator Experiment, several innovations have been made that may be useful in future stellarator design efforts. These include: the use of singular value decomposition methods for obtaining families of smooth current potentials on distant coil winding surfaces from which low current density solutions may be identified; the use of a control matrix method for identifying which few of the many detailed elements of a stellarator boundary must be targeted if a coil set is to provide fields to control the essential physics of the plasma; the use of a genetic algorithm for choosing an optimal set of discrete coils from a continuum of potential contours; the evaluation of alternate coil topologies for balancing the trade-off between physics objectives and engineering constraints; the development of a new coil optimization code for designing modular coils and the identification of a `natural' basis for describing current sheet distributions.

Simulation studies of plasma shape identification and shape control for the proposed Korea superconducting tokamak advanced research (KSTAR) are described. It is shown that the total number of magnetic measurements can be effectively reduced by considering the patterns of magnetic flux and fields, generated by plasma, along a prescribed measurement contour. The effect of eddy currents on shape identification is investigated in dynamic simulations. The isoflux control scheme and a standard PID control law are adopted for the development of a model shape control system. It is shown that appropriate weighting factors of poloidal field coils, incorporating the efficacy of each coil to a shape control point, can significantly reduce the total feedback power required for a shape control action. Finally, a shape control simulation using calculated flux errors, which correspond to a more realistic experimental situation, is presented.

The National Spherical Torus Experiment (NSTX) is being built at the Princeton Plasma Physics Laboratory to test the fusion physics principles for the Spherical Torus (ST) concept at the MA level. The NSTX nominal plasma parameters are R {sub 0} = 85 cm, a = 67 cm, R/a greater than or equal to 1.26, B {sub T} = 3 kG, I {sub p} = 1 MA, q {sub 95} = 14, elongation {kappa} less than or equal to 2.2, triangularity {delta} less than or equal to 0.5, and plasma pulse length of up to 5 sec. The plasma heating/current drive (CD) tools are High Harmonic Fast Wave (HHFW) (6 MW, 5 sec), Neutral Beam Injection (NBI) (5 MW, 80 keV, 5 sec), and Coaxial Helicity Injection (CHI). Theoretical calculations predict that NSTX should provide exciting possibilities for exploring a number of important new physics regimes including very high plasma beta, naturally high plasma elongation, high bootstrap current fraction, absolute magnetic well, and high pressure driven sheared flow. In addition, the NSTX program plans to explore fully noninductive plasma start-up, as well as a dispersive scrape-off layer for heat and particle flux handling.

Key physics issues in the design of a high- quasi-axisymmetric stellarator configuration are discussed. The goal of the design study is a compact stellarator configuration with aspect ratio comparable to that of tokamaks and good transport and stability properties. Quasi- axisymmetry has been used to provide good drift trajectories. Ballooning stabilization has been accomplished by strong axisymmetric shaping, yielding a stellarator configuration whose core is in the second stability regime for ballooning modes. A combination of externally generated shear and non-axisymmetric corrugation of the plasma boundary provides stability to external kink modes even in the absence of a conducting wall. The resulting configuration is also found to be robustly stable to vertical modes, increasing the freedom to perform axisymmetric shaping. Stability to neoclassical tearing modes is conferred by a monotonically increasing profile. A gyrokinetic f code has been used to confirm the adequacy of the neoclassical confinement. Neutral beam losses have been evaluated with Monte Carlo codes.

The Korea Superconducting Tokamak Advanced Research (KSTAR) tokamak will have superconducting magnets for both the poloidalfield (PF) coils and the toroidal field (TF) coils. The physical arrangement of the PF configuration has 14 coils external to the TF coils. The analysis of the equilibrium flexibility of the KSTAR PF system determines the coil currents required to maintain prescribed equilibrium configurations over the desired range ofoperational parameters specified for I p (q 95 ), β N , and i (3). Constraints on the plasma separatrix and the flux linkage through the geometric center of the plasma are specified for the free-boundary equilibrium calculations. The ripple magnitude due to the finite number of TF coils and the size of the port for the neutral beam (NB) injector determine the number, size, and shape of TF coils. Two ripple criteria for a shaped plasma are used for types of ripple transport. The current design of the TF coil, with 16 coils and a D shape, is big enough to satisfy requirements for the ripple magnitude at the plasma and to provide adequate access for tangential NB injection. The external magnetic diagnostics, magnetic probes and flux loops to detect the plasma boundary are designed by the EFIT code, which uses a realistic distributed current source constrained by equilibrium. The proposed configuration with 52 full toroidal flux loops and 78 magnetic probes results in

The effect of the passive plate stabilizer on the ideal magnetohydrodynamic (MHD) stability is numerically studied in order to guide its design in the proposed Korea Superconducting Tokamak Advanced Research (KSTAR). The parametric study is systematically performed by taking into account the two major variables: the plate’s distance from the plasma surface, and the poloidal (toroidally continuous) vacuum gap required for the access of neutral beam ports and other diagnostics near the outboard mid-plane. Extensive calculations are carried out on the plasma beta limits for low-n (n being toroidal mode number) MHD modes in several major operating regimes. The results lead to a practical and optimistic design point: plasma-wall separation ≈10 cm, and the outboard gap having a vertical separation of about 80 cm between the upper and lower plates. This is one of the choices that will make it feasible to achieve the advanced operation with bootstrap current fraction of over 80% at βn=5 in the reversed shear mode in KSTAR.

The mission of the National Spherical Torus Experiment (NSTX) is to prove the principles of spherical torus physics by producing high-beta toroidal plasmas that are non-inductively sustained, and whose current profiles are in steady-state. NSTX will be one of the first ultra low a[P(input) up to 11 MW] in order to produce high-beta toroidal (25 to 40%), low collisionality, high bootstrap fraction (less than or equal to 70%) discharges. Both radio-frequency (RF) and neutral-beam (NB) heating and current drive will be employed. Built into NSTX is sufficient configurational flexibility to study a range of operating space and the resulting dependences of the confinement, micro- and MHD stability, and particle and power handling properties. NSTX research will be carried out by a nationally based science team.

Recent progress in the theoretical understanding and design of compact stellarators is described. Hybrid devices, which depart from canonical stellarators by deriving benefits from the bootstrap current which flows at finite beta, comprise a class of low aspect ratio A

We present the results of fast time scale plasma control simulations for the proposed Korea Superconducting Tokamak Advanced Research (KSTAR) tokamak. Here, the fast plasma control includes stabilization of the vertical instability and rapid radial position control. As a simulation tool, we use the tokamak simulation code (TSC). We evaluate the power supply requirements for both the vertical and radial position control with a similar approach to that which was employed in the analysis of the tokamak physics experiments (TPX). In particular, we investigate the efficacy of control coil locations to minimize the power supply requirements. From this study, it is shown that two separate sets of control coils, one responsible for vertical control and the other responsible for radial control, are required to provide robust control of both vertical and radial position for all the anticipated plasmas in KSTAR experiments.

Recently, various schemes for controlling the resistive wall mode have been proposed. Here, the problem of resistive wall mode feedback control is formulated utilizing concepts from electrical circuit theory. Each of the coupled elements (the perturbed plasma current, the poloidal passive shell system and the active coil system) is considered as lumped parameter electrical circuits obeying the usual laws of linear circuit theory. A dispersion relation is derived using different schemes for the feedback logic. The various schemes differ in the choice of sensor signal, which is determined by some combination of the three independent circuit currents. Feedback schemes are discussed which can, ideally, completely stabilize the kink mode. These schemes depend, for their success, on a suitable choice for the location of the sensors. A feedback scheme based on sensing the passive shell eddy current is discussed which seeks to drive the feedback system response to a point of marginal stability. For realizable feedback gain factors, this feedback system can suppress the kink mode amplitude for times that are very long compared with the L/R time-scale of the passive shell system. The circuit equation approach discussed provides a useful means for comparing various control strategies for n ≥ 1 kink mode control, and allows useful analogies to be drawn between kink mode control and the control of n = 0 vertical position instabilities.

Global stability of field-reversed configuration (FRC) plasmas has been studied using a simple rigid body model in the parameter space of s (the ratio of the separatrix radius to the average ion gyro-radius) and plasma elongation E (the ratio of the separatrix length to the separatrix diameter). Tilt stability is predicted, independent of s, for FRC’s with low E (oblate), while the tilt stability of FRC’s with large E (prolate) depends on s/E. It is found that plasma rotation due to ion diamagnetic drift can stabilize the tilt mode when s/E≲1.7. The so-called collisionless ion gyro-viscosity also is identified to stabilize tilt when s/E≲2.2. Combining these two effects, the stability regime broadens to s/E≲2.8, consistent with previously developed theories. A small additional rotation (e.g., a Mach number of 0.2) can improve tilt stability significantly at large E. A similar approach is taken to study the physics of the shift stability. It is found that radial shift is unstable when E 1. However, unlike tilt stability, gyro-viscosity has little effect on shift stability.

The results of two-dimensional calculations of eddy currents induced on external conducting walls surrounding a tokamak are reported. The computed eddy currents are generated by low-n (n=1,2,3) external ideal-magnetohydrodynamic (MHD) instabilities. For a given toroidal mode number n the eddy current patterns are found to be very similar in a variety of plasma configurations, e.g., different edge safety factors and different plasma–wall separation distances, in high beta plasmas. This result is promising for the design of active feedback coils for the stabilization of the resistive wall mode. Also, the effects of having a partial wall that has a poloidal gap on the outboard side are considered. Using the expected gap size in the proposed Korea Superconducting Tokamak Advanced Research (KSTAR) [“The KSTAR tokmak,” in Proceedings of the 17th Symposium on Fusion Engineering, San Diego, 1997 (Institute of Electrical and Electronics Engineers, New York, in press), Paper No. O3.1], the calculation shows that ac...

The National Spherical Tokamak Experiment (NSTX) is an ultra low aspect ratio device with a plasma current of 1 MA. The tokamak features auxiliary heating and current drive with a close-fitting conducting shell to maximize the plasma pressure. NSTX is designed for an experimental pulse length that will demonstrate quasi-steady state non-inductively driven advanced tokamak operation. The design also takes maximum advantage of existing facilities and components from previous Princeton devices to reduce the overall program costs.

Extremely fast vertical displacement events (VDEs) induced by a strong collapse were found in a vertically elongated , high tokamak with a resistive shell through computer simulations using the tokamak simulation code. Although the plasma current quench which has been shown to be the prime cause of VDEs in a relatively low tokamak (Nakamura Y et al 1996 Nucl. Fusion 36 643), was not observed during the VDE evolution, the observed growth rate of VDEs was almost five times faster than the growth rate of the usual positional instability . The essential mechanism of the -collapse-induced VDE was clarified to be the intense enhancement of positional instability due to a large and sudden degradation of the magnetic field decay n-index in addition to the significant destabilization due to a reduction in the stability index . The radial shift of the magnetic axis caused by the collapse induces eddy currents on the resistive shell, and these eddy currents produce a large degradation of the n-index. It is pointed out that the shell geometry characterizes the VDE dynamics, and that the VDE rate depends strongly both on the magnitude of the collapse and the n-index of the equilibria just before the collapse occurs. The JT-60U vacuum vessel is shown to possess the capability of preventing -collapse-induced VDEs.

By introducing a slender current carrying conductor through the geometric centre axis of the TS-3 device at Tokyo University, ultralow aspect ratio tokamak (ULART) configurations have been generated with aspect ratios as low as 1.1. In this extreme limit the transition of the spheromak (qedge=0, Itf=0) to an ULART plasma (qedge=2-20) is studied. The global MHD characteristics of ULART are investigated by comparing the theoretical results with the experimental data obtained. A small current (compared with the plasma current) in the centre conductor is found to improve significantly the global MHD stability characteristics of the plasmas formed by effectively stabilizing the global tilt/shift mode. Theoretical calculations of the threshold toroidal field current required for stability and the growth rates of the tilt/shift modes agree well with the TS-3 data

The characteristics of high- beta , low-q disruptions have been studied in PBX-M, a device with a nearby conducting shell. The coupling between the wall and the plasma was varied by choosing different plasma shapes, including nearly circular plasmas, D-shaped plasmas and bean-shaped plasmas (indented on the midplane), and by increasing the effective coverage of the plasma by the shell. Disruption precursors were observed to have a strong dependence on the coupling between the plasma and the shell. Measured mode growth times vary from between several times the Alfven time-scale (~100 mu s) to the L/R time-scale of the wall (~20 ms). The behaviour of observed disruption precursors is interpreted in terms of the resistive wall mode theory of ideal plasmas, and a detailed calculation of the stability of a strongly coupled bean configuration using the NOVA-W linear stability code is presented. The experimental observations are in good agreement with the theoretical predictions

Vertical displacement events (VDEs), which are frequently observed in disruptive discharges of elongated tokamaks, are investigated using the Tokamak Simulation Code. We show that disruption events such as a sudden plasma pressure drop (β p collapse) and the subsequent plasma current quench (I p quench) can accelerate VDEs due to the adverse destabilizing effect of the resistive shell, which has previously been thought to stabilize VDEs. In a tokamak with a surrounding shell which is asymmetric with respect to the geometric midplane, the I p quench also causes an additional VDE acceleration due to the vertical imbalance of the attractive force. While the shell-geometry characterizes the VDE dynamics, the growth rate of VDEs depends strongly on the magnitude of the β p collapse, the speed of the I p quench and the n-index of the plasma equilibrium just before the disruption. An amelioration of I p quench-induced VDEs was experimentally established in the JT-60U tokamak by optimizing the vertical location of the plasma just prior to the disruption. The JT-60U vacuum vessel is shown to be suitable for preventing the β p collapse-induced VDE.

Enhanced vertical displacement events (VDEs), which are frequently observed in JT-60U disruptive discharges, are investigated using the Tokamak Simulation Code (TSC). The rapid plasma current quench can accelerate the vertical displacement, owing to both the up/down asymmetry of the eddy current distribution arising from the asymmetric geometry of the JT-60U vacuum vessel and the degradation of magnetic field decay index n, leading to high growth rates of positional instability. For a slightly elongated configuration (n=-0.9), the asymmetry of attractive forces on the toroidal plasma plays a dominant role in the VDE mechanism. For a more elongated configuration (n=-1.7), the degradation of field decay index n plays an important role on VDEs, in addition to the effect of asymmetric attractive forces. It is shown that the VDE characteristics of a highly elongated configuration with a rapid plasma current quench can be dominated by the field decay index degradation. It is also pointed out that both the softening of current quenches as was experimentally developed in the JT-60U tokamak, and the optimization of the allowable elongation of the plasma cross-section are critical issues in the development of a general control strategy of discharge termination

We investigate experimentally and theoretically the global MHD characteristics of an ultra-low aspect ratio tokamak (ULART). Since the ULART requires a substantially smaller toroidal field current,...

In this paper a laboratory investigation is made on magnetic reconnection in high‐temperature Tokamak Fusion Test Reactor (TFTR) plasmas [Plasma Physics and Controlled Nuclear Fusion Research 1986 (International Atomic Energy Agency, Vienna, 1987), Vol. 1, p. 51]. The motional Stark effect (MSE) diagnostic is employed to measure the pitch angle profile of magnetic field lines, and hence the q profile. An analytical expression that relates pitch angle to q profile is presented for a toroidal plasma with circular cross section. During the crash phase of sawtooth oscillations in plasma discharges, the ECE (electron cyclotron emission) diagnostic measures a fast flattening of the two‐dimensional (2‐D) electron temperature profile in a poloidal plane, an observation consistent with the Kadomtsev reconnection theory. On the other hand, the MSE measurements indicate that central q values do not relax to unity after the crash, but increase only by 5%–15%, typically from 0.7 to 0.8. The latter result is in contrad...

Two computational models have been applied to calculate the poloidal flux linkage requirements for the current ramp-up and for the flat-top phase of the proposed International Thermonuclear Experimental Reactor (ITER). For the current ramp-up phase, the TSC code has been used to simulate the entire current ramp-up period as described in the TAC-3 Report. The time of the simulation has been extended to cover the full current penetration time, that is, until the loop voltage is a constant throughout the plasma. Sensitivity studies have been performed with respect to current ramp-up time, impurity concentration and to the time of onset of auxiliary heating. A steady state plasma equilibrium code has been used that has the constant loop voltage constraint built in to survey the dependence of the steady state loop voltage on the density and temperature profiles. This calculation takes into account the plasma bootstrap current contribution, including non-circular and collisional corrections. The results can be displayed as contours of the loop voltage on a POPCON-like diagram

A tokamak reactor will operate at the maximum value of β ≡ 2μ0 〈p〉/B2 that is compatible with magnetohydrodynamic (MHD) stability. This value depends on the plasma current and pressure profiles, the plasma shape and aspect ratio, and the location of nearby conducting structures. In addition, a steady state reactor will minimize its external current drive requirements and thus achieve its maximum economic benefit with a bootstrap fraction near unity, IBS/IP ≈ 1, which constrains the product of the inverse aspect ratio and the plasma poloidal β to be near unity, ϵβP ≈ 1. An inductively driven pulsed reactor has different constraints set by the steady-state Ohm's law which relates the plasma temperature and density profiles to the parallel current density. We present the results obtained during ARIES I, II/IV, and III and PULSAR reactor studies where these quantities were optimized subject to different design philosophies. The ARIES-II/IV and ARIES-III designs are both in the second stability regime, but differ in requirements in the form of the profiles at the plasma edge, and in the location of the conducting wall. The relation between these, as well as new attractive MHD regimes not utilized in the ARIES or PULSAR studies, is also discussed.

Stability analysis of advanced regime tokamaks is presented. Here advanced regimes are defined to include configurations where the ratio of the bootstrap current, IBS, to the total plasma current, Ip, approaches unity, and the normalized stored energy, βN* = 80π〈p2〉1/2a/IpB0, has a value greater than 4.5. Here, p is the plasma pressure, a the minor radius in meters, Ip is in mega‐amps, B0 is the magnetic field in Tesla, and 〈⋅〉 represents a volume average. Specific scenarios are discussed in the context of Toroidal Physics Experiment (TPX) [Proceedings of the 20th European Physical Society Conference on Controlled Fusion and Plasma Physics, Lisbon, 1993, edited by J. A. Costa Cabral, M. E. Manso, F. M. Serra, and F. C. Schuller (European Physical Society, Petit‐Lancy, 1993), p. I‐80]. The best scenario is one with reversed shear, in the q profile, in the central region of the tokamak. The bootstrap current obtained from the plasma profiles provides 90% of the required current, and is well aligned with the...

The Tokamak Physics Experiment is designed to develop the scientific basis for a compact and continuously operating tokamak fusion reactor. It is based on an emerging class of tokamak operating modes, characterized by beta limits well in excess of the Troyon limit, confinement scaling well in excess of H-mode, and bootstrap current fractions approaching unity. Such modes are attainable through the use of advanced, steady state plasma controls including strong shaping, current profile control, and active particle recycling control. Key design features of the TPX are superconducting toroidal and poloidal field coils; actively-cooled plasma-facing components; a flexible heating and current drive system; and a spacious divertor for flexibility. Substantial deuterium plasma operation is made possible with an in-vessel remote maintenance system, a lowactivation titanium vacuum vessel, and shielding of ex-vessel components. The facility will be constructed as a national project with substantial participation by U.S. industry. Operation will begin with first plasma in the year 2000.

The Tokamak Simulation Code (TSC) has been used to model the time dependence of several Ohmic discharges in the TFTR experiment. The semi-empirical thermal conductivity model and the sawtooth model in TSC have been refined so that good agreement between the simulation and the experiment is obtained in the electron and ion temperature profiles and in the current profiles for the entire duration of the discharges. Neoclassical resistivity gives good agreement with the measured surface voltage and the rate of poloidal flux consumption

The plasma shaping flexibility of the Compact Ignition Tokamak (CIT) poloidal field (PF) coil set is demonstrated through MHD equilibrium calculations of optimal PF coil current distributions and their variation with poloidal beta, internal inductance, plasma 95% elongation, and 95% triangularity. Calculations of the magnetic stored energy are used to compare solutions associated with various plasma parameters. The Control Matrix (CM) equilibrium code, together with the nonlinear equation and numerical optimization software packages HYBRD, and VMCON, respectively, are used to find equilibrium coil current distributions for fixed divertor geometry, volt-seconds, and plasma profiles in order to isolate the dependence on individual parameters. A reference equilibrium and coil current distribution are chosen, and correction currents dI are determined using the CM equilibrium method to obtain other specified plasma shapes. The reference equilibrium is the {kappa} = 2 divertor at beginning of flattop (BOFT) with a minimum stored energy solution for the coil current distribution. The pressure profile function is fixed.

The Compact Ignition Tokamak is a high-performance device designed to study the physics of burning plasmas. Key physics aspects of the design are described, including plasma performance, disruption...

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.

The maintenance of the magnetic configuration of a Reversed Field Pinch (RFP) is an unsolved problem. Even a toroidal loop voltage does not suffice to maintain the magnetic configuration in axisymmetry but could if the plasma had helical shaping. The theoretical tools for plasma optimization using helical shaping have advanced, so an RFP could be relatively easily designed for optimal performance with a spatially constant toroidal loop voltage. A demonstration that interesting solutions exist is given.

Simulation results obtained with the axisymmetric Princeton Tokamak Simulation Code TSC are compared with experimental results for the time evolution of the Tokamak de Varennes plasma. The code correctly predicts experimental conditions; of special interest are the favourable comparisons of the simulation with experiments during fast current ramp-down (from 250 kA in 40 ms, three times faster than the L/R time).

A time-dependent zero-dimensional code has been developed to assess the pulse length and auxiliary heating requirements of compact ignition tokamak (CIT) designs. By taking a global approach to the calculation, parametric studies can be easily performed. The accuracy of the procedure is tested by comparison with the tokamak simulation code, which uses theory-based thermal diffusivities. A series of runs is carried out at various levels of energy confinement for each of three possible CIT configurations. It is found that for cases of interest ignition or an energy multiplication factor Q {ge} 7 can be attained within the first half of the planned 5-s flattop with 10 to 40 MW of auxiliary heating. These results are supported by analytic calculations.

The national compact stellarator experiment (NCSX) will have an extensive set of external magnetic diagnostics. These include flux loops on the exterior surface of the vacuum vessel. Data from these sensors will be integrated with other magnetic sensors and used for plasma control and to constrain magnetic equilibrium reconstructions. NCSX is currently under construction at the Princeton Plasma Physics Laboratory (PPPL). The ex-vessel flux loops must be installed during machine construction since they will ultimately be trapped in the space between the vacuum vessel and the modular coil support shell. Detailed designs have been completed, locator templates have been fabricated and approximately one third of the 225 total loops have been installed as of mid February 2007. Modeling was performed by PPPL to determine the optimum size, placement and number of turns. Engineering of the flux loops was challenging as they must be accurately positioned, optimized geometry maintained and they must be robust and reliable in a bake and cryogenic environment for the lifetime of NCSX. Designs for the ex-vessel flux loops that meet these requirements are presented.

The first studies of pure electron plasmas confined on magnetic surfaces in the Columbia Non‐neutral Torus are overviewed. The electron plasma is created by a thermionic emitter filament and similar filaments mounted on ceramic rods are used as Langmuir and emissive probes. The equilibrium density, temperature and potential profiles are experimentally measured. Numerical calculations of the equilibrium agree well with measurements and also predict a toroidal density variation of a factor of four. The confinement time is found to decrease with increased neutral pressure and emitter bias voltage, and it is presently limited to 20 ms by the insulated emitter and probe rods. A retractable electron emitter and external diagnostics will be used to determine the confinement time in the absence of rods. Ion driven instabilities are observed at high neutral pressure and low magnetic field strength. Further research of these instabilities will be carried out.

The free-boundary equilibrium code VEQ provides equilibrium data that are used by the Tokamak Simulation Code (TSC) in designing and analyzing the poloidal-field (PF) system for the Compact Ignition Tokamak (CIT). VEQ serves as an important design tool for locating the PF coils and defining coil current trajectories and control systems for the TSC. VEQ and its role in the TSC analysis of the CIT PF system are described. >

The Columbia Non‐neutral Torus (CNT) is a tabletop (R=0.3 m, a=0.1 m, B=0.2 T) stellarator now being constructed at Columbia University. The goal of CNT is to study the equilibrium, stability, and transport of non‐neutral plasmas confined on magnetic surfaces. CNT will use four circular, planar coils: two interlocking coils with a variable tilt angle, plus two additional poloidal field coils. By varying the angle between the interlocking coils, the rotational transform can be varied from 0.2 to 0.6 and the magnetic shear from essentially zero to 20%. The results of a numerical study of how error fields affect the quality of the magnetic surfaces will be presented. The plasma will be diagnosed by numerous Langmuir and sector probes, connected to a computer data acquisition and control system.

A control matrix MHD (magnetohydrodynamic) equilibrium code, BEQ, and the Tokamak Simulation Code (TSC) are used to compute programmed double-null (DN) divertor sweep trajectories that maximize sweep distance while simultaneously satisfying a set of strict constraints: minimum lengths of the field lines between the X-point and strike points, minimum spacing between the inboard plasma edge and the limiter, maximum spacing between the outboard plasma edge and the ICRF (ion cyclotron range of frequencies) antennas, minimum safety factor, and linked poloidal flux. A sequence of DN diverted equilibria and a consistent TSC fiducial discharge simulation are used in evaluating the performance of the BPX (Burning Plasma Experiment) divertor shape and possible modifications. >

The KSTAR (Korea Superconducting Tokamak Advanced Research) project is the major effort of the Korean National Fusion Program to design, construct, and operate a steady-state-capable superconducting tokamak. The project is led by Korea Basic Science Institute and shared by national laboratories, universities, and industry along with international collaboration. It is in the conceptual design phase and aims for the first plasma by mid 2002. The key design features of KSTAR are: major radius 1.8 m, minor radius 0.5 m, toroidal field 3.5 T, plasma current 2 MA, and flexible plasma shaping (elongation 2.0; triangularity 0.8; double-null poloidal divertor). Both the toroidal and the poloidal field magnets are superconducting coils. The device is configured to be initially capable of 20 s pulse operation and then to be upgraded for operation up to 300 s with non-inductive current drive. The auxiliary heating and current drive system consists of neutral beam, ICRF, lower hybrid, and ECRF. Deuterium operation is planned with a full radiation shielding.

The role of the resistive wall mode in limiting tokamak plasma performance is well chronicled and is a central topic of the Feedback Stabilization Initiative (FSI). It is believed that stabilization of this mode, which is a converted branch of the ideal-MHD external kink mode, may lead to the design of devices capable of accessing higher performance advanced operating regimes. We have developed a formulation of the resistive wall mode, for the limiting case of infinite aspect ratio, using the elementary physical concepts of self and mutual inductance. This results in a set of coupled lumped-parameter circuit equations with the variables being the perturbed plasma current, the helical component of induced current in the resistive shell, and (with feedback) the current in the active coil. These equations, which describe plasma perturbations of n/spl ges/1, have a one to one correspondence with plasma vertical positional n=0 control. Comparisons between the dispersion relations for the two cases show that the quantity that carries the strength of the instability for the resistive wall mode, equivalent to the negative decay index in vertical position control, is L/sub pl/(1-f) where L/sub pl/ is the helical inductance of the perturbed plasma current and (1-f) is related to the helicity of the ideal-MHD kink mode. This method has been applied successfully to describe the resistive wall mode in general terms and to describe analytically resistive wall mode feedback stabilization schemes. Formulation in this manner should facilitate numerical simulation of resistive wall mode feedback schemes. In this paper, we describe the formulation in detail, show how the resulting circuit equations compare to the equations arrived at using traditional MHD analysis methods (particularly with the inclusion of feedback), and compare the resistive wall mode equations to those that describe the (n=0) vertical instability.

The National Compact Stellarator Experiment (NCSX) will study the physics of low aspect ratio, high beta quasi-axisymmetric stellarators. In order to achieve the scientific goals of the NCSX mission, the device must be capable of supporting a wide range of variations in plasma configuration about a reference equilibrium. Numerical experiments are presented which demonstrate this capability.

An exploration of stellarator configuration space z for quasi-axisymmetric stellarator (QAS) designs is discussed, using methods which provide a more global view of that space. To this end, we have implemented a ''differential evolution'' (DE) search algorithm in an existing stellarator optimizer, which is much less prone to become trapped in local, suboptimal minima of the cost function chi than the local search methods used previously. This search algorithm is complemented by mapping studies of chi over z aimed at gaining insight into the results of the automated searches. We find that a wide range of the attractive QAS configurations previously found fall into a small number of classes, with each class corresponding to a basin of chi(z). We develop maps on which these earlier stellarators can be placed, the relations among them seen, and understanding gained into the physics differences between them. It is also found that, while still large, the region of z space containing practically realizable QAS configurations is much smaller than earlier supposed.