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Within the ITPA Topical Group on Energetic Particles, we have investigated the impact that various mechanisms breaking the tokamak axisymmetry can have on the fusion alpha particle confinement in ITER as well as on the wall power loads due to these alphas. In addition to the well-known TF ripple, the 3D effect due to ferromagnetic materials (in ferritic inserts and test blanket modules) and ELM mitigation coils are included in these mechanisms. ITER scenario 4 was chosen since, due to its lower plasma current, it is more vulnerable for various off-normal features. First, the validity of using a 2D equilibrium was investigated: a 3D equilibrium was reconstructed using the VMEC code, and it was verified that no 3D equilibrium reconstruction is needed but it is sufficient to add the vacuum field perturbations onto an axisymmetric equilibrium. Then the alpha particle confinement was studied using three independent codes, ASCOT, DELTA5D and F3D OFMC, all of which assume MHD quiescent background plasma and no anomalous diffusion. All the codes gave a loss power fraction of about 0.2%. The distribution of the peak power load was found to depend on the first wall shape. We also made the first attempt to accommodate the effect of fast-ion-related MHD on the wall loads in ITER using the HMGC and ASCOT codes. The power flux to the wall was found to increase due to the redistribution of fast ions by the MHD activity. Furthermore, the effect of the ELM mitigation field on the fast-ion confinement was addressed by simulating NBI ions with the F3D OFMC code. The loss power fraction of NBI ions was found to increase from 0.3% without the ELM mitigation field to 4‐5% with the ELM mitigation field. (Some figures in this article are in colour only in the electronic version)

The expulsion of runaway electrons (REs) during different types of tokamak instabilities is analysed by means of a Cherenkov probe inserted into the scrape-off layer of the FTU tokamak. One such type of instability, the well-known tearing mode, is involved in disruptive plasma termination events, during which the risk of RE avalanche multiplication is highest. The second type, known as anomalous Doppler instability, influences RE dynamics by enhancing pitch angle scattering. Three scenarios are analysed here, characterised by different RE generation rates and mechanisms. The main conclusions are drawn from correlations between the Cherenkov probe and other diagnostics. In particular, the Cherenkov probe permits the detection of fast electron expulsion with a high level of detail, presenting peaks with 100% signal contrast during tearing mode growth and rotation, and sub-peak structures reflecting the interplay between the magnetic island formed by the tearing mode, RE diffusion during island rotation and the geometry of obstacles in the vessel. Correlations between the Cherenkov signal, hard x-ray emission and electron cyclotron emission reveal the impulsive development of the anomalous Doppler instability with instability rise time in the microsecond scale resolved by the high time-resolution of the Cherenkov probe.

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.

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

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.

This work presents the results of a multi mode ITER study on Toroidal Alfven Eigenmodes, using the nonlinear hybrid HAGIS-LIGKA model. It is found that main conclusions from earlier studies of ASDEX Upgrade discharges can be transferred to the ITER scenario: global, nonlinear effects are crucial for the evolution of the multi mode scenario. This work focuses on the ITER 15 MA baseline scenario with with a safety factor at the magnetic axis of $q_0 =$ 0.986. The least damped eigenmodes of the system are identified with the gyrokinetic, non-perturbative LIGKA solver, concerning mode structure, frequency and damping. Taking into account all weakly damped modes that can be identified linearly, nonlinear simulations with HAGIS reveal strong multi mode behavior: while in some parameter range, quasi-linear estimates turn out to be reasonable approximations for the nonlinearly relaxed energetic particle profile, under certain conditions low-n TAE branches can be excited. As a consequence, not only grow amplitudes of all modes to (up to orders of magnitude) higher values compared to the single mode cases but also, strong redistribution is triggered in the outer radial area between $\rho_\mathrm{pol} =$ 0.6 and 0.85, far above quasi-linear estimates., Comment: 14 pages, 20 figures; To be published as special issue in PPCF 12/2015 for EPS Lisbon invited talk

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.

The linear dynamics of Alfven modes in tokamaks is investigated here by means of the global gyrokinetic particle-in-cell code NEMORB. The model equations are shown and the local shear Alfven wave dispersion relation is derived, recovering the continuous spectrum in the incompressible ideal MHD limit. A verification and benchmark analysis is performed for continuum modes in a cylinder and for toroidicity-induced Alfven Eigenmodes. Modes in a reversed-shear equilibrium are also investigated, and the dependence of the spatial structure in the poloidal plane on the equilibrium parameters is described. In particular, a phase-shift in the poloidal angle is found to be present for modes whose frequency touches the continuum, whereas a radial symmetry is found to be characteristic of modes in the continuum gap., Comment: Submitted to "Physics of Plasmas"

A systematic study of high energetic alpha particle interaction with microinstability driven turbulence (ITG) is presented. The alpha particles are considered to be passive, thus not modifying the fine structure of the turbulence, and modelled as Maxwellian distributed. Both the turbulent fields and the evolution of the alpha distribution are computed by means of an Eulerian, flux tube code. It is shown how significant transport of high pressure distributions can occur, and how the direction and the intensity of the particle flux is sensitive to the choice of the temperature scale length of the alpha distribution, due to thermodiffusive phenomena. The diffusivity of an ITER-like case is studied, starting from an analytical treatment of the density and temperature profiles, which we show to be significant. New interpretative tools, by means of a single particle following code, are also presented. © 2008 American Institute of Physics.

This paper discusses the first nonlinear numerical simulation results of fishbone excitation by a magnetically trapped supra-thermal electron population with pressure profile peaked on axis due to, e.g. electron cyclotron resonance heating. The precession resonance underlying the linear instability is clearly identified. Meanwhile, mode saturation is shown to occur because of the secular resonant particle motion, pumping particles out of the radial region where the wave–particle power exchange is initially localized. The mode nonlinear saturation is accompanied by downward frequency chirping, due to phase-locking of the mode with resonant particles, consistent with the ‘mode particle pumping’ mechanism. (Some figures may appear in colour only in the online journal)

A new diagnostic has been developed to investigate the wave-particle interaction in the phase-space in gyrokinetic particle-in-cell codes. Based on the projection of energy transfer terms onto the velocity space, the technique has been implemented and tested in the global code ORB5 and it gives an opportunity to localise velocity domains of maximum wave-plasma energy exchange for separate species. Moreover, contribution of different species and resonances can be estimated as well, by integrating the energy transfer terms in corresponding velocity domains. This Mode-Plasma-Resonance (MPR) diagnostic has been applied to study the dynamics of the Energetic-particle-induced Geodesic Acoustic Modes (EGAMs) in an ASDEX Upgrade shot, by analysing the influence of different species on the mode time evolution. Since the equations on which the diagnostic is based, are valid in both linear and nonlinear cases, this approach can be applied to study nonlinear plasma effects. As a possible future application, the technique can be used, for instance, to investigate the nonlinear EGAM frequency chirping, or the plasma heating due to the damping of the EGAMs., 39 pages, 21 figures

Since the 2010 IAEA-FEC Conference, FTU has exploited improvements in cleaning procedures and in the density control system to complete a systematic exploration of access to high-density conditions in a wide range of plasma currents and magnetic fields. The line-averaged densities at the disruptive limit increased more than linearly with the toroidal field, while no dependence on plasma current was found; in fact, the maximum density of 4.3 × 10 20 m-3 was reached at B = 8 T even at the minimum current of 0.5 MA, corresponding to twice the Greenwald limit. The lack of plasma current dependence was due to the increase in density peaking with the safety factor. Experiments with the 140 GHz electron cyclotron resonance heating (ECRH) system were focused on the sawtooth (ST) period control and on the commissioning of a new launcher with real-time steering capability that will act as the front-end actuator of a real-time system for ST period control and tearing mode stabilization. Various ECRH and electron cyclotron current-drive modulation schemes were used; with the fastest one, the ST period synchronized with an 8 ms modulation period. The observed period variations were simulated using the JETTO code with a critical shear model for the crash trigger. The new launcher was of the plug-in type, allowing quick insertion and connection to the transmission line. Both beam characteristics and steering speed were in line with design expectation. Experimental results on the connection between improved coupling of lower hybrid waves in high-density plasmas and reduced wave spectral broadening were interpreted by fully kinetic, non-linear model calculations. A dual-frequency, time-of-flight diagnostic for the measurement of density profiles was developed and successfully tested. Fishbone-like instabilities driven by energetic electrons were simulated by the hybrid MHD-gyrokinetic XHMGC code. © 2013 IAEA, Vienna.

Resonant interaction between energetic particles (EPs), produced by fusion reactions and/or additional heating systems, and shear Alfvén modes can destabilize global Alfvénic modes enhancing the EP transport. In order to investigate the EP transport in present and next generation fusion devices, numerical simulations are recognized as a very important tool. Among the various numerical models, the hybrid MHD gyrokinetic one has shown to be a valid compromise between a sufficiently accurate wave-particle interaction description and affordable computational resource requirements. This paper presents a linear benchmark between the hybrid codes HYMAGYC and HMGC. The HYMAGYC code solves the full, linear MHD equations in general curvilinear geometry for the bulk plasma and describes the EP population by the nonlinear gyrokinetic Vlasov equation. On the other side, HMGC solves the nonlinear, reduced O ( ϵ 0 3 ) , pressureless MHD equations ( ϵ 0 being the inverse aspect ratio) for the bulk plasma and the drift kinetic Vlasov equation for the EPs. The results of the HYMAGYC and HMGC codes have been compared both in the MHD limit and in a wide range of the EP parameter space for two test cases (one of which being the so-called TAE n = 6 ITPA Energetic Particle Group test case), both characterized by ϵ 0 ≪ 1 . In the first test case (test case A), good qualitative agreement is found w.r.t. real frequencies, growth rates and spatial structures of the most unstable modes, with some quantitative differences for the growth rates. For the so-called ITPA test case (test case B), at the nominal energetic particle density value, the disagreement between the two codes is, on the contrary, also qualitative, as a different mode is found as the most unstable one.

The role of energetic particles (EPs) in fusion plasmas is unique as they could act as mediators of cross-scale couplings. More specifically, EPs can drive instabilities on the macro- and meso-scales and intermediate between the microscopic thermal ion Larmor radius and the macroscopic plasma equilibrium scale lengths. On one hand, EP driven shear Alfvén waves (SAWs) could provide a nonlinear feedback onto the macro-scale system via the interplay of plasma equilibrium and fusion reactivity profiles. On the other hand, EP-driven instabilities could also excite singular radial mode structures at SAW continuum resonances, which, by mode conversion, yield microscopic fluctuations that may propagate and be absorbed elsewhere, inducing nonlocal behaviors. The above observations thus suggest that a theoretical approach based on advanced kinetic treatment of both EPs and thermal plasma is more appropriate for burning fusion plasmas. Energetic particles, furthermore, may linearly and nonlinearly (via SAWs) excite zonal structures, acting, thereby, as generators of nonlinear equilibria that generally evolve on the same time scale of the underlying fluctuations. These issues are presented within a general theoretical framework, discussing evidence from both numerical simulation results and experimental observations. Analogies of fusion plasmas dynamics with problems in condensed matter physics, nonlinear dynamics, and accelerator physics are also emphasized. © 2015 IOP Publishing Ltd.