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Toroidal Alfvén eigenmodes (TAEs) associated with runaway electrons are observed in low density EAST Ohmic discharges (Zhu et al 2022 Phys. Plasmas 29 062504), which motivate the present work to explore the possible destabilization mechanism using simplified hybrid MHD-kinetic simulations. We show that the barely circulating energetic electrons can satisfy the resonance condition with the TAE, mainly due to vanishing transit frequency near the phase space circulating/trapped separatrix. In addition, the nonlinear saturation study suggests that the phase space resonance structure plays an important role in the eventual saturation amplitude, where a low toroidal mode number is favored in this scenario.

One of the major challenges in magnetic confinement thermonuclear fusion research concerns the confinement of the energetic particles (EPs) produced by fusion reactions and/or by additional heating systems. In such experiments, EPs can resonantly interact with the shear Alfven waves. In the frame of the EUROfusion 2019- 2020 Enabling Research project "Multi-scale Energetic particle Transport in fusion devices" (MET), a detailed benchmark activity has been undertaken among few of the state-of-the-art codes available to study the self-consistent interaction of an EP population with the shear Alfven waves. In this paper linear studies of EP driven modes with toroidal mode number n = 1 will be presented, in real magnetic equilibria and in regimes of interest for the forthcoming generation devices (e.g., ITER, JT-60SA, DTT). The codes considered are HYMAGYC, MEGA, and ORB5, the first two being hybrid MHD-Gyrokinetic codes (bulk plasma is represented by MHD equations, while the EP species is treated using the gyrokinetic formalism), the third being a global electromagnetic gyrokinetic code. The so-called NLED-AUG reference case has been considered, both for the peaked on-axis and peaked off-axis EP density profile cases, using its shaped cross section version. Comparison of the spatial mode structure, growth rate and real frequency of the modes observed will be considered in detail. The dependence of mode characteristics when several parameters are varied, as, e.g., the ratio between EP and bulk ion density and energetic particle temperature, will be presented. A remarkable agreement is observed among the three codes for the peaked off-axis case, obtaining all of them a TAE localized close to the magnetic axis. On the other hand, some differences are observed when considering the peaked on-axis case, where two modes are observed (a TAE localized in the radial external region, and a RSAE around mid-radius). A careful analysis of the stability of this equilibrium, in particular by varying self-consistently the EP drive, will allow to reconcile the results of the three codes.

This paper presents a study of the interaction between Alfvén modes and zonal structures, considering a realistic ASDEX Upgrade equilibrium. The results of gyrokinetic simulations with the global, electromagnetic, particle-in-cell code ORB5 are presented, where the modes are driven unstable by energetic particles with a bump-on-tail equilibrium distribution function, with radial density gradient. Two regimes have been observed. At low energetic particle concentration, the zonal structure (identified as an energetic particle-driven geodesic acoustic mode) is more unstable than the Alfvén mode. In the regime at high energetic particle concentration, the Alfvén mode is more unstable than the zonal structure. The interplay between the modes leads to a modification of their growth rates as well as to a modification of their saturation levels. The theoretical explanation of the mode interaction is given in terms of three-wave coupling of the energetic particle-driven geodesic acoustic mode and Alfvén mode, mediated by the curvature–pressure coupling term of the energetic particles.

In this paper we analyze fast ion motion in the divertor tokamak test (DTT) device (Albanese et al 2017 Nucl. Fusion 57 016010). It is planned that DTT will be heated through a mix of 45 MW heating power, including 15 MW negative-ion-based neutral beam heating (NNBI) which is currently being developed by Consorzio RFX in Padova, Italy (Agostinetti et al 2019 Fusion Eng. Design 146 441-446). An issue for DTT is that a toroidal field (TF) ripple with a maximum value of about similar to 0.42% (with respect to the on-axis magnetic field B (0)) is expected on the low-field side, and this ripple interacts with fast ions through the rather well-known phenomena of ripple-precession resonances, in addition to prompt losses of ions which do not complete a full orbit in the poloidal plane. We will show that, with the planned geometry of NNBI, prompt losses are negligible, and ripple-precession losses amount to a maximum of 0.15%. The calculations are performed with the guiding center code Orbit using two different equilibria, and a beam with an energy of 400 keV and the injection angle alpha (inj) = 40 degrees (measured w.r.t. the first wall), which corresponds to a pitch of injected particles lambda = v (parallel to)/v approximate to sin alpha (inj) = 0.65. The main resonances are of the form omega (b) - nN omega (d) = 0, omega (b) and omega (d) being the bounce and precession frequency, respectively, N = 18 the ripple periodicity and 3

In this work, the FALCON code is adopted for illustrating the features of shear Alfvén and sound continuous spectra in toroidal fusion plasmas. The FALCON codes employ the local Floquet analysis discussed in (Phys. Plasmas, vol. 26, issue 8, 2019, 082502) for computing global structures of continuous spectra in general toroidal geometry. As particular applications, reference equilibria for the divertor tokamak test and ASDEX Upgrade plasmas are considered. In particular, we illustrate the importance of mode polarization for recognizing the physical relevance of the various branches of the continuous spectra in the ideal magnetohydrodynamics limit. We also analyse the effect of plasma compression and the validity of the slow sound approximation.

Hybrid MHD-gyrokinetic code simulations are used to investigate the dynamics of frequency sweeping reversed shear Alfv\'en eigenmode (RSAE) strongly driven by energetic particles (EPs) during plasma current ramp-up in a conventional tokamak configuration. A series of weakly reversed shear equilibria representing time slices of long timescale MHD equilibrium evolution is considered, where the self-consistent RSAE-EP resonant interactions on the short timescale are analyzed in detail. Both linear and nonlinear RSAE dynamics are shown to be subject to the non-perturbative effect of EPs by maximizing wave-EP power transfer. In linear stage, EPs induce evident mode structure and frequency shifts; meanwhile, RSAE saturates by radial decoupling with resonant EPs due to weak magnetic shear, and gives rise to global EP convective transport and non-adiabatic frequency chirping. The spatiotemporal scales of phase space wave-EP interactions are characterized by the perpendicular wavelength and wave-particle trapping time. The simulations provide insights into general as well as specific features of RSAE spectra and EP transport from experimental observations, and illustrate the fundamental physics of wave-EP resonant interaction with the interplay of magnetic geometry, plasma non-uniformity and non-perturbative EPs., Comment: 36 pages, 21 figures

The results of a set of simulations of Alfvén modes driven by an energetic particle population are presented, with the specific aim of comparing single-n and multiple-n simulations (n being the toroidal mode number). The hybrid reduced O(ϵ0 3) MHD gyrokinetic code HMGC is used ( being the inverse aspect ratio of the torus, with a and R 0 the minor and major radius, respectively), retaining both fluid (wave-wave) and energetic particle nonlinearities. The code HMGC retains self-consistently, in the time evolution, the wave spatial structures as modified by the energetic particle (EP) term. Simulations with toroidal mode numbers 1 < n < 15 have been considered. For the specific energetic particle drive considered, single-n simulations are either stable (n = 1), or weakly unstable (n = 2,3,13,14,15), or strongly unstable (4 < n < 12), with 4 < n < 12 modes exhibiting similar growth-rates, while n = 4 the largest saturated amplitude. A variety of modes are observed (TAEs, upper and lower KTAEs, EPMs). Nevertheless, no appreciable global modification of the EP density profile is observed at saturation. On the contrary, a multi-n, fully nonlinear simulation exhibits an appreciable broadening of the EP radial density profile at saturation, thus demonstrating an enhanced radial transport w.r.t. the single-n simulations. Moreover, the sub-dominant modes are strongly modified by nonlinear coupling which results both from the MHD and from the EP terms. © EURATOM 2018.

The Divertor Tokamak Test (DTT) facility is proposed for studying power exhaust solutions as well as integrated physics and technology aspects for the demonstration power plant. To illuminate the richness of new novel plasma physics that can be explored in this device, linear stability properties and shear Alfvén fluctuation spectra of a typical DTT reference scenario are investigated by self-consistent hybrid magnetohydrodynamic-gyrokinetic simulations. The DTT core plasmas can be divided into two regions, characterized by reverse shear Alfvén eigenmode in the central core and by toroidal Alfvén eigenmode in the outer core region. The non-perturbative effect of energetic particles (EPs) and the wave-EP resonance condition as well as power transfer is analyzed in great detail, demonstrating the peculiar role played by EPs in multi-scale dynamics. The most unstable mode numbers of dominant Alfvénic fluctuations are shown to be of the order of 10, consistent with the typical orbit widths of the EPs normalized to the plasma minor radius and the DTT target design. © 2018 EURATOM.

Nonlinear dynamics of single toroidal number Alfvén eigenmodes destabilised by the the resonant interaction with fast ions is investigated, in tokamak equilibria, by means of Hamiltonian mapping techniques. The results obtained by two different simulation codes, XHMGC and HAGIS, are presented for n = 2 Beta induced Alfvén eigenmodes and, respectively n = 6 toroidal Alfvén eigenmodes. Simulations of the bump-on-tail instability performed by a 1-dimensional code, PIC1DP, are also analysed for comparison. As a general feature, modes saturate as the resonant-particle distribution function is flattened over the whole region where mode-particle power transfer can take place in the linear phase. Such region is limited by the narrowest of resonance width and mode width. In the former case, mode amplitude at saturation exhibits a quadratic scaling with the linear growth rate; in the latter case, the scaling is linear. These results are explained in terms of the approximate analytic solution of a nonlinear pendulum model. They are also used to prove that the radial width of the single poloidal harmonic sets an upper limit to the radial displacement of circulating fast ions produced by a single-toroidal-number gap mode in the large n limit, irrespectively of the possible existence of a large global mode structure formed by many harmonics. © 2017 Associazione Euratom-ENEA sulla Fusione.

Following the analysis on linear spectra of shear Alfv\'en fluctuations excited by energetic particles (EPs) in the Divertor Tokamak Test (DTT) facility plasmas [T. Wang et al., Phys. Plasmas 25, 062509 (2018)], in this work, nonlinear dynamics of the corresponding mode saturation and the fluctuation induced EP transport is studied by hybrid magnetohydrodynamic-gyrokinetic simulations. For the reversed shear Alfv\'en eigenmode driven by magnetically trapped EP precession resonance in the central core region of DTT plasmas, the saturation is mainly due to radial decoupling of resonant trapped EPs. Consistent with the wave-EP resonance structure, EP transport occurs in a similar scale to the mode width. On the other hand, passing EP transport is analyzed in detail for toroidal Alfv\'en eigenmode in the outer core region, with mode drive from both passing and trapped EPs. It is shown that passing EPs experience only weak redistributions in the weakly unstable case; and the transport extends to meso-scale diffusion in the strongly unstable case, due to orbit stochasticity induced by resonance overlap. Here, weakly/strongly unstable regime is determined by Chirikov condition for resonance overlap. This work then further illuminates rich and diverse nonlinear EP dynamics related to burning plasma studies, and the capability of DTT to address these key physics., Comment: 32 pages, 20 figures

International audience; Recent developments and achievements of the EUROfusion Code Development for Integrated Modelling project (WPCD), which aim is to provide a validated integrated modelling suite for the simulation and prediction of complete plasma discharges in any tokamak, are presented. WPCD develops generic complex integrated simulations, workflows, for physics applications, using the standardized European Integrated Modelling (EU-IM) framework. Selected physics applications of EU-IM workflows are illustrated in this paper.

Internal kink instabilities exhibiting fishbone like behavior have been observed in a variety of experiments where a high energy electron population, generated by strong auxiliary heating and/or current drive systems, was present. After briefly reviewing the experimental evidences of energetic electrons driven fishbones, and the main results of linear and nonlinear theory of electron fishbones, the results of global, self-consistent, nonlinear hybrid MHD-Gyrokinetic simulations will be presented. To this purpose, the extended/hybrid MHD-Gyrokinetic code XHMGC will be used. Linear dynamics analysis will enlighten the effect of considering kinetic thermal ion compressibility and diamagnetic response, and kinetic thermal electrons compressibility, in addition to the energetic electron contribution. Nonlinear saturation and energetic electron transport will also be addressed, making extensive use of Hamiltonian mapping techniques, discussing both centrally peaked and off-axis peaked energetic electron profiles. It will be shown that centrally peaked energetic electron profiles are characterized by resonant excitation and nonlinear response of deeply trapped energetic electrons. On the other side, off-axis peaked energetic electron profiles are characterized by resonant excitation and nonlinear response of barely circulating energetic electrons which experience toroidal precession reversal of their motion. © 2016 EUROfusion.

Fast particles in fusion plasmas may drive Alfvén modes unstable leading to fluctuations of the internal electromagnetic fields and potential loss of particles. Such instabilities can have an impact on the performance and the wall-load of machines with burning plasmas such as ITER. A linear benchmark for a toroidal Alfvén eigenmode (TAE) is done with 11 participating codes with a broad variation in the physical as well as the numerical models. A reasonable agreement of around 20% has been found for the growth rates. Also, the agreement of the eigenfunctions and mode frequencies is satisfying. However, they are found to depend strongly on the complexity of the used model. © EURATOM 2018.

This chapter reviews the progress accomplished since the redaction of the first ITER Physics Basis (1999 Nucl. Fusion 39 2137-664) in the field of energetic ion physics and its possible impact on burning plasma regimes. New schemes to create energetic ions simulating the fusion-produced alphas are introduced, accessing experimental conditions of direct relevance for burning plasmas, in terms of the Alfvénic Mach number and of the normalised pressure gradient of the energetic ions, though orbit characteristics and size cannot always match those of ITER. Based on the experimental and theoretical knowledge of the effects of the toroidal magnetic field ripple on direct fast ion losses, ferritic inserts in ITER are expected to provide a significant reduction of ripple alpha losses in reversed shear configurations. The nonlinear fast ion interaction with kink and tearing modes is qualitatively understood, but quantitative predictions are missing, particularly for the stabilisation of sawteeth by fast particles that can trigger neoclassical tearing modes. A large database on the linear stability properties of the modes interacting with energetic ions, such as the Alfvén eigenmode has been constructed. Comparisons between theoretical predictions and experimental measurements of mode structures and drive/damping rates approach a satisfactory degree of consistency, though systematic measurements and theory comparisons of damping and drive of intermediate and high mode numbers, the most relevant for ITER, still need to be performed. The nonlinear behaviour of Alfvén eigenmodes close to marginal stability is well characterized theoretically and experimentally, which gives the opportunity to extract some information on the particle phase space distribution from the measured instability spectral features. Much less data exists for strongly unstable scenarios, characterised by nonlinear dynamical processes leading to energetic ion redistribution and losses, and identified in nonlinear numerical simulations of Alfvén eigenmodes and energetic particle modes. Comparisons with theoretical and numerical analyses are needed to assess the potential implications of these regimes on burning plasma scenarios, including in the presence of a large number of modes simultaneously driven unstable by the fast ions. © 2007 IAEA, Vienna.

Some of the crucial physics aspects of burning plasmas magnetically confined in toroidal systems are presented from the viewpoint of nonlinear dynamics. Most of the discussions specifically refer to tokamaks, but they can be readily extended to other toroidal confinement devices. Particular emphasis is devoted to fluctuation induced transport processes of mega electron volts energetic ions and charged fusion products as well as to energy and particle transports of the thermal plasma. Long time scale behaviours due to the interplay of fast ion induced collective effects and plasma turbulence are addressed in the framework of burning plasmas as complex self-organized systems. The crucial roles of mutual positive feedbacks between theory, numerical simulation and experiment are shown to be the necessary premise for reliable extrapolations from present day laboratory to burning plasmas. Examples of the broader applications of fundamental problems to other fields of plasma physics and beyond are also given.

A tokamak plasma with internal transport barriers (ITBs) is the best candidate for a steady ITER operation, since the high energy confinement allows working at plasma currents (Ip) lower than the reference scenario. To build and sustain an ITB at the ITER high density (>=1020 m-3) and largely dominant electron (e-) heating is not trivial in most existing tokamaks. FTU can instead meet both requests, thanks to its radiofrequency heating systems, lower hybrid (LH, up to 1.9 MW) and electron cyclotron (EC up to 1.2 MW). By the combined use of them, ITBs are obtained up to peak densities ne0 > 1.3 × 1020 m-3, with central e- temperatures Te0 ? 5.5 keV, and are sustained for as long as the heating pulse is applied (>35 confinement times, ?E). At ne0 ? 0.8 × 1020 m-3 Te0 can be larger than 11 keV. Almost full current drive (CD) and an overall good steadiness is attained within about one ?E, 20 times faster than the ohmic current relaxation time. The ITB extends over a central region with an almost flat or slightly reversed q profile and qmin ? 1.3 that is fully sustained by off-axis lower hybrid current drive. Consequent to this is the beneficial good alignment of the bootstrap current, generated by the ITB large pressure gradients, with the LH driven current. Reflectometry shows a clear change in the turbulence close to the ITB radius, consistent with the reduced e- transport. Ions (i+) are significantly heated via collisions, but thermal equilibrium with electrons cannot be attained since the e--i+ equipartition time is always 4-5 times longer than ?E. No degradation of the overall ion transport, rather a reduction of the i+ heat diffusivity, is observed inside the ITB. The global confinement has been improved up to 1.6 times over the scaling predictions. The ITB radius can be controlled by adjusting the LH power deposition profile that is affected mostly by the q value of the discharge, while the ITB strength can be varied through central EC heating. FTU experiments have shown that ITER-like e-ITBs are achievable.

The change in nonlinear energetic particle mode (EPM) dynamics that accompanies the transition from weak to strong energetic ion transport is discussed in this work. It is demonstrated that the nonlinear threshold in fast ion energy density for the onset of strong convective transport occurring in avalanches is close to the linear EPM excitation threshold. This phenomenology is strictly related to the resonant character of the modes, which tend to be radially localized where the drive is strongest. After the convective loss phase, during which nonlinear EPM mode structure is displaced outwards, fast ion transport continues owing to diffusive processes. Theoretical analyses, presented here, are the basis for consistency analyses of operation scenarios in proposed burning plasma experiments. Comparisons between theoretical predictions and both simulation and experimental results are also briefly discussed.

In the burning fusion plasmas of next step devices such as ITER (2001 ITERFEAT Outline Design Report IAEA/ITER EDA/DS/18 (Vienna: IAEA) p 21), the majority of the heating of the fusing fuel will come from the plasma self-heating by fusion born α-particles. Recent advances in theoretical understanding, together with the development of new diagnostic techniques, make this a timely opportunity to survey the role of energetic particles in fusion plasmas and how it projects to future burning plasma devices. (Some figures in this article are in colour only in the electronic version)

The stability of proposed burning-plasma scenarios (for ITER-FEAT, IGNITOR and FIRE) with respect to shear-Alfven modes possibly driven by fusion-produced alpha particles is investigated along with the effects of such modes on the transport and confinement properties of the alpha particles themselves. The results of numerical particle-in-cell model simulations show that one of the proposed scenarios (namely, the ITER-FEAT reversed-shear case) could be characterized by fast-growing energetic-particle modes, saturating via a convective displacement of the energetic ions. The consequent broadening pressure profile of the alpha particles and their additional diffusion due to scattering by the saturated electromagnetic fields show that the envisaged scenario cannot be considered consistent with the constraints imposed by nonlinear energetic-particle interactions with the Alfven modes. The validity of the above results is discussed with reference to the approximations used in the model.

A thorough analysis of energetic particle modes (EPM) stability and mode structures is presented for tokamaks with hollow q profiles. Focusing on the region near the minimum-q surface, EPM gap modes and resonant EPMs are shown to exist as solutions of the same dispersion relation. By controlling the fast ion distribution function, or, equivalently, their fundamental dynamical properties, a smooth transition between these two classes of modes is obtained within the EPM dispersion relation. When toroidal coupling becomes important, it is demonstrated that EPMs may have either single or double hump radial structures. The local analyses of EPM stability and mode structures near the minimum-q surface are put in the broader framework of EPM stability and EPM induced transport in tokamaks with hollow q profiles and a brief summary is also given of present understanding of such problems based on results of three-dimensional nonlinear hybrid magneto–hydrodynamic–gyrokinetic simulations. Possible implications of pr...

Self-consistent nonlinear dynamics of Energetic Particle Modes, which are relevant for burning plasma conditions, are analyzed with respect to both saturation mechanisms and energetic particle transport. It is found that a “sensitive” parameter for Tokamak equilibria with hollow-q profiles is q at the minimum-q surface, higher q corresponding to larger particle transport. This fact has clear implications on the choice of current profiles in a burning plasma.

SUMMARY In this paper we address the issue of workload decomposition in programming hierarchical distributedshared memory parallel systems. The workload decomposition we have devised consists of a two-stage procedure: a higher-level decomposition among the computational nodes; and a lower-level one among the processors of each computational node. By focusing on porting of a case study particle-in-cell application, we have implemented the described work decomposition without large programming effort by using and integrating the high-level language extensions High-Performance Fortran and OpenMP. Copyright  2002 John Wiley & Sons, Ltd.

One of the main FAST (Fusion Advanced Studies Torus) goals is to have a flexible experiment capable to test tools and scenarios for safe and reliable tokamak operation, in order to support ITER and help the final DEMO design. In particular, in this paper, we focus on operation close to a possible border of stability related to low-q operation. To this purpose, a new FAST scenario has then been designed at I-p = 10 MA, B-T = 8.5 T, q(95) approximate to 2.3. Transport simulations, carried out by using the code JETTO and the first principle transport model GLF23, indicate that, under these conditions, FAST could achieve an equivalent Q approximate to 3.5. FAST will be equipped with a set of internal active coils for feedback control, which will produce magnetic perturbation with toroidal number n = 1 or n = 2. Magnetohydrodynamic (MHD) mode analysis and feedback control simulations performed with the codes MARS, MARS-F, CarMa (both assuming the presence of a perfect conductive wall and using the exact 3D resistive wall structure) show the possibility of the FAST conductive structures to stabilize n = 1 ideal modes. This leaves therefore room for active mitigation of the resistive mode (down to a characteristic time of 1 ms) for safety purposes, i.e., to avoid dangerous MHD-driven plasma disruption, when working close to the machine limits and magnetic and kinetic energy density not far from reactor values.

We present a series of numerical simulation experiments set up to illustrate the fundamental physics processes underlying the nonlinear dynamics of Alfvénic modes resonantly excited by energetic particles in tokamak plasmas and of the ensuing energetic particle transports. These phenomena are investigated by following the evolution of a test particle population in the electromagnetic fields computed in self-consistent MHD-particle simulation performed by the HMGC code. Hamiltonian mapping techniques are used to extract and illustrate several features of wave-particle dynamics. The universal structure of resonant particle phase space near an isolated resonance is recovered and analyzed, showing that bounded orbits and untrapped trajectories, divided by the instantaneous separatrix, form phase space zonal structures, whose characteristic non-adiabatic evolution time is the same as the nonlinear time of the underlying fluctuations. Bounded orbits correspond to a net outward resonant particle flux, which produces a flattening and/or gradient inversion of the fast ion density profile around the peak of the linear wave-particle resonance. The connection of this phenomenon to the mode saturation is analyzed with reference to two different cases: a Toroidal Alfvén eigenmode in a low shear magnetic equilibrium and a weakly unstable energetic particle mode for stronger magnetic shear. It is shown that, in the former case, saturation is reached because of radial decoupling (resonant particle redistribution matching the mode radial width) and is characterized by a weak dependence of the mode amplitude on the growth rate. In the latter case, saturation is due to resonance detuning (resonant particle redistribution matching the resonance width) with a stronger dependence of the mode amplitude on the growth rate.

High density plasmas (n0 ≈ 8 × 1020m-3) featuring steady improved core confinement have been obtained in FTU up to the maximum nominal toroidal field (8 T) by deep multiple pellet injection. These plasmas also feature high purity efficient electron-ion coupling and peaked density profiles sustained for several confinement times. Neutron yields in excess of 1 × 1013 n/s are measured, consistent with the reduction of the ion transport to neoclassical levels.

The article presents an analysis of the typical features of shear Alfven waves in tokamak plasmas in a frequency domain ranging from the `high' frequencies (ω vA/2qR0, where vA is the Alfven speed and qR0 is the tokamak connection length) of the toroidal gap to the `low' frequencies, comparable with the thermal ion diamagnetic frequency ω*pi and/or the thermal ion transit frequency ωti = vti/qR0 (where vti is the ion thermal speed).

Electron temperatures in excess of 8 keV have been obtained by electron-cyclotron-resonance heating on FTU plasmas at peak densities up to $8\ifmmode\times\else\texttimes\fi{}{10}^{19}\mathrm{m}{}^{\ensuremath{-}3}$. The magnetic shear in the plasma core is low or negative, and the electron heat diffusivity remains at, or below, the Ohmic level $(0.2\mathrm{m}{}^{2}/\mathrm{s})$, in spite of the very large heating power density $(10--20\mathrm{MW}/\mathrm{m}{}^{3})$ which produces extremely high temperature gradients (up to 120 keV/m). The ion heat transport remains at the neoclassical level.

Linear and nonlinear properties of moderate-toroidal-number (n) shear-Alfven modes in tokamaks are investigated by using a hybrid MHD-particle simulation code, which solves the coupled set of MHD (magnetohydrodynamic) equations for the electromagnetic fields and gyrocenter Vlasov equation for a population of energetic ions. The existence of unstable toroidal Alfven eigenmodes (TAE’s) and their kinetic counterpart is shown for low values of the energetic-ion pressure gradient. Above a certain threshold value, the energetic particle continuum mode (EPM) is destabilized, with growth rate fast increasing with increasing energetic-particle pressure gradient. The threshold shows an inverse dependence on n. High-n EPM’s could then be unstable in realistic plasma conditions. Neglecting MHD nonlinearities, for the sake of simplicity, it is shown that nonlinear TAE saturation appears to be due to the trapping of resonant energetic ions in the potential well of the wave. Saturation of the EPM occurs instead because ...

The Fusion Advanced Study Torus (FAST) has been proposed as a high magnetic field, compact size tokamak providing a flexible integrated environment to study physics and technology issues in ITER and DEMO relevant conditions. FAST has a quite large natural toroidal field ripple (around 1.5%) due to its compactness and to the number of access ports: this ripple must be lowered to an acceptable level to allow safe operations and a good confinement quality. An Active Ripple Compensating System (ARCS) has been designed, based on a set of poloidal coils placed between the plasma chamber and the Toroidal Field Coils (TFCs). These ARCS coils will be fed with adjustable currents, opposite in direction respect to the TFC currents, and will allow lowering the ripple up to zero and beyond. The CAD model of FAST including the ARCS coils has been completed and preliminary electromagnetic and thermal analyses have been carried out. Moreover, a Feedback Active Control System (FACS) composed of two arrays of in-vessel saddle coils has been designed to allow safe high plasma current, low safety factor operation and to mitigate possibly large ELMs effects in FAST. These FACS coils will be fed by a feedback system to control MHD modes: a first engineering assessment of the current requirements has been carried out. © 2013 Euratom-ENEA Association sulla Fusione.

The Fusion Advanced Study Torus (FAST) has been proposed as a possible European satellite, in view of ITER and DEMO, in order to: (a) explore plasma wall interaction in reactor relevant conditions, (b) test tools and scenarios for safe and reliable tokamak operation up to the border of stability, and (c) address fusion plasmas with a significant population of fast particles. A new FAST scenario has been designed focusing on low-q operation, at plasma current IP = 10 MA, toroidal field BT = 8.5 T, with a q 95 ≈ 2.3 that would correspond to IP ≈ 20 MA in ITER. The flat-top of the discharge can last a couple of seconds (i.e. half the diffusive resistive time and twice the energy confinement time), and is limited by the heating of the toroidal field coils. A preliminary evaluation of the end-of-pulse temperatures and of the electromagnetic forces acting on the central solenoid pack and poloidal field coils has been performed. Moreover, a VDE plasma disruption has been simulated and the maximum total vertical force applied on the vacuum vessel has been estimated. © 2013 Euratom-ENEA Association sulla Fusione.

In the present work, we analyse the two dimensional (2-D) mode structures and global stability of the Alfven branches, whose frequencies are close to the toroidicity induced Alfven continuum gap. The fully 2-D problem is solved using a two spatial-scale WKBJ formalism without employing perturbation theory in treating drive and damping terms. A code that solves the 2-D mode structures and global stability of the Alfven branches is presented. Applications to a model toroidal equilibrium with ITER relevant plasma parameters are analysed. Results indicate that no unstable modes are present in the considered reference scenario

Nonlinear saturation of beta induced Alfv\'en eigenmode, driven by slowing down energetic particles via transit resonance, is investigated by the nonlinear hybrid magnetohyrodynamic gyro-kinetic code (XHMGC). Saturation is characterized by frequency chirping and symmetry breaking between co- and counter-passing particles, which can be understood as the the evidence of resonance-detuning. The scaling of the saturation amplitude with the growth rate is also demonstrated to be consistent with radial resonance detuning due to the radial non-uniformity and mode structure.

New FTU ohmic discharges with a liquid lithium limiter at I P = 0.7–0.75 MA, B T = 7 T and n e0 ⩾ 5 × 1020 m−3 confirm the spontaneous transition to an enhanced confinement regime, 1.3–1.4 times ITER-97-L, when the density peaking factor is above a threshold value of 1.7–1.8. The improved confinement derives from a reduction of electron thermal conductivity (χe) as density increases, while ion thermal conductivity (χi) remains close to neoclassical values. Linear microstability reveals the importance of lithium in triggering a turbulent inward flux for electrons and deuterium by changing the growth rates and phase of the ion-driven turbulence, while lithium flux is always directed outwards. A particle diffusion coefficient, D ∼ 0.07 m2 s−1, and an inward pinch velocity, V ∼ 0.27 m s−1, in qualitative agreement with Bohm–gyro-Bohm predictions are inferred in pellet fuelled lithized discharges. Radio frequency heated plasmas benefit from cleaner plasmas with edge optimized conditions. Lower hybrid waves penetration and current drive effects are clearly demonstrated at and above ITER densities thanks to a good control of edge parameters obtained by plasma operations with the external poloidal limiter, lithized walls and pellet fuelling. The electron cyclotron (EC) heating system is extensively exploited in FTU for contributing to ITER-relevant issues such as MHD control: sawtooth crash is actively controlled and density limit disruptions are avoided by central and off-axis deposition of 0.3 MW of EC power at 140 GHz. Fourier analysis shows that the density drop and the temperature rise, stimulated by modulated EC power in low collisionality plasmas are synchronous, implying that the heating method is the common cause of both the electron heating and the density drop. Perpendicularly injected electron cyclotron resonance heating is demonstrated to be more efficient than the obliquely injected one, reducing the minimum electric field required at breakdown by a factor of 3. Theoretical activity further develops the model to interpret high-frequency fishbones on FTU and other experiments as well as to characterize beta-induced Alfvén eigenmodes induced by magnetic islands in ohmic discharges. The theoretical framework of the general fishbone-like dispersion relation is used for implementing an extended version of the HMGC hybrid MHD gyrokinetic code. The upgraded version of HMGC will be able to handle fully compressible non-linear gyrokinetic equations and 3D MHD.

Progress in thermonuclear fusion energy research based on deuterium plasmas magnetically confined in toroidal tokamak devices requires the development of efficient current drive methods. Previous experiments have shown that plasma current can be driven effectively by externally launched radio frequency power coupled to lower hybrid plasma waves. However, at the high plasma densities required for fusion power plants, the coupled radio frequency power does not penetrate into the plasma core, possibly because of strong wave interactions with the plasma edge. Here we show experiments performed on FTU (Frascati Tokamak Upgrade) based on theoretical predictions that nonlinear interactions diminish when the peripheral plasma electron temperature is high, allowing significant wave penetration at high density. The results show that the coupled radio frequency power can penetrate into high-density plasmas due to weaker plasma edge effects, thus extending the effective range of lower hybrid current drive towards the domain relevant for fusion reactors.

High performance scientific applications are currently implemented using native languages for optimizing performance and utilization of resources. It often deals with thousands of code lines in FORTRAN or in C built of legacy applications. On the other hand new technologies can be exploited to improve flexibility and portability of services on heterogeneous and distributed platforms. We propose here an approach that allows programmers to extend their applications to exploit this kind of services for management purposes. It can be done simply by adding some methods to the original code, which specialize application management on occurrence of particular events. We mean that applications do not need to be rewritten into different languages or adopting specific programming models. We implemented a native console that is used by Mobile Agents to control the application life-cycle. Agents implement a mobile service that supports check-pointing, suspension, resume, cloning and migration of managed applications. A WSRF interface has been provided to Grid users who do not need to be aware about agents technology. We used a FORTRAN code for simulation of plasma turbolence as a real case study.

FAST is a new machine proposed to support ITER experimental exploitation as well as to anticipate DEMO relevant physics and technology. FAST is aimed at studying, under burning plasma relevant conditions, fast particle (FP) physics, plasma operations and plasma wall interaction in an integrated way. FAST has the capability to approach all the ITER scenarios significantly closer than the present day experiments using deuterium plasmas. The necessity of achieving ITER relevant performance with a moderate cost has led to conceiving a compact tokamak (R = 1.82 m, a = 0.64 m) with high toroidal field (B(T) up to 8.5 T) and plasma current (I(p) up to 8 MA). In order to study FP behaviours under conditions similar to those of ITER, the project has been provided with a dominant ion cyclotron resonance heating system (ICRH; 30 MW on the plasma). Moreover, the experiment foresees the use of 6 MW of lower hybrid (LHCD), essentially for plasma control and for non-inductive current drive, and of electron cyclotron resonance heating (ECRH, 4 MW) for localized electron heating and plasma control. The ports have been designed to accommodate up to 10 MW of negative neutral beams (NNBI) in the energy range 0.5-1 MeV. The total power input will be in the 30-40 MW range under different plasma scenarios with a wall power load comparable to that of ITER (P/R similar to 22 MW m(-1)). All the ITER scenarios will be studied: from the reference H mode, with plasma edge and ELMs characteristics similar to the ITER ones (Q up to approximate to 1.5), to a full current drive scenario, lasting around 170s. The first wall (FW) as well as the divertor plates will be of tungsten in order to ensure reactor relevant operation regimes. The divertor itself is designed to be completely removable by remote handling. This will allow us to study (in view of DEMO) the behaviour of innovative divertor concepts, such as those based on liquid lithium. FAST is capable of operating with very long pulses, up to 170s, despite being a copper machine. The magnets initial operation temperature is 30 K, with cooling provided by helium gas. The in vessel components, namely FW and divertor, are actively cooled by pressurized water above 80 degrees C. The same water is also used to bake the vacuum vessel. FAST is equipped with ferromagnetic inserts to keep the toroidal field magnet ripple down to 0.3%.

The linear resistive magnetohydrodynamical stability of the n = 1 internal kink mode in tokamaks is studied numerically. The stabilizing influence of small aspect ratio [Holmes et al., Phys. Fluids B 1, 788 (1989)] is confirmed, but it is found that shaping of the cross section influences the internal kink mode significantly. For finite pressure and small resistivity, curvature effects at the q= 1 surface make the stability sensitively dependent on shape, and ellipticity is destabilizing. Only a very restricted set of finite pressure equilibria is completely stable for q0 < 1. A typical result is that the resistive kink mode is slowed down by toroidal effects to a weak resistive tearing/interchange mode. It is suggested that weak resistive instabilities are stabilized during the ramp phase of the sawteeth by effects not included in linear resistive magnetohydrodynamics. Possible mechanisms for triggering a sawtooth crash are discussed.

Since the 2012 IAEA-FEC Conference, FTU operations have been largely devoted to runaway electrons generation and control, to the exploitation of the 140GHz electron cyclotron (EC) system and to liquid metal limiter elements. Experiments on runaway electrons have shown that the measured threshold electric field for their generation is larger than predicted by collisional theory and can be justified considering synchrotron radiation losses. A new runaway electrons control algorithm was developed and tested in presence of a runaway current plateau, allowing to minimize the interactions with plasma facing components and safely shut down the discharges. The experimental sessions with 140GHz EC system have been mainly devoted to experiments on real-time control of magnetohydrodynamic (MHD) instabilities using the new EC launcher with fast steering capability. Experiments with central EC injection have shown the onset of 3/2 and 2/1 tearing modes, while EC assisted breakdown experiments have been focused on ITER start-up issues, exploring the polarization conversion at reflection from inner wall and the capability to assure plasma start-up even in presence of a large stray magnetic field. A new actively cooled lithium limiter has been installed and tested. The lithium limiter was inserted in the scrape-off layer, without any damage to the limiter surface. First elongated FTU plasmas with EC additional heating were obtained with the new cooled limiter. Density peaking and controlled MHD activity driven by neon injection were investigated at different plasma parameters. A full real-time algorithm for disruption prediction, based on MHD activity signals from Mirnov coils, was developed exploiting a large database of disruptions. Reciprocating Langmuir probes were used to measure the heat flux e-folding length in the scrape-off layer, with the plasma kept to lay on thea internal limiter to resemble the ITER start-up phase. New diagnostics were successfully installed and tested, as a diamond probe to detect Cherenkov radiation produced by fast electrons and a gamma camera for runaway electrons studies. Laser induced breakdown spectroscopy measurements were performed under vacuum and with toroidal magnetic field, so demonstrating their capability to provide useful information on the surface elemental composition and fuel retention in present and future tokamaks, such as ITER. © 2015 EURATOM.

The authors propose a scaling of the sawtooth repetition time for Ohmic discharges. This scaling has been obtained from simulations with reduced magnetohydrodynamic equations together with a simple profile consistent transport model. The choice of a profile consistent perpendicular thermal diffusion coefficient allows the scaling of the sawtooth repetition time to be obtained in terms of the diffusion coefficients and the safety factor at the edge, thus generalizing the scaling given by Vlad and Bondeson (Nucl. Fusion 29 (1989) 1139). The scaling is in good agreement with the experimental results for Ohmic discharges in the Frascati Tokamak.

The full text of this introduction is available in the PDF. Boris Sharkov Programme Committee Chairman ITEP-Moscow, Russia Gregorio Vlad Scientific Secretary ENEA, Frascati, Italy

Collective communication libraries are widely developed and used in scientific community to support parallel and Grid programming. On the other side they often lack in Mobile Agents systems even if message passing is always supported to grant communication ability to the agents. Collective communication primitives can help to develop agents based parallel application. They can also benefit social ability and interactions of collaborative agents. Here we present a collective communication service implemented in the Jade agent platform. Furthermore we propose its exploitation to interface transparently heterogeneous executions instances of a scientific parallel application that runs in a distributed environment.

In this paper the results of the experiments of combined injection of LH waves and EC waves performed in the FTU tokamak are reported. Such experiments were mainly devoted to study and to control the access to the advanced tokamak scenarios in plasma conditions close to ITER parameters (Bt≈5T or higher, ne,line≈10 20 m -3 ). Two different absorption mechanisms were used for the EC waves. In the first one the cold resonance absorption of EC waves launched with a toroidal angle was used to induce small modification of the current profile mainly maintained by LH waves. In the second one the absorption through Doppler shift due to the fast electron tails generated by LHCD was used.