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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.

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.

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.

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 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 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...

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.

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

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.

The full three-dimensional (3D) approach is now becoming an important issue for all magnetic confinement configurations. It is a necessary condition for the stellarator but also the tokamak and the reversed field pinch (RFP) now cannot be completely described in an axisymmetric framework. For the RFP the observation of self-sustained helical configurations with improved plasma performances require a better description in order to assess a new view on this configuration. In this new framework plasma configuration studies for RFX-mod have been considered both with tools developed for the RFP as well as considering codes originally developed for the stellarator and adapted to the RFP. These helical states are reached through a transition to a very low/reversed shear configuration leading to internal electron transport barriers. These states are interrupted by MHD reconnection events and the large Te gradients at the barriers indicate that both current and pressure driven modes are to be considered. Furthermore the typically flat Te profiles in the helical core have raised the issue of the role of electrostatic and electromagnetic turbulence in these reduced chaos regions, so that a stability analysis in the correct 3D geometry is required to address an optimization of the plasma setup. In this viewtheVMECcode proved to be an effectiveway to obtain helical equilibria to be studied in terms of stability and transport with a suite of well tested codes. In this work, the equilibrium reconstruction technique as well as the experimental evidence of 3D effects and their first interpretation in terms of stability and transport are presented using both RFP and stellarator tools. © 2010 IOP Publishing Ltd.

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.

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.

Recent progress in reducing turbulent transport in stellarators and tokamaks by 3D shaping using a stellarator optimization code in conjunction with a gyrokinetic code is presented. The original applications of the method focused on ion temperature gradient transport in a quasi-axisymmetric stellarator design. Here, an examination both of other turbulence channels and other starting configurations is initiated. It is found that the designs evolved for transport from ion temperature gradient turbulence also display reduced transport from other transport channels whose modes are also stabilized by improved curvature, such as electron temperature gradient and ballooning modes. The optimizer is also applied to evolving from a tokamak, finding appreciable turbulence reduction for these devices as well. From these studies, improved understanding is obtained of why the deformations found by the optimizer are beneficial, and these deformations are related to earlier theoretical work in both stellarators and tokamaks.

An extensive numerical simulation of the Ignitor-Ult plasma dynamics has been carried out using both the free boundary equilibrium code TEQ and the transport and MHD free boundary code TSC. The stability behavior of the plasma - vacuum vessel - poloidal field coils - passive plate system has been analyzed for different machine and plasma configurations. The response of several feedback systems has been studied taking into account the real characteristics of the power supply. The converter and its controller behavior has been extensively studied by means of the simulation program CSMP that uses a lumped parameter model of the system. The results show a good stability behavior over a wide operating range.

The current density in the vicinity of a rational surface of a force-free magnetic field subjected to an ideal perturbation is shown to be the sum of both a smooth and a delta-function distribution, which give comparable currents. The maximum perturbation to the smooth current density is comparable to a typical equilibrium current density and the width of the layer in which the current flows is shown to be proportional to the perturbation amplitude. In the standard linearized theory, the plasma displacement has an unphysical jump across the rational surface, but the full theory gives a continuous displacement. A resolution of the paradox of a jump in the displacement is required for interpreting perturbed tokamak equilibria.

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 a RFP could be relatively easily designed for optimal performance with a spatially constant toroidal loop voltage. A demonstration that interesting solutions exist is given.

We describe a numerical model of a free boundary axisymmetric tokamak plasma and its associated control systems. The plasma is modeled with a hybrid method using two-dimensional velocity and flux functions with surface-averaged MHD equations describing the evolution of the adiabatic invariants. Equations are solved for the external circuits and for the effects of eddy currents in nearby conductors. The method is verified by application to several test problems and used to simulate the formation of a bean-shaped plasma in the PBX experiment.

The role of shear in determining the ideal MHD stability properties of tokamaks is discussed. In particular, the effects of low shear within the plasma upon pressure driven modes are assessed. The standard ballooning theory is shown to break down as the shear is reduced, and the growth rate is shown to be an oscillatory function of n, the toroidal mode number, treated as a continuous parameter. The oscillations are shown to depend on both the pressure profile and the safety factor profile. When the shear is sufficiently weak, the oscillations can result in bands of unstable n-values, which are present even when the standard ballooning theory predicts complete stability. These instabilities are named 'infernal modes'. The occurrence of these instabilities at integer n is shown to be a sensitive function of the q-axis, raising the possibility of a sharp onset as the plasma parameters evolve.

The free-boundary, axisymmetric tokamak simulation code TSC is used to model the transport time-scale evolution and positional stability of the Princeton Beta Experiment (PBX). A disruptive thermal quench will cause the plasma column to move inwards in major radius. It is shown that the plasma can then lose axisymmetric stability, causing it to displace exponentially off the midplane, terminating the discharge. The accuracy of the code is verified by modelling several controlled experimental shots in PBX.

The free-boundary, axisymmetric tokamak simulation code TSC is used to model the transport time scale evolution and positional stability of PBX. A disruptive thermal quench will cause the plasma column to move inward in major radius. It is shown that the plasma can then lose axisymmetric stability, causing it to displace exponentially off the midplane, terminating the discharge. We verify the accuracy of the code by modeling several controlled experiments shots in PBX.

Concerns about the flexibility and robustness of a compact quasiaxial stellarator design are addressed by studying the effects of varied pressure and rotational transform profiles on expected performance. For thirty, related, fully three-dimensional configurations the global, ideal magnetohydrodynamic (MHD) stability and energetic particle transport are evaluated. It is found that tokamak intuition is relevant to understanding the magnetohydrodynamic stability, with pressure gradient driving terms and shear stabilization controlling both the periodicity preserving, N=0, and the nonperiodicity preserving, N=1, unstable kink modes. Global kink modes are generated by steeply peaked pressure profiles near the half radius and edge localized kink modes are found for plasmas with steep pressure profiles at the edge as well as with edge rotational transform above 0.5. Energetic particle transport is not strongly dependent on these changes of pressure and current (or rotational transform) profiles, although a weak inverse dependence on pressure peaking through the corresponding Shafranov shift is found. While good transport and MHD stability are not anticorrelated in these equilibria, stability only results from a delicate balance of the pressure and shear stabilization forces. A range of interesting MHD behaviors is found for this large set of equilibria, exhibiting similar particle transport properties. (C) 2000 American Institute of Physics. [S1070-664X(00)03606-5].

High-beta, low-aspect-ratio ("compact") stellarators are promising solutions to the problem of developing a magnetic plasma configuration for magnetic fusion power plants that can be sustained in steady state without disrupting. These concepts combine features of stellarators and advanced tokamaks and have aspect ratios similar to those of tokamaks (2-4). They are based on computed plasma configurations that are shaped in three dimensions to provide desired stability and transport properties. Experiments are planned as part of a program to develop this concept. A beta = 4% quasi-axisymmetric plasma configuration has been evaluated for the National Compact Stellarator Experiment (NCSX). It has a substantial bootstrap current and is shaped to stabilize ballooning, external kink, vertical, and neoclassical tearing modes without feedback or close-fitting conductors. Quasi-omnigeneous plasma configurations stable to ballooning modes at beta = 4% have been evaluated for the Quasi-Omnigeneous Stellarator (QOS) experiment. These equilibria have relatively low bootstrap currents and are insensitive to changes in beta. Coil configurations have been calculated that reconstruct these plasma configurations, preserving their important physics properties. Theory- and experiment-based confinement analyses are used to evaluate the technical capabilities needed to reach target plasma conditions. The physics basis for these complementary experiments is described. (C) 2000 American Institute of Physics. [S1070-664X(00)94905-X].