Showing papers in "Plasma Physics and Controlled Fusion in 2010"

Stabilization of the external kink and the resistive wall mode

Abstract: The pursuit of steady-state economic production of thermonuclear fusion energy has led to research on the stabilization of the external kink and the resistive wall mode. Advances in both experiment and theory, together with improvements in diagnostics, heating and feedback methods have led to substantial and steady progress in the understanding and stabilization of these instabilities. Many of the theory and experimental techniques and results that have been developed are useful not only for the stabilization of the resistive wall mode. They can also be used to improve the general performance of fusion confinement devices. The conceptual foundations and experimental results on the stabilization of the external kink and the resistive wall mode are reviewed.

Divertor power load feedback with nitrogen seeding in ASDEX Upgrade

Abstract: Feedback control of the divertor power load by means of nitrogen seeding has been developed into a routine operational tool in the all-tungsten clad ASDEX Upgrade tokamak. For heating powers above about 12?MW, its use has become inevitable to protect the divertor tungsten coating under boronized conditions. The use of nitrogen seeding is accompanied by improved energy confinement due to higher core plasma temperatures, which more than compensates the negative effect of plasma dilution by nitrogen on the neutron rate. This paper describes the technical details of the feedback controller. A simple model for its underlying physics allows the prediction of its behaviour and the optimization of the feedback gain coefficients used. Storage and release of nitrogen in tungsten surfaces were found to have substantial impact on the behaviour of the seeded plasma, resulting in increased nitrogen consumption with unloaded walls and a latency of nitrogen release over several discharges after its injection. Nitrogen is released from tungsten plasma facing components with moderate surface temperature in a sputtering-like process; therefore no uncontrolled excursions of the nitrogen wall release are observed. Overall, very stable operation of the high-Z tokamak is possible with nitrogen seeding, where core radiative losses are avoided due to its low atomic charge Z and a high ELM frequency is maintained.

On the requirements to control neoclassical tearing modes in burning plasmas

Abstract: Neoclassical tearing modes (NTMs) are magnetic islands which increase locally the radial transport and therefore degrade the plasma performance. They are self-sustained by the bootstrap current perturbed by the enhanced radial transport. The confinement degradation is proportional to the island width and to the position of the resonant surface. The q = 2 NTMs are much more detrimental to the confinement than the 3/2 modes due to their larger radii. NTMs are metastable in typical scenarios with βN ≥ 1 and in the region where the safety factor is increasing with radius. This is due to the fact that the local perturbed pressure gradient is sufficient to self-sustain an existing magnetic island. The main questions for burning plasmas are whether there is a trigger mechanism which will destabilize NTMs, and what is the best strategy to control/avoid the modes. The latter has to take into account the main aim which is to maximize the Q factor, but also the controllability of the scenario. Standardized and simplified equations are proposed to enable easier prediction of NTM control in burning plasmas from present experimental results. The present expected requirements for NTM control with localized electron cyclotron current drive (ECCD) in ITER are discussed in detail. Other aspects of the above questions are also discussed, in particular the role of partial stabilization of NTMs, the possibility to control NTMs at small size with little ECH power and the differences between controlling NTMs at the resonant surface or controlling the main trigger source, for the standard scenario namely the sawteeth. It is shown that there is no unique best strategy, but several tools are needed to most efficiently reduce the impact of NTMs on burning plasmas.

The role of ion and electron electrostatic turbulence in characterizing stationary particle transport in the core of tokamak plasmas

Abstract: A general feature of particle transport in the core of tokamak plasmas is that when core particle sources are small, a stationary peaked density profile is provided by a balance of outward diffusion and inward convection, driven by either neoclassical or turbulent mechanisms. The turbulent contribution to the off-diagonal elements of the transport matrix is very sensitive to the type of dominant instability of the background turbulence. We present here a detailed quasi-linear gyrokinetic analysis of stationary turbulent particle transport by means of analytical and numerical calculations to show how the actual parametric dependence of the stationary normalized density gradient can strongly vary between an ion temperature gradient (ITG) dominated turbulence and a trapped electron mode dominated turbulence regime. It is also shown how the maximal achievable normalized density gradient is reached when the turbulence regime is in a mixed state. This result is interpreted as the interplay of different physical mechanisms arising from (linear) wave–particle resonances. The results presented here are addressed to interpret some of the still unresolved issues in interpreting known experimental results.

Particle-in-cell simulations of laser?plasma interaction for the shock ignition scenario

Abstract: Numerical simulations of the laser pulse interaction with an inhomogeneous, large size, high temperature plasma are presented. The laser pulse intensity, 1016 W cm−2, plasma temperature, 5 keV, and the density scale length of 300 µm correspond to the conditions of the shock ignition scenario. It is demonstrated that after a short initial burst of backscattering, a significant part of the incident laser radiation is absorbed in the underdense plasma and the energy is transported to the dense plasma by electrons with energies 20–40 keV. The absorption mechanism is associated with a self-organized resonator and cavitation of large-amplitude plasma waves in the density range below the quarter critical density. The temporal and spectral properties of reflected light are discussed.

Nonlocal theory of energetic-particle-induced geodesic acoustic mode

Abstract: Excitation of energetic-particle (EP)-induced geodesic acoustic modes (EGAMs) by velocity space anisotropy is investigated taking into account the coupling to the GAM continuous spectrum. The response of EPs is studied nonperturbatively and both local and nonlocal dispersion relations of EGAM are derived assuming a single pitch angle slowing-down energetic ion equilibrium distribution function. For a sharply localized EP source, it is shown that the mode is self-trapped where the EP drive is strongest, with an exponentially small damping due to the tunneling coupling to the GAM continuous spectrum. (Some figures in this article are in colour only in the electronic version)

Inter-ELM behaviour of the electron density and temperature pedestal in ASDEX Upgrade

Abstract: The behaviour of the recovery of the electron temperature and density during individual ELM (edge localized mode) cycles has been examined closely for a series of type I ELMy H-mode discharges with different fuelling levels and medium collisionality. A characterization of the typical ELM recovery cycle has been established. Distinct phases have been observed in the build-up of the plasma edge profiles after their relaxation caused by the ELM crash. A thorough evaluation of ELM-synchronized data has revealed that the recovery of the electron temperature and density pedestals are correlated. A new behaviour has been discovered in the build-up phase of the plasma edge, during which the temperature stagnates while the density profile steepens. It was found that in some cases the ELM is triggered immediately after the recovery of the pressure profile, consistent with the expectations from edge ballooning theory, while in other cases all edge profiles reached their final shape a long time before the next ELM occurred. The theory that a delayed edge current induces the actual crash could not be confirmed; the current diffusion seems only to play a minor role in the edge of the plasma.

Oscillatory processes in solar flares

Abstract: Electromagnetic (radio, visible-light, UV, EUV, x-ray and gamma-ray) emission generated by solar and stellar flares often contains pronounced quasi-periodic pulsations (QPPs). Physical mechanisms responsible for the generation of long-period QPP (with periods longer than 1 s) are likely to be associated with MHD processes. The observed modulation depths, periods and anharmonicity of QPP suggest that they can be linked with some kind of MHD auto-oscillations, e.g. an oscillatory regime of magnetic reconnection. Such regimes, of both spontaneous and induced nature, have been observed in resistive-MHD numerical simulations. The oscillations are essentially nonlinear and non-stationary. We demonstrate that a promising novel method for their analysis is the empirical mode decomposition technique.

Particle distribution modification by low amplitude modes

Abstract: Modification of a high energy particle distribution by a spectrum of low amplitude modes is investigated using a guiding center code. Only through resonance are modes effective in modifying the distribution. Diagnostics are used to illustrate the mode–particle interaction and to find which effects are relevant in producing significant resonance, including kinetic Poincare plots and plots showing those orbits with time averaged mode–particle energy transfer. Effects of pitch angle scattering and drag are studied, as well as plasma rotation and time dependence of the equilibrium and mode frequencies. A specific example of changes observed in a DIII-D deuterium beam distribution in the presence of low amplitude experimentally validated Toroidal Alfven eigenmodes and reversed shear Alfven eigenmodes is examined in detail. Comparison with experimental data shows that multiple low amplitude modes can account for significant modification of high energy beam particle distributions. It is found that there is a stochastic threshold for beam profile modification, and that the experimental amplitudes are only slightly above this threshold.

Generation of blobs and holes in the edge of the ASDEX Upgrade tokamak

Abstract: The intermittent character of turbulent transport is investigated with Langmuir probes in the scrape-off layer and across the separatrix of ASDEX Upgrade Ohmic discharges. Radial profiles of plasma parameters are in reasonable agreement with results from other diagnostics. The probability density functions of ion-saturation current fluctuations exhibit a parabolic relation between skewness and kurtosis. Intermittent blobs and holes are observed outside and inside the nominal separatrix, respectively. They seem to be born at the edge of the plasma and are not the foothills of avalanches launched in the plasma core. A strong shear flow was observed 1 cm radially outside the location where blobs and holes seem to be generated.

JET disruption studies in support of ITER

Abstract: Plasma disruptions affect plasma-facing and structural components of tokamaks due to electromechanical forces, thermal loads and generation of high energy runaway electrons (REs). Asymmetries in poloidal halo and toroidal plasma current can now be routinely measured in four positions 90° apart. Their assessment is used to validate the design of the ITER vessel support system and its in-vessel components. The challenge of disruption thermal loads comes from both the short duration over which a large energy has to be lost and the potential for asymmetries. The focus of this paper will be on localized heat loads. Resonant magnetic perturbations failed to reduce the generation of REs in JET. An explanation of the limitations applying to these attempts is offered together with a minimum guideline. The REs generated by a moderate, but fast, Ar injection in limiter plasmas show evidence of milder and more efficient losses due to the high Ar background density.

Theory and simulation of discrete kinetic beta induced Alfvén eigenmode in tokamak plasmas

Abstract: It is shown, both analytically and by numerical simulations, that, in the presence of thermal ion kinetic effects, the beta induced Alfven eigenmode (BAE)–shear Alfven wave continuous spectrum can be discretized into radially trapped eigenstates known as kinetic BAE (KBAE). While thermal ion compressibility gives rise to finite BAE accumulation point frequency, the discretization occurs via the finite Larmor radius and finite orbit width effects. Simulations and analytical theories agree both qualitatively and quantitatively. Simulations also demonstrate that KBAE can be readily excited by the finite radial gradients of energetic particles.

Modeling and comparison of sinusoidal and nanosecond pulsed surface dielectric barrier discharges for flow control

Abstract: Surface dielectric barrier discharges have been proposed as means of airflow actuation. A simplified air plasma model fully coupled with gas dynamics is presented and solved numerically using asynchronous mesh adaptation and time integration. Two modes of actuation depending on the driving voltage waveform are presented and analyzed. The first one uses high-voltage sine waveform in the kilohertz frequency range to transfer momentum from ions to gas molecules. The second one uses high-voltage nanosecond pulses to transfer energy to the neutral gas on a short time scale thus generating shockwaves.

Electrostatic instabilities, turbulence and fast ion interactions in the TORPEX device

Abstract: Electrostatic turbulence, related structures and their effect on particle, heat and toroidal momentum transport are investigated in TORPEX simple magnetized plasmas using high-resolution diagnostics, control parameters, linear fluid models and nonlinear numerical simulations. The nature of the dominant instabilities is controlled by the value of the vertical magnetic field, Bv, relative to that of the toroidal field, BT. For Bv/BT > 3%, only ideal interchange instabilities are observed. A critical pressure gradient to drive the interchange instability is experimentally identified. Interchange modes give rise to blobs, radially propagating filaments of enhanced plasma pressure. Blob velocities and sizes are obtained from electrostatic probe measurements using pattern recognition methods. The observed values span a wide range and are described by a single analytical expression, from the small blob size regime in which the blob velocity is limited by cross-field ion polarization currents, to the large blob size regime in which the limitation to the blob velocity comes from parallel currents to the sheath. As a first attempt at controlling the blob dynamical properties, limiter configurations with varying angles between field lines and the conducting surface of the limiter are explored. Mach probe measurements clearly demonstrate a link between toroidal flows and blobs. To complement probe data, a fast framing camera and a movable gas puffing system are installed. Density and light fluctuations show similar signatures of interchange activity. Further developments of optical diagnostics, including an image intensifier and laser-induced fluorescence, are under way. The effect of interchange turbulence on fast ion phase space dynamics is studied using movable fast ion source and detector in scenarios for which the development from linear waves into blobs is fully characterized. A theory validation project is conducted in parallel with TORPEX experiments, based on quantitative comparisons of observables that are defined in the same way in the data and in the output of numerical codes, including 2D and 3D local and global simulations.

Edge turbulence and flows in the presence of resonant magnetic perturbations on MAST

Abstract: The impact of resonant magnetic perturbations (RMPs) on the edge of MAST L-mode plasmas is studied using a mid-plane reciprocating probe equipped with a Gundestrup probe head. A strong impact on the characteristics of the ion saturation current fluctuations is observed just inside the separatrix, with a broadening of the power spectrum and an asymmetrization of the probability distribution functions towards non-Gaussian shapes. No major effect is found in the scrape-off layer (SOL). Floating potential measurements are used to evaluate the modification of the plasma potential profiles. The radial electric field profile flattens when RMPs are applied, leading to a theoretically expected increase in Er inside the separatrix and a decrease in the SOL. A consistent change is observed on the perpendicular and parallel flows which tend to increase inside the separatrix. In contrast, in the SOL, a braking of the rotation is observed with the application of RMPs. All these effects occur only above a threshold in the amplitude of the current applied in the RMP coils and are not toroidally localized.

Toroidal rotation braking with n = 1 magnetic perturbation field on JET

Abstract: A strong toroidal rotation braking has been observed in plasmas with application of an n = 1 magnetic perturbation field on the JET tokamak. Calculation results from the momentum transport analysis show that the torque induced by the n = 1 perturbation field has a global profile. The maximal value of this torque is at the plasma core region (ρ < 0.4) and it is about half of the neutral beam injection torque. The calculation shows that the plasma is mainly in the regime in the plasma core, but it is close to the transition between the 1/ν and regimes. The neoclassical toroidal viscosity (NTV) torque in the 1/ν and regimes is calculated. The observed torque is of a magnitude in between that of the NTV torque in the 1/ν and regimes. The NTV torque in the regimes is enhanced using the Lagrangian variation of the magnetic field strength. However, it is still smaller than the observed torque by one order of magnitude.

Estimation of profiles of the effective ion charge at ASDEX Upgrade with Integrated Data Analysis

Abstract: The knowledge of the effective ion charge Zeff which indicates the degree of plasma pollution is of high interest, since the tolerable impurity concentration to achieve successful ignition of a fusion plasma is limited. The quantification of Zeff at ASDEX Upgrade has been carried out by means of Integrated Data Analysis in the framework of Bayesian probability theory which allows the combined analysis of different bremsstrahlung and charge exchange diagnostics to obtain one joint Zeff profile. With this tool it is possible to assess the quality of the data acquired by the individual diagnostics and to find a reasonable selection of data for the routine Zeff analysis. The Zeff results are validated by the examination of different discharge scenarios and successfully applied to simulations of the neutron rate and the loop voltage. The investigation of Zeff for nitrogen seeded discharges reveals a correlation between the confinement improvement and the increase in Zeff.

Turbulent transport of toroidal angular momentum in low flow gyrokinetics

Abstract: We derive a self-consistent equation for the turbulent transport of toroidal angular momentum in tokamaks in the low flow ordering that only requires solving gyrokinetic Fokker–Planck and quasineutrality equations correct to second order in an expansion on the gyroradius over scale length. We also show that according to our orderings the long wavelength toroidal rotation and the long wavelength radial electric field satisfy the neoclassical relation that gives the toroidal rotation as a function of the radial electric field and the radial gradients of pressure and temperature. Thus, the radial electric field can be solved for once the toroidal rotation is calculated from the transport of toroidal angular momentum. Unfortunately, even though this methodology only requires a gyrokinetic model correct to second order in gyroradius over scale length, current gyrokinetic simulations are only valid to first order. To overcome this difficulty, we exploit the smallish ratio Bp/B, where B is the total magnetic field and Bp is its poloidal component. When Bp/B is small, the usual first order gyrokinetic equation provides solutions that are accurate enough to employ for our expression for the transport of toroidal angular momentum. We show that current δf and full f simulations only need small corrections to achieve this accuracy. Full f simulations, however, are still unable to determine the long wavelength, radial electric field from the quasineutrality equation.

Comparison of neoclassical predictions with measured flows and evaluation of a poloidal impurity density asymmetry

Abstract: The study and prediction of velocities in the pedestal region of Alcator C-Mod are important for understanding plasma confinement and transport. In this study we examine the simplified neoclassical predictions for impurity flows using equations developed for plasmas with background ions in the Pfirsch–Schluter (PS) (high collisionality) and banana (low collisionality) regimes. B5+ flow profiles for H-mode plasmas are acquired using the charge-exchange recombination spectroscopy diagnostic on Alcator C-Mod and are compared with calculated profiles for the region just inside the last closed flux surface. Reasonable agreement is found between the predictions from the PS regime formalism and the measured poloidal velocities for the steep gradient region of the H-mode pedestals, regardless of the collisionality of the plasma. The agreement is poorer between the neoclassical predictions and measured velocity profiles using the banana regime formalism. Additionally, comparisons of measured velocities from the low- and high-field sides (LFS and HFS) of the plasma lead us to infer the strong possibility of a poloidal asymmetry in the B5+ density. This asymmetry can be a factor of 2–3 for the region of the steepest gradients, with the density at the HFS being larger. The magnitude of the density asymmetry is found to be correlated with the magnitude of the poloidal velocity at the LFS of the plasma.

MHD equilibrium variational principles with symmetry

Abstract: ThechainruleforfunctionalsisusedtoreducethenoncanonicalPoissonbracket formagnetohydrodynamics(MHD)tooneforaxisymmetricandtranslationally symmetric MHD and hydrodynamics. The procedure for obtaining Casimir invariants from noncanonical Poisson brackets is reviewed and then used to obtain the Casimir invariants for the considered symmetrical theories. It is shown why extrema of the energy plus Casimir invariants correspond to equilibria, thereby giving an explanation for the ad hoc variational principles thathaveexistedinplasmaphysics. Variationalprinciplesforgeneralequilibria are obtained in this way.

Resistive wall mode control code maturity: progress and specific examples

Abstract: Two issues of the resistive wall mode (RWM) control code maturity are addressed: the inclusion of advanced mode damping physics beyond the ideal MHD description, and the possibility of taking into account the influence of 3D features of the conducting structures on the mode stability and control. Examples of formulations and computational results are given, using the MARS-F/K codes and the CarMa code. The MARS-K calculations for a DIII-D plasma shows that the fast ion contributions, which can give additional drift kinetic stabilization in the perturbative approach, also drive an extra unstable branch of mode in the self-consistent kinetic modelling. The CarMa modelling for the ITER steady state advanced plasmas shows about 20% reduction in the RWM growth rate by the volumetric blanket modules. The multi-mode analysis predicts a weak interaction between the n = 0 and the n = 1 RWMs, due to the 3D ITER walls. The CarMa code is also successfully applied to model the realistic feedback experiments in RFX.

Imaging x-ray crystal spectrometer on EAST

Abstract: A high-resolution imaging x-ray crystal spectrometer is described for implementation on the EAST tokamak to provide spatially and temporally resolved data on the ion temperature, electron temperature and poloidal plasma rotation. These data are derived from observations of the satellite spectra of helium-like argon, Ar XVII, which is the dominant charge state for electron temperatures in the range from 0.4 to 3.0 keV and which is accessible to EAST. Employing a novel design, which is based on the imaging properties of spherically bent crystals, the spectrometers will provide spectrally and spatially resolved images of the plasma for all experimental conditions, which include ohmically heated discharges as well as plasmas with rf and neutral-beam heating. The experimental setup and initial experimental results are presented.

Statistical characterization of blob turbulence across the separatrix in HL-2A tokamak

Abstract: Blob statistical characteristics across the separatrix of HL-2A tokamak plasma have been studied using a reciprocating Langmuir five-probe array. The radial profile of inverse pressure gradient scale length has a maximum just inside the last closed flux surface (LCFS), where the skewness is close to zero. Conditional average reveals that the density holes and blobs are produced just inside the LCFS and they propagate in opposite directions. The poloidal velocity of blobs changes its sign when it is across the separatrix, which is consistent with E × B drift flow. The dramatic change in phase shift between density and potential fluctuations across the separatrix suggests the distinct properties of turbulence when the magnetic field line changes from a closed to an open one. The dependence of a weak three-wave interaction in terms of wavelet bicoherence on strong time-asymmetry blobs is observed for the first time. Moreover, the effective blob generation rate is estimated as 8.0 × 103 s−1 and the convective particle flux induced by the ejective blobs can lead to about 58% loss of radial particle flux.

Real-time control of tearing modes using a line-of-sight electron cyclotron emission diagnostic

Abstract: The stability and performance of tokamak plasmas are limited by instabilities such as neoclassical tearing modes. This paper reports on an experimental proof of principle of a feedback control approach for real-time, autonomous suppression and stabilization of tearing modes in a tokamak. The system combines an electron cyclotron emission diagnostic for sensing of the tearing modes in the same sight line with a steerable electron cyclotron resonance heating and current drive (ECRH/ECCD) antenna. A methodology for fast detection of q = m/n = 2/1 tearing modes and retrieval of their location, rotation frequency and phase is presented. Set-points to establish alignment of the ECRH/ECCD deposition location with the centre of the tearing mode are generated in real time and forwarded in closed loop to the steerable launcher and as a modulation pulse train to the gyrotron. Experimental results demonstrate the capability of the control system to track externally perturbed tearing modes in real time.

Fast ion stabilization of the ion temperature gradient driven modes in the Joint European Torus hybrid-scenario plasmas: a trigger mechanism for internal transport barrier formation

Abstract: Understanding and modelling turbulent transport in thermonuclear fusion plasmas are crucial for designing and optimizing the operational scenarios of future fusion reactors. In this context, plasmas exhibiting state transitions, such as the formation of an internal transport barrier (ITB), are particularly interesting since they can shed light on transport physics and offer the opportunity to test different turbulence suppression models. In this paper, we focus on the modelling of ITB formation in the Joint European Torus (JET) [1] hybrid-scenario plasmas, where, due to the monotonic safety factor profile, magnetic shear stabilization cannot be invoked to explain the transition. The turbulence suppression mechanism investigated here relies on the increase in the plasma pressure gradient in the presence of a minority of energetic ions. Microstability analysis of the ion temperature gradient driven modes (ITG) in the presence of a fast-hydrogen minority shows that energetic ions accelerated by the ion cyclotron resonance heating (ICRH) system (hydrogen, nH,fast/nD,thermal up to 10%, TH,fast/TD,thermal up to 30) can increase the pressure gradient enough to stabilize the ITG modes driven by the gradient of the thermal ions (deuterium). Numerical analysis shows that, by increasing the temperature of the energetic ions, electrostatic ITG modes are gradually replaced by nearly electrostatic modes with tearing parity at progressively longer wavelengths. The growth rate of the microtearing modes is found to be lower than that of the ITG modes and comparable to the local E × B-velocity shearing rate. The above mechanism is proposed as a possible trigger for the formation of ITBs in this type of discharges.

On the heating mix of ITER

Abstract: This paper considers the heating mix of ITER for the two main scenarios. Presently, 73 MW of absorbed power are foreseen in the mix 20/33/20 for ECH, NBI and ICH. Given a sufficient edge stability, Q = 10-the goal of scenario 2-can be reached with 40MW power irrespective of the heating method but depends sensitively inter alia on the H-mode pedestal temperature, the density profile shape and on the characteristics of impurity transport. ICH preferentially heats the ions and would contribute specifically with Delta Q 0.5, and strong off-axis current drive (CD). The findings presented here are based on revised CD efficiencies gamma for ECCD and a detailed benchmark of several CD codes. With ECCD alone, the goals of scenario 4 can hardly be reached. Efficient off-axis CD is only possible with NBI. With beams, inductive discharges with f(ni) > 0.8 can be maintained for 3000 s. The conclusion of this study is that the present heating mix of ITER is appropriate. It provides the necessary actuators to induce in a flexible way the best possible scenarios. The development risks of NBI at 1 MeV can be reduced by operation at 0.85 MeV.

Neutron spectroscopy measurements and modeling of neutral beam heating fast ion dynamics

Abstract: The energy spectrum of the neutron emission from beam-target reactions in fusion plasmas at the Joint European Torus (JET) has been investigated. Different beam energies as well as injection angles were used. Both measurements and simulations of the energy spectrum were done. The measurements were made with the time-of-flight spectrometer TOFOR. Simulations of the neutron spectrum were based on first-principle calculations of neutral beam deposition profiles and the fast ion slowing down in the plasma using the code NUBEAM, which is a module of the TRANSP package. The shape of the neutron energy spectrum was seen to vary significantly depending on the energy of the beams as well as the injection angle and the deposition profile in the plasma. Cross validations of the measured and modeled neutron energy spectra were made, showing a good agreement for all investigated scenarios.

Perturbative studies of transport phenomena in fusion devices

Abstract: Perturbative experiments are essential to understand the complex transport phenomena in fusion plasmas The perturbative methods used for transport studies are summarized and the main properties discussed Based on this approach, transport of particles, heat and momentum has been intensively investigated The main results obtained for the different channels are described and illustrated with selected examples

Consistency of atomic data for the interpretation of beam emission spectra

Abstract: Several collisional–radiative (CR) models (Anderson et al 2000 Plasma Phys. Control. Fusion 42 781–806, Hutchinson 2002 Plasma Phys. Control. Fusion 44 71–82, Marchuk et al 2008 Rev. Sci. Instrum. 79 10F532) have been developed to calculate the attenuation and the population of excited states of hydrogen or deuterium beams injected into tokamak plasmas. The datasets generated by these CR models are needed for the modelling of beam ion deposition and (excited) beam densities in current experiments, and the reliability of these data will be crucial to obtain helium ash densities on ITER combining charge exchange and beam emission spectroscopy. Good agreement between the different CR models for the neutral beam (NB) is found, if corrections to the fundamental cross sections are taken into account. First the Hα and Hβ beam emission spectra from JET are compared with the expected intensities. Second, the line ratios within the Stark multiplet are compared with the predictions of a sublevel resolved model. The measured intensity of the full multiplet is ≈30% lower than expected on the basis of beam attenuation codes and the updated beam emission rates, but apart from the atomic data this could also be due to the characterization of the NB path and line of sight integration and the absolute calibration of the optics. The modelled n = 3 to n = 4 population agrees very well with the ratio of the measured Hα to Hβ beam emission intensities. Good agreement is found as well between the NB power fractions measured with beam emission in plasma and on the JET Neutral Beam Test Bed. The Stark line ratios and σ/π intensity ratio deviate from a statistical distribution, in agreement with the CR model in parabolic states from Marchuk et al (2010 J. Phys. B: At. Mol. Opt. Phys. 43 011002).

Local properties of the magnetic field in a snowflake divertor

Abstract: The power-law series for the poloidal magnetic flux function, up to the third-order terms, is presented for the case where two nulls of the poloidal magnetic field are separated by a small distance, as in a snowflake divertor. Distinct from the earlier results, no assumptions about the field symmetry are made. Conditions for the realization of an exact snowflake are expressed in terms of the coefficients of the power series. It is shown that, by a proper choice of the coordinate frame in the poloidal plane, one can obtain efficient similarity solutions for the separatrices and flux surfaces in the divertor region: the whole variety of flux surface shapes can be characterized by a single dimensionless parameter. Transition from a snowflake-minus to a snowflake-plus configuration in the case of no particular symmetry is described. The effect of the finite toroidal current density in the divertor region is assessed for the case of no particular symmetry.