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Progress in the area of MHD stability and disruptions, since the publication of the 1999 ITER Physics Basis document (1999 Nucl. Fusion 39 2137-2664), is reviewed. Recent theoretical and experimental research has made important advances in both understanding and control of MHD stability in tokamak plasmas. Sawteeth are anticipated in the ITER baseline ELMy H-mode scenario, but the tools exist to avoid or control them through localized current drive or fast ion generation. Active control of other MHD instabilities will most likely be also required in ITER. Extrapolation from existing experiments indicates that stabilization of neoclassical tearing modes by highly localized feedback-controlled current drive should be possible in ITER. Resistive wall modes are a key issue for advanced scenarios, but again, existing experiments indicate that these modes can be stabilized by a combination of plasma rotation and direct feedback control with non-axisymmetric coils. Reduction of error fields is a requirement for avoiding non-rotating magnetic island formation and for maintaining plasma rotation to help stabilize resistive wall modes. Recent experiments have shown the feasibility of reducing error fields to an acceptable level by means of non-axisymmetric coils, possibly controlled by feedback. The MHD stability limits associated with advanced scenarios are becoming well understood theoretically, and can be extended by tailoring of the pressure and current density profiles as well as by other techniques mentioned here. There have been significant advances also in the control of disruptions, most notably by injection of massive quantities of gas, leading to reduced halo current fractions and a larger fraction of the total thermal and magnetic energy dissipated by radiation. These advances in disruption control are supported by the development of means to predict impending disruption, most notably using neural networks. In addition to these advances in means to control or ameliorate the consequences of MHD instabilities, there has been significant progress in improving physics understanding and modelling. This progress has been in areas including the mechanisms governing NTM growth and seeding, in understanding the damping controlling RWM stability and in modelling RWM feedback schemes. For disruptions there has been continued progress on the instability mechanisms that underlie various classes of disruption, on the detailed modelling of halo currents and forces and in refining predictions of quench rates and disruption power loads. Overall the studies reviewed in this chapter demonstrate that MHD instabilities can be controlled, avoided or ameliorated to the extent that they should not compromise ITER operation, though they will necessarily impose a range of constraints.

The chapter summarizes the physics issues of the demonstration toroidal fusion power plant (Demo) that can be addressed by ITER operation. These include burning plasma specific issues, i.e. energetic particle behaviour and plasma self-heating effects, and a broader class of power-plant scale physics issues that cannot be fully resolved in present experiments. A critical issue for Demo is whether MHD and energetic particle modes driven by fast particles will become unstable and affect plasma performance. Self-heating effects are expected to be especially important for control of steady-state plasmas with internal transport barriers (ITBs) and high bootstrap current fractions. Experimental data from ITER will improve strongly the physics basis of projections to Demo of major plasma parameters such as the energy confinement time, beta and density limits, edge pedestal temperature and density, and thermal loads on in-vessel components caused by ELMs and disruptions. ITER will also serve as a test bed for fusion technology studies, such as power plant plasma diagnostics, heating and current drive systems, plasma facing components, divertor and blanket modules. Finally, ITER is expected to provide benefits for the understanding of burning plasma behaviour in other magnetic confinement schemes.

The 'Progress in the ITER Physics Basis' (PIPB) document is an update of the 'ITER Physics Basis' (IPB), which was published in 1999 [1]. The IPB provided methodologies for projecting the performance of burning plasmas, developed largely through coordinated experimental, modelling and theoretical activities carried out on today's large tokamaks (ITER Physics R&D). In the IPB, projections for ITER (1998 Design) were also presented. The IPB also pointed out some outstanding issues. These issues have been addressed by the Participant Teams of ITER (the European Union, Japan, Russia and the USA), for which International Tokamak Physics Activities (ITPA) provided a forum of scientists, focusing on open issues pointed out in the IPB. The new methodologies of projection and control are applied to ITER, which was redesigned under revised technical objectives. These analyses suggest that the achievement of Q > 10 in the inductive operation is feasible. Further, improved confinement and beta observed with low shear (= high βp = 'hybrid') operation scenarios, if achieved in ITER, could provide attractive scenarios with high Q (> 10), long pulse (>1000 s) operation with beta

Results from MAST concerning the effect of toroidal rotation driven by neutral beam injection (NBI) on sawteeth are presented. The sawtooth period is shown to increase as the co-NBI power, and thus the toroidal plasma rotation, is increased. As the counter-NBI power is increased, the sawtooth period decreases to a minimum that is shorter than in Ohmically heated plasmas, before lengthening at high toroidal flows. The sawtooth period reaches a minimum when the sawtooth precursor changes the direction of rotation. This can be interpreted as the counter-NBI inducing a toroidal flow which balances the intrinsic ion diamagnetic rotation of the plasma, at which point the mode precursor changes direction. Magnetohydrodynamic stability analyses of the ideal n = 1 internal kink mode with respect to toroidal rotation at finite ion diamagnetic frequency show good accordance with the experimental results. When MAST discharges are modelled at the experimental ion diamagnetic frequency, , the ideal n = 1 internal kink mode is stabilized completely by co-rotation approaching the ion sound speed. When the rotation is oriented in the counter- direction, the mode is initially driven more unstable, before being stabilized by high toroidal flows. Experimentally, the radial extent of the sawtooth crash, and hence the q = 1 surface, varies with respect to the sawtooth period. Stability analyses show that the marginally stable radial location of the q = 1 surface reaches a minimum at approximately the same counter-toroidal rotation as that which minimizes the sawtooth period experimentally. The magnitude of the toroidal rotation at the q = 1 surface determines the stabilizing effect of the toroidal flow upon the ideal n = 1 internal kink mode.

First results are reported on the prediction of disruptions in one tokamak, based on neural networks trained on another tokamak. The studies use data from the JET and ASDEX Upgrade devices, with a neural network trained on just seven normalized plasma parameters. In this way, a simple single layer perceptron network trained solely on JET correctly anticipated 67% of disruptions on ASDEX Upgrade in advance of 0.01 s before the disruption. The converse test led to a 69% success rate in advance of 0.04 s before the disruption in JET. Only one overall time scaling parameter is allowed between the devices, which can be introduced from theoretical arguments. Disruption prediction performance based on such networks trained and tested on the same device shows even higher success rates (JET, 86%; ASDEX Upgrade, 90%), despite the small number of inputs used and simplicity of the network. It is found that while performance for networks trained and tested on the same device can be improved with more complex networks and many adjustable weights, for cross-machine testing the best approach is a simple single layer perceptron. This offers the basis of a potentially useful technique for large future devices such as ITER, which with further development might help to reduce disruption frequency and minimize the need for a large disruption campaign to train disruption avoidance systems.

Joint experiments have been conducted on JET and DIII-D to study m = 2, n = 1 neo-classical tearing modes (NTMs). Very similar instability behaviour is observed on both machines and the scaling of the mode island width with β and the observation of n = 1 islands at q = 2, strongly points to these modes being driven by neo-classical effects. Identity experiments using closely matched non-dimensional parameters (plasma shape, aspect ratio, q, ρ* and collisionality) on JET and DIII-D show similar global β-limits for the NTM. Further scalings, which combine broader data sets from JET and DIII-D, show an approximately linear scaling, or slightly stronger, with ion gyro-radius and a relatively weak dependence on collisionality.

A detailed study has been made of the onset and behaviour of (m = 3, n = 2) neoclassical tearing modes (NTMs) on JET, validating many of the underlying concepts in NTM physics. In particular, fitting onset thresholds in terms of the correctly motivated physics parameters produces scalings closer to theoretical expectations. The use of such locally measured parameters also removes previous inconsistencies in the data between different divertor configurations. The evolution of island size with β confirms the predicted levels of bootstrap current, and highlights the role of small island size stabilization terms, which give rise to a seeding requirement for NTMs from some other instability. This seeding requirement is confirmed, and is generally provided by sawteeth in the cases studied here. Although there are a variety of possible seeding mechanisms, for the particular cases studied here, it appears doubtful that the seeds are induced by magnetic coupling. In particular the NTM always appears well below the n = 2 sawtooth precursor harmonic frequency—although they often lock together once the NTM has grown close to saturation. Also, while plasma rotation profiles are favourable for a three wave interaction involving (4, 3) and n = 1 modes, with irregular matches to the appropriate mode frequency condition, there is no clear correlation between such matches and (3, 2) NTM growth rates. Thus, other seeding models should be considered—we have discussed two possibilities: a temporary change to classical tearing stability due to the sawtooth, and flow variation leading to a change in ion polarization current polarity, but neither of these are yet confirmed by the data. A complete resolution of this issue is essential if a predictive theory of NTMs is to be obtained, but it requires further, more detailed experimental measurements, and development of theoretical models. Finally, the nature of the (4, 3) NTM has also been explored. This mode also requires a seed perturbation to be triggered (in these cases supplied by a sawtooth), and occurs at similar local parameter values as the (3, 2) NTM, but with lower heating powers and βN. A cascade process emerges in which successively lower mode number NTMs occur as β is raised.

Experiments have established the regions of parameter space in JET that lead to runaway generation in disruptions. Previous measurements on the structure of the runaway beam have been confirmed. The delay in runaway generation following temperature collapse is found to be caused by the very high density generated by the disruption. It is shown that runaway generation in JET can be best modelled and understood by including avalanche processes.

The non-axisymmetric magnetic field, naturally present in every tokamak, constraints the machine operational space. A set of dedicated ‘Error Field Correction Coils’ (EFCC) is proposed for JET, which will replace the unreliable existing ‘saddle coils’. The new coils are specified to compensate the main harmonic contribution to error field induced modes. The EFCC structural design comprises a cable coil wound in a metallic casing supported on the JET iron magnetic circuit. Existing power supplies will drive the coils. The EFCC are expected to be installed in 2001 JET shutdown.

New experiments on JET, COMPASS-D and DIII-D have identified the critical scalings of error field sensitivity and harmonic content effects, enabling predictions to be made of the requirements for larger devices such as ITER. Thresholds are lowest at low density, a regime proposed for H mode access on ITER. Results suggest a moderate error field sensitivity (δB/B ≈ 10-4) for ITER, comparable with the size of its intrinsic error, although there are uncertainties in scaling behaviour. Other studies on COMPASS-D and DIII-D show that sideband harmonics to the (2, 1) component play an important role. Thus, a correction system for ITER will be important, with flexibility to correct sidebands desirable, possibly assisted by beam rotation. Such a system has been designed and is capable of reducing multiple harmonic error levels to ~ 2 × 10-5.

Details are discussed of a volume neutron source for testing assemblies such as blanket sections in a 14 MeV neutron environment. This neutron source is based on the spherical tokamak. The experimentally confirmed ability of the spherical tokamak to reach very high plasma pressures makes it ideally suited as the basis for a very compact neutron source ( R ∼0.7 m, I p ∼7–12 MA). An outline engineering design for such a device has been established and a detailed thermo-hydraulic and stress analysis is presented, which demonstrates its engineering feasibility. Availability has been estimated by a bottom-up approach and shows a fluence target of 6 MWa m −2 is achievable over a 10 year operational life. Detailed 3D neutronics calculations establish damage and material activation rates and show that the neutron spectrum is very close to that expected in ITER.

The physical understanding of the transport of heavy impurities, like W, is important for the achievement of practical fusion energy. Among the plasma parameters which affect impurity transport, rotation has only recently received the deserved consideration. In addition to the off-diagonal contribution related to the presence of a radial gradient of the toroidal rotation (usually dubbed roto­diffusion), even in moderately rotating plasmas, centrifugal effects of heavy impurities become non-negligible. Plasmas obtained in the hybrid scenario in JET with the ITER-like wall (JETILW) can be used to study these effects on W, since the deuterium toroidal rotation reaches central thermal Mach numbers around 0.4 (Mach of W up to 3.8). At the same time, this study allows us to explore the transport mechanisms which are responsible for the central W accumulation which is often observed in this type of discharges.

An important effect observed in ILW discharges is the change of q = 1 MHD activity in hybrid discharges. The q = 1 activity with the JET C-wall had usually shown no effect on plasma confinement, except for NTM triggering, its main experimental signature being a rotating kink activity interleaving sawteeth crashes. In the C-Wall hybrid scenario sawteeth had low amplitude and frequency, and the rotating precursor had often fishbone characteristic. The radial profile of the mode fluctuation has been calculated using a coherence technique between one pick up coil and 96 ECE measurements along the red L.o.S in Figure 1. As explained in ref.[1], the coherence phase radial profile shows a -jump whenever an island is crossed moving along the plasma radius, this effect is due to the radial displacement of magnetic field lines produced by the rotating island, which has opposite directions on the outer side of the island x-point than on the inner side of the x-point. In the C-Wall hybrid pulses the ECE fluctuation at the q = 1 magnetic frequency did not show any radial phase jump, as can be seen in Figure 2, and therefore had kink characteristic.

A key feature of disruptions during Vertical Displacement Events (VDEs) in JET is the long lasting toroidal variation in the measured plasma currents, i.e. the plasma current asymmetries. The unique magnetic diagnostics at JET (either 2 toroidal opposite or 4 toroidal orthogonal locations) allow for a comprehensive statistical analysis of asymmetrical disruptions with a large scale database. This paper presents analysis of 4854 disruptions over an 18 year period that includes both the JET carbon (C) wall and the ITER-Like (IL) wall (a mixed beryllium/tungsten first wall). In spite of the Ip quench time significantly increasing for IL-wall compared to C-wall disruptions, the observed toroidal asymmetry time integral (~sideways force impulse), did not increase for IL-wall disruptions. The Ip asymmetry is found to have a dominantly m = n = 1 structure and rotates with a sporadic behaviour, in general. The distributions of the number of rotation periods are found to be very similar for both C- and IL-wall disruptions, and multi-turn mode rotation was sometimes observed. The Ip asymmetry amplitude has no degradation with mode rotation frequency for both the C- and IL-wall disruption data, and therefore dynamic amplification remains a potentially serious issue for ITER due to possible mechanical resonance of the machine components with the rotating asymmetry.

Disruptions are a critical issue for ITER because of the high thermal and magnetic energies that are released on short time scales, which results in extreme forces and heat loads. The choice of material of the plasma facing components (PFCs) can have significant impact on the loads that arise during a disruption. With the ITER-like wall (ILW) in JET made of beryllium in the main chamber and tungsten in the divertor, the main finding is a low fraction of radiation. This has dropped significantly with the ILW from 50­100% of the total energy being dissipated during disruptions in CFC wall plasmas, to less than 50% on average and down to just 10% for VDEs. All other changes in disruption properties and loads are consequences of this low radiation: long current quenches, high vessel forces caused by halo currents and toroidal current asymmetries as well as severe heat loads. Temperatures close to the melting limit have been locally observed on upper first wall structures during deliberate VDE and even at plasma currents as low as 1.5MA and thermal energy of about 1.5MJ only. A high radiation fraction can be regained by massive injection of a mixture of 10%Ar with 90%D2. This accelerates the current quench thus reducing the halo current and sideways impulse. The temperature of PFCs stays below 400oC. MGI is now a mandatory tool to mitigate disruptions in closed-loop operation for currents at and above 2.5MA in JET.

The behaviour of tungsten in the core of hybrid scenario plasmas in JET with the ITER-like wall is analyzed and modelled with a combination of neoclassical and gyrokinetic codes. In these discharges, good confinement conditions can be maintained only for the first 2 - 3 seconds of the high power phase. Later W accumulation is regularly observed, often accompanied by the onset of magnetohydrodynamical activity, in particular neoclassical tearing modes (NTMs), both of which have detrimental effects on the global energy confinement. The dynamics of the accumulation process is examined, taking into consideration the concurrent evolution of the background plasma profiles, and the possible onset of NTMs. Two time slices of a representative discharge, before and during the accumulation process, are analysed with two indipendent methods, in order to reconstruct the W density distribution over the poloidal cross-section. The same time slices are modelled, computing both neoclassical and turbulent transport components and consistently including the impact of centrifugal effects, which can be significant in these plasmas, and strongly enhanceW neoclassical transport. The modelling closely reproduces the observations and identifies inward neoclassical convection due to the density peaking of the bulk plasma in the central region as the main cause of the accumulation. The analysis of a large set of discharges provides clear indications that this effect is generic in this scenario. The unfavorable impact of the onset of NTMs on the W behaviour, observed in several discharges, is suggested to be a consequence of a detrimental combination of the effects of neoclassical transport and of the appearance of an island.

This paper examines the economics of magnetic fusion power generation, makes comparisons with other generation sources, and draws attention to some key issues. For other generation sources, the dat...

Rapid variations in the rotation frequency of a 2/1 tearing mode have been observed in the COMPASS-D tokamak when the frequency is in the range 5 kHz-500 Hz. This range of frequencies, referred to as the `forbidden` frequency band, is explained in terms of an analytical model for toroidal force balance. The model balances the toroidal torque due to viscous fluid coupling between the island and the naturally rotating plasma against the electromagnetic forces on the mode due to interaction with a resistive wall and interaction with any error fields which may be resonant with the mode. Simple analytical expressions are derived for the values of the upper and lower bounds of the forbidden band. The size of the forbidden band is found to depend only on the initial mode rotation frequency and the wall time for the mode. The model is also employed to explain modes that alternate in frequency between the upper and lower limits of the forbidden band, a phenomenon referred to as mode `skipping`, when a low level error field is applied

The theory of the marfe stability in a plasma is generalized by using the equilibrium temperature as the independent variable. The description incorporates both perpendicular and parallel transport

A formalism has been developed and incorporated in the computer code FAR to solve the magnetohydrodynamic (MHD) equations compressibly or incompressibly for either ideal or resistive modes. A linear subset or the full nonlinear set of equations can be solved, in toroidal geometry, with no ordering assumptions. Significant features of the formalism include (1) the addition of compressibility by adding two equations to a basic incompressible set, (2) the ability of the code to converge very rapidly for linear calculations, and (3) the use of a diffusive term in the evaluation of the compressible part of the velocity. This term damps the short-wavelength waves and allows a time step size which is comparable to that needed for incompressible simulations.

The START experiment (Small Tight Aspect Ratio Tokamak) is a low-budget device under construction that is specifically intended to investigate MHD behavior at extremely tight aspect ratios (as low as R/a-1.2) as well as the effectiveness of a major radius compression technique to produce high toroidal current in such plasmas. The main components of the START assembly are described along with the mode of operation. >

A new scenario to delay or prevent neoclassical tearing mode (NTM) onset is presented. By active sawtooth destabilization, short period and low amplitude sawteeth are generated, such that the sawtooth produced NTM seed island is reduced and the threshold normalized plasma pressure for triggering of NTMs, beta(Nonset), is increased. The scenario has been explored experimentally in the Joint European Torus (JET). Ion cyclotron resonance frequency (ICRF) waves tuned to the 2nd harmonic H-minority resonance have been used for sawtooth control. Whereas ICRF waves generally induce sawtooth stabilization, favouring the triggering of NTMs and reducing beta(Nonset), the present experiments show that by toroidally directed waves, ion cyclotron current drive is produced, and that sawteeth can be destabilized by careful positioning of the 2nd harmonic H resonance layer with respect to the sawtooth inversion radius. As a result, NTM onset is delayed and beta(Nonset) is increased above its value obtained in discharges with additional heating from neutral beam injection alone.

A range of ITER relevant plasma stability issues has been studied in the JET tokamak; these include the effects of fast particles on sawteeth, control of NTMs via sawtooth seeds, scaling of m=2, n=1 NTM thresholds and the effect of error fields on plasma rotation and vice-versa. The sawtooth studies have examined both the effects of ICRF and NBI fast particles, and models used for ITER predictions have been validated. Large sawteeth, due to fast particle stabilisation, have been shown to trigger m=3, n=2 NTMs at low beta. Conversely the use of ICRF to produce small short-period sawteeth has been shown to raise the NTM ?-limit, indicating the value of local heating and current drive near q=1. The marginal-? (??,marg) below which the m=3, n=2 NTM is unconditionally stable has been examined; it is found that ??,marg scales almost linearly with ?* and typical H-mode (with q95?3) discharges are meta-stable to NTMs (ie a sufficiently large seed can always destabilise an NTM). The m=2, n=1 NTM has been studied in a joint scaling experiment with the DIII-D tokamak. These experiments, using closely matched non-dimensional parameters (plasma shape, R/a, q, gyroradius and collisionality) on DIII-D and JET, show similar NTM ?-limits and consistent scalings. The issue of error field thresholds and their variation with plasma rotation has also been studied, helping to clarify scalings to ITER.

The transport, flow shear, and linear growth rates of microturbulence are studied for a Joint European Torus (JET) plasma with high central q in which an internal transport barrier (ITB) forms and grows to a large radius. The linear microturbulence growth rates of the fastest growing (most unstable) toroidal modes with high toroidal mode number are calculated using the GS2 and FULL gyrokinetic codes. These linear growth rates, gamma (subscript lin) are large, but the flow-shearing rates, gamma (subscript ExB) (dominated by the toroidal rotation contribution) are also comparably large when and where the ITB exists.

Several improvements to the MAST plant and diagnostics have facilitated new studies advancing the physics basis for ITER and DEMO, as well as for future spherical tokamaks (STs). Using the increased heating capabilities P NBI ⩽ 3.8 MW H-mode at I p = 1.2 MA was accessed showing that the energy confinement on MAST scales more weakly with I p and more strongly with B t than in the ITER IPB98(y, 2) scaling. Measurements of the fuel retention of shallow pellets extrapolate to an ITER particle throughput of 70% of its original designed total throughput capacity. The anomalous momentum diffusion, χϕ, is linked to the ion diffusion, χi, with a Prandtl number close to P ϕ ≈ χϕ/χi ≈ 1, although χi approaches neoclassical values. New high spatial resolution measurements of the edge radial electric field, E r , show that the position of steepest gradients in electron pressure and E r (i.e. shearing rate) are coincident, but their magnitudes are not linked. The T e pedestal width on MAST scales with rather than ρpol. The edge localized mode (ELM) frequency for type-IV ELMs, new in MAST, was almost doubled using n = 2 resonant magnetic perturbations from a set of four external coils (n = 1, 2). A new internal 12 coil set (n ⩽ 3) has been commissioned. The filaments in the inter-ELM and L-mode phase are different from ELM filaments, and the characteristics in L-mode agree well with turbulence calculations. A variety of fast particle driven instabilities were studied from 10 kHz saturated fishbone like activity up to 3.8 MHz compressional Alfvén eigenmodes. Fast particle instabilities also affect the off-axis NBI current drive, leading to fast ion diffusion of the order of 0.5 m2 s−1 and a reduction in the driven current fraction from 40% to 30%. EBW current drive start-up is demonstrated for the first time in a ST generating plasma currents up to 55 kA. Many of these studies contributed to the physics basis of a planned upgrade to MAST.

Summary form only given. Simulation studies of cylindrical MILO (magnetically insulated transmission line oscillator) devices have been performed. The simulations were performed using VENUSRZ, a 2-D relativistic electromagnetic particle-mesh program. The main focus of the simulation studies has been an investigation of the effect of variation of the MILO and loading circuit parameters on the efficiency of power extraction. A number of single-cavity and multicavity power extraction schemes were investigated. Poor efficiencies (~1%) often occur even when the MILO configuration oscillates strongly; however, minor changes are able to convert these efficiencies to over 10% for single-cavity power extraction, with a further doubling for multicavity extraction. Efficient single-cavity extraction needs a large electromagnetic power flow to the output cavity, namely a finite group velocity, n, whereas the typical MILO structure encourages oscillation near the p mode where n is zero

Linear stability properties of the ideal internal kink mode in toroidal geometry are calculated for equilibria in which the q(r) profile is very flat and q ≈ 1 in the core region of the plasma. Marginal stability criteria and growth rates are calculated analytically in the large aspect ratio limit and compared with numerical results from the FAR code. The theory is developed for m = n = 1 modes and for higher m (= n) modes. The temperature perturbation due to adiabatic expansion in the linear phase of the 1/1 mode is calculated and compared with experimental data, showing that the predictions from ideal MHD theory cannot account for the observed temperature increase on JET. Comparison with collisionless theory suggests that the observed temperature increase can be accounted for by compression of the trapped particles.

The non-linear development of the m = 0 resistive 'g' mode has been studied in the reverse-field pinch. A saturation process is shown to exist in which the perturbations cause a quasi-linear flattening of the equilibrium pressure near the m = 0 resonant surface. The mechanism for this flattening is discussed.

Details are given of a numerical study of finite-beta tearing modes in the tokamak. The linear compressible resistive MHD equations are solved in full toroidal geometry with no ordering assumptions. The results show a strong stabilizing effect as beta is increased, arising from the average curvature within the resistive layer. This stabilizing effect is particularly pronounced for high conductivity temperatures and small aspect ratios.

This paper describes the main engineering aspects of the flexible heliac TJ-II, as well as the ECRH scheme that will be used for initial operation. Previous papers have described the physics of the device 1, 2. For description of the concept of a flexible heliac refer to 3, 4.

Calculation of neutral beam deposition and heating in stellarators is complicated by the twisty stellarator geometry and by the usual beam focusing, divergence, and cross-sectional shape considerations. A new deposition code has been written that takes all of this geometry into account. A unique feature of this code is that it gives particle deposition in field-line coordinates, enabling the thermalization problem to be solved more efficiently.