Fusion Technol Research Articles

Divertor for a steady-state gas-dynamic trap

An analysis is carried out into the possibility of using a device topologically equivalent to a nonparaxial magnetohydrodynamic (MHD) stabilizer as a divertor for the projected ALIANCE source of fusion neutrons based on the gas-dynamic trap, which should operate in a continuous mode. A side effect of adding a divertor to a linear trap is the expected improvement in plasma MHD stability, which was previously observed at the TARA (Casey et al 1988 Phys. Fluids 31 2009–16) and HIEI (Yasaka et al 2001 Fusion Technol. 39 350–3) facilities. To assess the effect of MHD stabilization by a divertor, the article indicates a method for finding stability rings, and also calculates the degree of expansion of the plasma flux in the divertor. The analysis showed that a good divertor, which provides a high degree of expansion, cannot be a good MHD stabilizer, which provides a large margin of stability. The divertor configurations made up of two and three coils are studied, their advantages and disadvantages are described. The final part of the article presents the calculations of the magnetic field in an end cell with a superconducting divertor designed for the GDMT gas-dynamic multi-core trap project (Beklemishev et al 2013 Fusion Sci. Technol. 63 46–51).

Tearing mode dynamics and locking in the presence of external magnetic perturbations

In normal operation, Madison Symmetric Torus (MST) [R. N. Dexter et al., Fusion Technol. 19, 131 (1991)] reversed-field pinch plasmas exhibit several rotating tearing modes (TMs). Application of a resonant magnetic perturbation (RMP) results in braking of mode rotation and, if the perturbation amplitude is sufficiently high, in a wall-locked state. The coils that produce the magnetic perturbation in MST give rise to RMPs with several toroidal harmonics. As a result, simultaneous deceleration of all modes is observed. The measured TM dynamics is shown to be in qualitative agreement with a magnetohydrodynamical model of the RMP interaction with the TM [R. Fitzpatrick, Nucl. Fusion 33, 1049 (1993)] adapted to MST. To correctly model the TM dynamics, the electromagnetic torque acting on several TMs is included. Quantitative agreement of the TM slowing-down time was obtained for a kinematic viscosity in the order of νkin≈10–20 m2/s. Analysis of discharges with different plasma densities shows an increase of the locking threshold with increasing density. Modeling results show good agreement with the experimental trend, assuming a density-independent kinematic viscosity. Comparison of the viscosity estimates in this paper to those made previously with other techniques in MST plasmas suggests the possibility that the RMP technique may allow for estimates of the viscosity over a broad range of plasmas in MST and other devices.

Effect of resonant magnetic perturbations on three dimensional equilibria in the Madison Symmetric Torus reversed-field pinch

The orientation of 3D equilibria in the Madison Symmetric Torus (MST) [R. N. Dexter et al., Fusion Technol. 19, 131 (1991)] reversed-field pinch can now be controlled with a resonant magnetic perturbation (RMP). Absent the RMP, the orientation of the stationary 3D equilibrium varies from shot to shot in a semi-random manner, making its diagnosis difficult. Produced with a poloidal array of saddle coils at the vertical insulated cut in MST's thick conducting shell, an m = 1 RMP with an amplitude br/B ∼ 10% forces the 3D structure into any desired orientation relative to MST's diagnostics. This control has led to improved diagnosis, revealing enhancements in both the central electron temperature and density. With sufficient amplitude, the RMP also inhibits the generation of high-energy (>20 keV) electrons, which otherwise emerge due to a reduction in magnetic stochasticity in the core. Field line tracing reveals that the RMP reintroduces stochasticity to the core. A m = 3 RMP of similar amplitude has little effect on the magnetic topology or the high-energy electrons.

TEM turbulence optimisation in stellarators

With the advent of neoclassically optimised stellarators, optimising stellarators for turbulent transport is an important next step. The reduction of ion-temperature-gradient-driven turbulence has been achieved via shaping of the magnetic field, and the reduction of trapped-electron mode (TEM) turbulence is addressed in the present paper. Recent analytical and numerical findings suggest TEMs are stabilised when a large fraction of trapped particles experiences favourable bounce-averaged curvature. This is the case for example in Wendelstein 7-X (Beidler et al 1990 Fusion Technol. 17 148) and other Helias-type stellarators. Using this knowledge, a proxy function was designed to estimate the TEM dynamics, allowing optimal configurations for TEM stability to be determined with the STELLOPT (Spong et al 2001 Nucl. Fusion 41 711) code without extensive turbulence simulations. A first proof-of-principle optimised equilibrium stemming from the TEM-dominated stellarator experiment HSX (Anderson et al 1995 Fusion Technol. 27 273) is presented for which a reduction of the linear growth rates is achieved over a broad range of the operational parameter space. As an important consequence of this property, the turbulent heat flux levels are reduced compared with the initial configuration.

Homoclinic tangle of the ideal separatrix in the DIII-D tokamak from (30, 10) + (40, 10) perturbation

Trajectories of magnetic field lines are a 1½ degree of freedom Hamiltonian system. The perturbed separatrix in a divertor tokamak is radically different from the unperturbed one. This is because magnetic asymmetries cause the separatrix to form extremely complicated structures called homoclinic tangles. The shape of flux surfaces in the edge region of divertor tokamaks such as the DIII (J. L. Luxon and L. G. Davis, Fusion Technol. 8, 441 (1985)) is fundamentally different from near-circular. Recently, a new method is developed to calculate the homoclinic tangle and lobes of the separatrix of divertor tokamaks in physical space (A. Punjabi and A. Boozer, Phys. Lett. A 378, 2410 (2014)). This method is based on three elements: preservation of the two invariants—symplectic and topological neighborhood—and a new set of canonical coordinates called the natural canonical coordinates. The very complicated shape of edge surfaces can be represented very accurately and very realistically in these new coordinates (A. Punjabi and H. Ali, Phys. Plasmas 15, 122502 (2008); A. Punjabi, Nucl. Fusion 49, 115020 (2009)). A symplectic map in the new coordinates can advance the separatrix manifold forward and backward in time. Every time the two manifolds meet in a fixed poloidal plane, they intersect and form homoclinic tangle to preserve the two invariants. The new coordinates can be mapped to physical space and the dynamical evolution of the homoclinic tangle can be seen and pictured in physical space. Here, the new method is applied to the DIII-D tokamak to study the basic features of the homoclinic tangle of the unperturbed separatrix from two Fourier components, which represent the peeling-ballooning modes of equal amplitude and no radial dependence, and the results are analyzed. Homoclinic tangle has a very complicated structure and becomes extremely complicated for as the lines take more toroidal turns, especially near the X-point. Homoclinic tangle is the most complicated near the X-point and forms the largest lobes there. On average, the field lines cover a distance of about 9 m per turn. Poloidal rotation of the lines has large gradients in the poloidal direction. The average normal displacement of the lines on the separatrix varies from 5 mm to 7 cm. Average outward displacement of the lines is considerably larger than the inward displacement; however, on the average more lines are displaced inside than outside of the separatrix. The field line diffusion normal to the separatrix has extremely wide variation and very large poloidal gradients. Half of all the lines are lost in less than 6 turns. Complicated electric potentials will be required to maintain the neutrality of the plasma, and the E × B drifts from these fields can modify plasma confinement and influence the edge physics (A. Punjabi and A. Boozer, Phys. Lett. A 378, 2410 (2014)).

Characterizing turbulent transport in ASDEX Upgrade L-mode plasmas via nonlinear gyrokinetic simulations

The nature and level of turbulent transport in the outer core of low-confinement (L-mode) discharges performed at the ASDEX Upgrade tokamak [Kallenbach et al., Nucl. Fusion 51, 094012 (2011)] are examined. Previously, it was found that for an L-mode discharge of the DIII-D tokamak [J. L. Luxon and L. G. Davis, Fusion Technol. 8, 441 (1985)] gyrokinetic simulations were unable to reproduce the experimental ion heat flux, underestimating it by almost an order of magnitude. In the present work, employing the GENE gyrokinetic turbulence code, an extensive nonlinear study is performed for L-mode discharges of ASDEX Upgrade in order to cross-check this observation. It is shown that no systematic underprediction can be found in these simulations—instead, discrepancies with respect to experimental transport levels are small enough to be resolved within the uncertainties of the experimental profiles. Moreover, it is shown that some turbulence properties resemble closely those of the underlying linear microinstabilities at least out to 90% of the minor radius, so that quasilinear transport models remain, in principle, applicable even for these parameters, provided that appropriate nonlinear saturation rules can be developed.

Symplectic calculation of magnetic footprints in the DIII-D with low mn and magnetic noise and error fields perturbations

The symplectic mathematical maps in natural canonical coordinates for forward and backward integration of magnetic field lines in the DIII-D tokamak [Luxon, J.L.; Davis, L.E. Fusion Technol. 1985, 8, 441] are used to calculate the magnetic footprints and their associated parameters on the inboard and outboard collector plates from the low mn magnetic perturbation with and without internal topological noise and magnetic field errors. The Grad–Shafranov solver equilibrium fit (EFIT) results from the experimental data for the DIII-D shot 115467 at 3000 ms [Lao, L.; St John, H.; Peng, Q.; Ferron, J.; Strait, E.; Taylor, T.; Meyer, W.; Zhang, C.; You, K. Fusion Sci. Technol. 2005, 48, 968] is used to construct an analytic expression for the equilibrium Hamiltonian function for the field line trajectories. The equilibrium Hamiltonian accurately represents the magnetic geometry of the DIII-D. The inboard and outboard footprints consist of a single toroidally winding stripe. Noise and error fields do not change the topology of the footprints, and have a marginal effect on the size of the footprint. Noise and error fields reduce the fraction of poloidal flux connecting the plates, and at the same time enhance the connection length. Noise and error fields reduce the safety factor. Backward trajectories starting close to the X-point have high safety factor. The new approach of symplectic mathematical maps in natural canonical coordinates can give an accurate and realistic picture of footprint reflecting the unique magnetic geometry of device in physical space.

A multichannel magnetic probe system for analysing magnetic fluctuations in helical axis plasmas

The need to understand the structure of magnetic fluctuations in H-1NF heliac [S. Hamberger et al., Fusion Technol. 17, 123 (1990)] plasmas has motivated the installation of a sixteen former, tri-axis helical magnetic probe Mirnov array (HMA). The new array complements two existing poloidal Mirnov arrays by providing polarisation information, higher frequency response, and improved toroidal resolution. The helical placement is ideal for helical axis plasmas because it positions the array as close as possible to the plasma in regions of varying degrees of favourable curvature in the magnetohydrodynamic sense, but almost constant magnetic angle. This makes phase variation with probe position near linear, greatly simplifying the analysis of the data. Several of the issues involved in the design, installation, data analysis, and calibration of this unique array are presented including probe coil design, frequency response measurements, mode number identification, orientation calculations, and mapping probe coil positions to magnetic coordinates. Details of specially designed digitally programmable pre-amplifiers, which allow gains and filters to be changed as part of the data acquisition initialisation sequence and stored with the probe signals, are also presented. The low shear heliac geometry [R. Jiménez-Gómez et al., Nucl. Fusion 51, 033001 (2011)], flexibility of the H-1NF heliac, and wealth of information provided by the HMA create a unique opportunity for detailed study of Alfvén eigenmodes, which could be a serious issue for future fusion reactors.

Reduction of edge localized mode intensity on DIII-D by on-demand triggering with high frequency pellet injection and implications for ITER

The injection of small deuterium pellets at high repetition rates up to 12× the natural edge localized mode (ELM) frequency has been used to trigger high-frequency ELMs in otherwise low natural ELM frequency H-mode deuterium discharges in the DIII-D tokamak [J. L. Luxon and L. G. Davis, Fusion Technol. 8, 441 (1985)]. The resulting pellet-triggered ELMs result in up to 12× lower energy and particle fluxes to the divertor than the natural ELMs. The plasma global energy confinement and density are not strongly affected by the pellet perturbations. The plasma core impurity density is strongly reduced with the application of the pellets. These experiments were performed with pellets injected from the low field side pellet in plasmas designed to match the ITER baseline configuration in shape and normalized β operation with input heating power just above the H-mode power threshold. Nonlinear MHD simulations of the injected pellets show that destabilization of ballooning modes by a local pressure perturbation is responsible for the pellet ELM triggering. This strongly reduced ELM intensity shows promise for exploitation in ITER to control ELM size while maintaining high plasma purity and performance.

The strongest magnetic barrier in the DIII-D tokamak and comparison with the ASDEX UG

Magnetic perturbations in tokamaks lead to the formation of magnetic islands, chaotic field lines, and the destruction of flux surfaces. Controlling or reducing transport along chaotic field lines is a key challenge in magnetically confined fusion plasmas. A local control method was proposed by Chandre et al. [Nucl. Fusion 46, 33–45 (2006)] to build barriers to magnetic field line diffusion by addition of a small second-order control term localized in the phase space to the field line Hamiltonian. Formation and existence of such magnetic barriers in Ohmically heated tokamaks (OHT), ASDEX UG and piecewise analytic DIII-D [Luxon, J.L.; Davis, L.E., Fusion Technol. 8, 441 (1985)] plasma equilibria was predicted by the authors [Ali, H.; Punjabi, A., Plasma Phys. Control. Fusion 49, 1565–1582 (2007)]. Very recently, this prediction for the DIII-D has been corroborated [Volpe, F.A., et al., Nucl. Fusion 52, 054017 (2012)] by field-line tracing calculations, using experimentally constrained Equilibrium Fit (EFIT) [Lao, et al., Nucl. Fusion 25, 1611 (1985)] DIII-D equilibria perturbed to include the vacuum field from the internal coils utilized in the experiments. This second-order approach is applied to the DIII-D tokamak to build noble irrational magnetic barriers inside the chaos created by the locked resonant magnetic perturbations (RMPs) (m, n)=(3, 1)+(4, 1), with m and n the poloidal and toroidal mode numbers of the Fourier expansion of the magnetic perturbation with amplitude δ. A piecewise, analytic, accurate, axisymmetric generating function for the trajectories of magnetic field lines in the DIII-D is constructed in magnetic coordinates from the experimental EFIT Grad-Shafranov solver [Lao, L, et al., Fusion Sci. Technol. 48, 968 (2005)] for the shot 115,467 at 3000 ms in the DIII-D. A symplectic mathematical map is used to integrate field lines in the DIII-D. A numerical algorithm [Ali, H., et al., Radiat. Eff. Def. Solids Inc. Plasma Sc. Plasma Tech. 165, 83 (2010)] based on continued fraction decomposition of the rotational transform labeling the barriers for selecting and identifying the strongest noble irrational barrier is used. The results are compared and contrasted with our previous results on the ASDEX UG. About six times stronger a barrier can be built in the DIII-D than in the ASDEX UG. High magnetic shear near the separatrix in the DIII-D is inferred as the possible cause of this. Implications of this for the DIII-D and the International Thermonuclear Experimental Reactor (ITER) are discussed.

Classical confinement and outward convection of impurity ions in the MST RFP

Impurity ion dynamics measured with simultaneously high spatial and temporal resolution reveal classical ion transport in the reversed-field pinch. The boron, carbon, oxygen, and aluminum impurity ion density profiles are obtained in the Madison Symmetric Torus [R. N. Dexter et al., Fusion Technol. 19, 131 (1991)] using a fast, active charge-exchange-recombination-spectroscopy diagnostic. Measurements are made during improved-confinement plasmas obtained using inductive control of tearing instability to mitigate stochastic transport. At the onset of the transition to improved confinement, the impurity ion density profile becomes hollow, with a slow decay in the core region concurrent with an increase in the outer region, implying an outward convection of impurities. Impurity transport from Coulomb collisions in the reversed-field pinch is classical for all collisionality regimes, and analysis shows that the observed hollow profile and outward convection can be explained by the classical temperature screening mechanism. The profile agrees well with classical expectations. Experiments performed with impurity pellet injection provide further evidence for classical impurity ion confinement.

First-order finite-Larmor-radius fluid modeling of tearing and relaxation in a plasma pinch

Drift and Hall effects on magnetic tearing, island evolution, and relaxation in pinch configurations are investigated using a non-reduced first-order finite-Larmor-radius (FLR) fluid model with the nonideal magnetohydrodynamics (MHD) with rotation, open discussion (NIMROD) code [C.R. Sovinec and J. R. King, J. Comput. Phys. 229, 5803 (2010)]. An unexpected result with a uniform pressure profile is a drift effect that reduces the growth rate when the ion sound gyroradius (ρs) is smaller than the tearing-layer width. This drift is present only with warm-ion FLR modeling, and analytics show that it arises from ∇B and poloidal curvature represented in the Braginskii gyroviscous stress. Nonlinear single-helicity computations with experimentally relevant ρs values show that the warm-ion gyroviscous effects reduce saturated-island widths. Computations with multiple nonlinearly interacting tearing fluctuations find that m = 1 core-resonant-fluctuation amplitudes are reduced by a factor of two relative to single-fluid modeling by the warm-ion effects. These reduced core-resonant-fluctuation amplitudes compare favorably to edge coil measurements in the Madison Symmetric Torus (MST) reversed-field pinch [R. N. Dexter et al., Fusion Technol. 19, 131 (1991)]. The computations demonstrate that fluctuations induce both MHD- and Hall-dynamo emfs during relaxation events. The presence of a Hall-dynamo emf implies a fluctuation-induced Maxwell stress, and the simulation results show net transport of parallel momentum. The computed magnitude of force densities from the Maxwell and competing Reynolds stresses, and changes in the parallel flow profile, are qualitatively and semi-quantitatively similar to measurements during relaxation in MST.

Deuterium beam acceleration with 3rd harmonic ion cyclotron resonance heating in Joint European Torus: Sawtooth stabilization and Alfvén eigenmodes

Experiments on accelerating NBI-produced deuterium (D) beam ions from their injection energy of ∼110 keV up to the MeV energy range with 3rd harmonic ion cyclotron resonance heating were performed on the Joint European Torus [P. H. Rebut and B. E. Keen, Fusion Technol. 11, 13 (1987)]. A renewed set of nuclear diagnostics was used for analysing fast D ions during sawtooth stabilization, monster sawtooth crashes, and during excitation of Alfvén eigenmodes (AEs) residing inside the q = 1 radius. The measurements and modeling of the fast ions with the nonlinear HAGIS code [S. D. Pinches et al., Comput. Phys. Commun. 111, 133 (1998)] show that monster sawtooth crashes are strongly facilitated by the AE-induced re-distribution of the fast D ions from inside the q = 1 radius to the plasma edge.

Symplectic calculation of the outboard magnetic footprint from noise and error fields in the DIII-D

AbstractThe backward symplectic DIII-D map and continuous symplectic analog of the map for magnetic field line trajectories in the DIII-D [10] (Luxon, J. L. and Davis, L. E. 1985 Fusion Technol.8, 441) in natural canonical coordinates are used to calculate the magnetic footprint on the outboard collector plate of the DIII-D tokamak from the field errors and internal topological noise. The equilibrium generating function for the DIII-D used in the map very accurately represents the magnetic geometry of the DIII-D. The step-size of the map is kept considerably small so that the magnetic perturbation added from symplectic discretization of the Hamiltonian equations of the magnetic field line trajectories is very small. The natural canonical coordinates allow inverting to the real physical space. The combination of highly accurate equilibrium generating function, natural canonical coordinates, symplecticity, and small step-size then together gives a very accurate calculation of magnetic footprint. Radial variation of magnetic perturbation and the response of plasma to perturbation are not included. The footprint is in the form of toroidally winding helical strips. The area of footprint scales as 1st power of amplitude. The physical parameters as toroidal angle, length, and poloidal angle covered before striking, and the safety factor all have fractal structure. The average field diffusion near X-point for lines that strike and that do not strike differs by about four orders of magnitude. The flux loss decreases for high values of amplitude of perturbation.

An accurate symplectic calculation of the inboard magnetic footprint from statistical topological noise and field errors in the DIII-D

Any canonical transformation of Hamiltonian equations is symplectic, and any area-preserving transformation in 2D is a symplectomorphism. Based on these, a discrete symplectic map and its continuous symplectic analog are derived for forward magnetic field line trajectories in natural canonical coordinates. The unperturbed axisymmetric Hamiltonian for magnetic field lines is constructed from the experimental data in the DIII-D [J. L. Luxon and L. E. Davis, Fusion Technol. 8, 441 (1985)]. The equilibrium Hamiltonian is a highly accurate, analytic, and realistic representation of the magnetic geometry of the DIII-D. These symplectic mathematical maps are used to calculate the magnetic footprint on the inboard collector plate in the DIII-D. Internal statistical topological noise and field errors are irreducible and ubiquitous in magnetic confinement schemes for fusion. It is important to know the stochasticity and magnetic footprint from noise and error fields. The estimates of the spectrum and mode amplitudes of the spatial topological noise and magnetic errors in the DIII-D are used as magnetic perturbation. The discrete and continuous symplectic maps are used to calculate the magnetic footprint on the inboard collector plate of the DIII-D by inverting the natural coordinates to physical coordinates. The combination of highly accurate equilibrium generating function, natural canonical coordinates, symplecticity, and small step-size together gives a very accurate calculation of magnetic footprint. Radial variation of magnetic perturbation and the response of plasma to perturbation are not included. The inboard footprint from noise and errors are dominated by m=3, n=1 mode. The footprint is in the form of a toroidally winding helical strip. The width of stochastic layer scales as 12 power of amplitude. The area of footprint scales as first power of amplitude. The physical parameters such as toroidal angle, length, and poloidal angle covered before striking, and the safety factor all have fractal structure. The average field diffusion near the X-point for lines that strike and that do not strike differs by about three to four orders of magnitude. The magnetic footprint gives the maximal bounds on size and heat flux density on collector plate.

Core magnetic islands and plasma confinement in the H-1NF heliac

Plasma confinement in the vicinity of vacuum magnetic islands near the magnetic axis in the H-1NF heliac [S. M. Hamberger et al., Fusion Technol. 17, 123 (1990)] has been experimentally studied in a low temperature argon plasma. Experimental results indicate that, under favorable conditions, these low order (m=2) islands near the core of the plasma serve as “pockets” of higher electron density. This results in significant profile modifications including enhancement of the core radial electric field to a large positive value, possibly through an electron-root ambipolar condition. The characteristics of islands are found to be dependent on the plasma collisionality and island width.

Equilibrium evolution in oscillating-field current-drive experiments

Oscillating-field current drive (OFCD) is a proposed method of steady-state toroidal plasma sustainment in which ac poloidal and toroidal loop voltages are applied to produce a dc plasma current. OFCD is added to standard, inductively sustained reversed-field pinch plasmas in the Madison Symmetric Torus [R. N. Dexter et al., Fusion Technol. 19, 131 (1991)]. Equilibrium profiles and fluctuations during a single cycle are measured and analyzed for different relative phases between the two OFCD voltages and for OFCD off. For OFCD phases leading to the most added plasma current, the measured energy confinement is slightly better than that for OFCD off. By contrast, the phase of the maximum OFCD helicity-injection rate also has the maximum decay rate, which is ascribed to transport losses during discrete magnetic-fluctuation events induced by OFCD. Resistive-magnetohydrodynamic simulations of the experiments reproduce the observed phase dependence of the added current.

Thermonuclear ignition in inertial confinement fusion and comparison with magnetic confinement

The physics of thermonuclear ignition in inertial confinement fusion (ICF) is presented in the familiar frame of a Lawson-type criterion. The product of the plasma pressure and confinement time Pτ for ICF is cast in terms of measurable parameters and its value is estimated for cryogenic implosions. An overall ignition parameter χ including pressure, confinement time, and temperature is derived to complement the product Pτ. A metric for performance assessment should include both χ and Pτ. The ignition parameter and the product Pτ are compared between inertial and magnetic-confinement fusion. It is found that cryogenic implosions on OMEGA [T. R. Boehly et al., Opt. Commun. 133, 495 (1997)] have achieved Pτ∼1.5 atm s comparable to large tokamaks such as the Joint European Torus [P. H. Rebut and B. E. Keen, Fusion Technol. 11, 13 (1987)] where Pτ∼1 atm s. Since OMEGA implosions are relatively cold (T∼2 keV), their overall ignition parameter χ∼0.02–0.03 is ∼5× lower than in JET (χ∼0.13), where the average temperature is about 10 keV.

Observation of energetic electron confinement in a largely stochastic reversed-field pinch plasma

Runaway electrons with energies >100 keV are observed with the appearance of an m=1 magnetic island in the core of otherwise stochastic Madison Symmetric Torus [Dexter et al., Fusion Technol. 19, 131 (1991)] reversed-field-pinch plasmas. The island is associated with the innermost resonant tearing mode, which is usually the largest in the m=1 spectrum. The island appears over a range of mode spectra, from those with a weakly dominant mode to those, referred to as quasi single helicity, with a strongly dominant mode. In a stochastic field, the rate of electron loss increases with electron parallel velocity. Hence, high-energy electrons imply a region of reduced stochasticity. The global energy confinement time is about the same as in plasmas without high-energy electrons or an island in the core. Hence, the region of reduced stochasticity must be localized. Within a numerical reconstruction of the magnetic field topology, high-energy electrons are substantially better confined inside the island, relative to the external region. Therefore, it is deduced that the island provides a region of reduced stochasticity and that the high-energy electrons are generated and well confined within this region.

Coupling of Alfvén and sound waves in stellarator plasmas

Recently, a low frequency mode possibly driven unstable by hot electrons [J. M. Canik et al., 21st IAEA Fusion Energy Conference, Chengdu (China) (IAEA, Vienna, 2006), CN-149EX/5-2] has been observed in the Helically Symmetric Experiment [F. S. B. Anderson et al., Fusion Technol. 27, 273 (1995)]. The emergence of such a mode has been investigated within the framework of computational three-dimensional magnetohydrodynamics (MHD). A three-dimensional MHD continuum code CONTI has been developed for a fast computation of the continuous Alfvén and sound spectrum. The global modes have been calculated using the CAS3D code. A possibly new class of modes has been identified which is generated by the interaction between sound and Alfvén waves. The respective gap still contains a continuum branch, so that because of the continuum interaction, a conclusive answer if these modes really exist cannot be achieved within the computational ideal MHD picture. Additionally, continuum gaps of similar type have been investigated also for other stellarators.