Table of contents

In magnetic fusion plasmas, a significant fraction of the kinetic pressure is contributed by superthermal charged particles produced by auxiliary heating (fast ions and electrons) and fusion reactions (a-particles). Since these energetic particles are often far away from thermal equilibrium due to their non-Maxwellian distribution and steep pressure gradients, the free energy can excite electromagnetic instabilities to intensity levels well above the thermal fluctuations. The resultant electromagnetic turbulence could induce large transport of energetic particles, which could reduce heating efficiency, degrade overall plasma confinement, and damage fusion devices. Therefore, understanding and predicting energetic particle confinement properties are critical to the success of burning plasma experiments such as ITER since the ignition relies on plasma self-heating by a-particles.

To promote international exchanges and collaborations on energetic particle physics, the biannual conference series under the auspices of the International Atomic Energy Agency (IAEA) were help in Kyiv (1989), Aspenas (1991), Trieste (1993), Princeton (1995), JET/Abingdon (1997), Naka (1999), Gothenburg (2001), San Diego (2003), Takayama (2005), Kloster Seeon (2007), Kyiv (2009), and Austin (2011). The papers in this special section were presented at the most recent meeting, the 13th IAEA Technical Meeting on Energetic Particles in Magnetic Confinement Systems, which was hosted by the Fusion Simulation Center, Peking University, Beijing, China (17–20 September 2013). The program of the meeting consisted of 71 presentations, including 13 invited talks, 26 oral contributed talks, 30 posters, and 2 summary talks, which were selected by the International Advisory Committee (IAC). The IAC members include H. Berk, L.G. Eriksson, A. Fasoli, W. Heidbrink, Ya. Kolesnichenko, Ph. Lauber, Z. Lin, R. Nazikian, S. Pinches, S. Sharapov, K. Shinohara, K. Toi, G. Vlad, and X.T. Ding. The conference program, abstracts of all papers, and slides of oral presentations are available at the conference website:www.phy.pku.edu.cn/fsc/w18419.jsp

As a measure of the breadth in current research activities, a wide range of topics in energetic particle physics were covered in the meeting program, including dynamics of various Alfvén eigenmodes and energetic particle modes, energetic particle transport, energetic particle effects on magnetohydrodynamic (MHD) modes, runaway electrons, and diagnostics of energetic particles and neutrons. Energetic particle experiments were reported on tokamaks, stellarators, spherical tori, reversed field pinches, and linear devices. Most of the papers have direct comparisons between experimental data and simulation results, a very healthy trend in the research of energetic particle physics.

As an indication for the depth in current research activities and possible future directions in energetic particle physics, some exciting progress reported at the meeting is highlighted here. The 3D fields of resonant magnetic perturbations (RMP) for controlling edge localized modes (ELM) are found to drive significant ripple loss of fast ions in DIII-D and ASDEX-U experiments. Similar loss is predicted for ITER RMP fields in the vacuum approximation. Fortunately, plasma response to RMP fields is found by the simulation to reduce the loss of fast ions and α-particles to a benign level. These results call for more accurate measurements and more reliable modeling of the plasma response to RMP fields in existing tokamak experiments and in future ITER experiments. Interesting progress on energetic particle transport by Alfvén eigenmodes was made in reduced 1D models based on the critical gradients model, in which energetic particle pressure gradients are relaxed to the local threshold of Alfvén eigenmode stability. Some experimental support for the critical gradient model was reported in DIII-D off-axis neutral beam injection (NBI) experiments, in which the fast-ion density relaxes to similar profiles for all injection angles. Further verification and validation of these reduced models by existing tokamak experiments and nonlinear simulations are needed.

Impressive progress in first-principles simulations of Alfvén eigenmodes and energetic particle transport was prominently featured at the meeting. Rigorous verification and validation have been successfully carried out for global gyrokinetic simulations of Alfvén eigenmodes with kinetic effects of thermal plasmas and non-perturbative contributions by energetic particles. The gyrokinetic turbulence simulation provides an indispensable new capability for studying the nonlinear physics of energetic particles and Alfvén eigenmodes by incorporating important physics of radial variations and toroidal mode coupling. For example, gyrokinetic simulations have found nonlinear oscillations of Alfvén eigenmode amplitude and frequency consistent with experimental observations. With better understanding of linear and nonlinear properties of Alfvén eigenmodes, a fruitful future direction is the self-consistent simulation of energetic particle transport, which requires long time simulations of nonlinear interactions between multiple Alfvén eigenmodes. A significant step in this direction has been taken by MHD-gyrokinetic hybrid simulations, which have demonstrated that fast ion profile is flattened by enhanced transport due to resonance overlaps in multiple interacting Alfvén eigenmodes with realistic amplitudes. A very interesting physics here is that the re-distribution of the energetic particle profile by an initially dominant Alfvén eigenmode leads to the excitation of other Alfvén eigenmodes. The broaden phase space volume for the extraction of free energy can then drive large fluctuation amplitudes and enhanced energetic particle transport. Some experimental evidences of such indirect interaction of multiple modes through energetic particles were observed in JT-60U and ASDEX-U experiments.

Thirteen papers presented at the meeting were reviewed to the usual high standard of Nuclear Fusion and published in this special section. On behalf of the IAC, I would like to thank all participants for their contributions to this conference and to thank Nuclear Fusion for publishing this special section. The next meeting of this series will be organized by Simon Pinches and will be held at the IAEA headquarters in Vienna, in the fall of 2015.

The effective sputtering yield of Be $(Y_{\rm Be}^{\rm tot})$ was determined in situ by emission spectroscopy of low ionizing Be as function of the deuteron impact energy (E_in = 25–175 eV) and Be surface temperature (T_surf = 200 °C–520 °C) in limiter discharges carried out in the JET tokamak. Be self sputtering dominates the erosion at high impact energies (E_in > 150 eV) and causes $Y_{\rm Be}^{\rm tot}$ far beyond 1. $Y_{\rm Be}^{\rm tot}$ drops to low values, below 4.5%, at the accessible lowest impact energy (E_in ≃ 25 eV) achievable in limiter configuration. At medium impact energies, E_in = 75 eV, two contributors to the measured $Y_{\rm Be}^{\rm tot}$ of 9% were identified: two third of the eroded Be originates from bare physical sputtering $(Y_{\rm Be}^{\rm phys})$ and one third from chemical assisted physical sputtering $(Y_{\rm Be}^{\rm chem})$. The later mechanism has been clearly identified by the appearance of BeD A–X emission and quantified in cause of a temperature dependence at which the BeD practically vanishes at highest observed Be limiter temperatures. The recorded T_surf dependence, obtained in a series of 34 identical discharges with ratch-up of T_surf by plasma impact and inertial cooling after the discharge, revealed that the reduction of BeD is correlated with an increase of D₂ emission. The release mechanism of deuterium in the Be interaction layer is exchanged under otherwise constant recycling flux conditions at the limiter.

The reduction of $Y_{\rm Be}^{\rm chem}$ with T_surf is also correlated to the reduction of the Be content in the core plasma providing information on the total source strength and Be screening. The chemical assisted physical sputtering, always present at the nominal limiter pre-heating temperature of T_surf = 200 °C, is associated with an additional sputtering channel with respect to ordinary physical sputtering which is surface temperature independent. These JET experiments in limiter configuration are used to benchmark the ERO code and verify ITER first wall erosion prediction. The ERO code overestimates the observed Be sputtering in JET by a factor of about 2.5 which can be transferred to ITER predictions and prolong the expected lifetime of first wall elements.

The turbulence and flows at the plasma edge during the L–I–H, L–I–L and single-step L–H transitions have been measured directly using two reciprocating Langmuir probe systems at the outer midplane with several newly designed probe arrays in the EAST superconducting tokamak. The E × B velocity, turbulence level and turbulent Reynolds stress at ∼1 cm inside the separatrix ramp-up in the last ∼20 ms preceding the single-step L–H transition, but remain nearly constant near the separatrix, indicating an increase in the radial gradients at the plasma edge. The kinetic energy transfer rate from the edge turbulence to the E × B flows is significantly enhanced only in the last ∼10 ms and peaks just prior to the L–H transition. The E × B velocity measured inside the separatrix, which is typically in the electron diamagnetic drift direction in the L-mode, decays towards the ion diamagnetic drift direction in response to fluctuation suppression at the onset of the single-step L–H, L–I–L as well as L–I–H transitions. One important distinction between the L–I–H and the L–I–L transitions has been observed, with respect to the evolution of the edge pressure gradient and mean E × B flow during the I-phase. Both of them ramp up gradually during the L–I–H transition, but change little during the L–I–L transition, which may indicate that a gradual buildup of the edge pedestal and mean E × B flow during the I-phase leads to the final transition into the H-mode. In addition, the transition data in EAST strongly suggest that the divertor pumping capability is an important ingredient in determining the transition behaviour and power threshold.

Flux-surface-averaged momentum loss and parallel rotation of the bulk ions at the edge of a tokamak plasma due to the ion orbit loss are calculated by computing the minimum loss energy of both the trapped and the passing thermal ions. The flux-surface-averaged parallel rotation of the bulk ions is in the co-current direction. The peak of the co-current rotation speed locates inside the last closed flux surface due to the orbit loss of the co-current thermal ions at the very edge of a tokamak plasma. The peaking position moves inward when the ion temperature increases.

It has been demonstrated that lower hybrid current drive (LHCD) systems play a crucial role for steady-state tokamak operation, owing to their high current drive (CD) efficiency and hence their capability to reduce flux consumption. This paper describes the extensive technology programmes developed for the Tore Supra (France) and the KSTAR (Korea) tokamaks in order to bring continuous wave (CW) LHCD systems into operation. The Tore Supra LHCD generator at 3.7 GHz is fully CW compatible, with RF power P_RF = 9.2 MW available at the generator to feed two actively water-cooled launchers. On Tore Supra, the most recent and novel passive active multijunction (PAM) launcher has sustained 2.7 MW (corresponding to its design value of 25 MW m⁻² at the launcher mouth) for a 78 s flat-top discharge, with low reflected power even at large plasma-launcher gaps. The fully active multijunction (FAM) launcher has reached 3.8 MW of coupled power (24 MW m⁻² at the launcher mouth) with the new TH2103C klystrons. By combining both the PAM and FAM launchers, 950 MJ of energy, using 5.2 MW of LHCD and 1 MW of ICRH (ion cyclotron resonance heating), was injected for 160 s in 2011. The 3.7 GHz CW LHCD system will be a key element within the W (for tungsten) environment in steady-state Tokamak (WEST) project, where the aim is to test ITER technologies for high heat flux components in relevant heat flux density and particle fluence conditions. On KSTAR, a 2 MW LHCD system operating at 5 GHz is under development. Recently the 5 GHz prototype klystron has reached 500 kW/600 s on a matched load, and studies are ongoing to design a PAM launcher. In addition to the studies of technology, a combination of ray-tracing and Fokker–Planck calculations have been performed to evaluate the driven current and the power deposition due to LH waves, and to optimize the N_∥ spectrum for the future launcher design. Furthermore, an LHCD system at 5 GHz is being considered for a future upgrade of the ITER Heating and Current Drive systems, with a power capability of 20 MW coupled to the plasma using a PAM launcher. An R&D programme is being conducted at CEA/IRFM to develop a BeO vacuum window which is a safety critical component of the transmission line. In addition, a mock-up of a TE₁₀–TE₃₀ mode converter at 5 GHz, designed for a rectangular transmission line, has been manufactured and successfully tested on Tore Supra at low RF power.

When a significant averaged poloidal flow is generated by the resistive pressure-gradient-driven turbulence the topological properties of the flow structures can change in some radial regions where the shear flow is large. We have applied the topological analysis approach that we have developed (2013 J. Phys. A: Math. Theor.46 375501) to this situation and found that in addition to the filamentary vortex structures there are deformed toroidal structures that seem to act as transport barriers. Analysis of all these structures is presented here.

Recent progress regarding the excitation of energetic-particle driven geodesic acoustic modes (EGAMs) in particle-in-cell simulations is presented in this paper. The exact dispersion relation with adiabatic electrons is derived and solved. The origin of the so-called EGAM is briefly analysed and we show that its nature changes, at least, with the safety factor. A simple expression for the GAM frequency modified in the presence of a small concentration of energetic particles is given in the fluid limit. We show that gyrokinetic simulations with Nemorb in the presence of adiabatic electrons are able to reproduce the analytic predictions. Also, different energy channels are analysed by means of dedicated energy diagnostics characterizing the wave-particle interaction. Finite Larmor radius and finite orbit width effects are studied regarding the excitation of geodesic acoustic modes, showing that these effects are likely to be negligible for sufficiently high concentration of energetic particles, but significant when approaching the threshold of excitation.

The behaviours of hydrogen and helium in tungsten are vitally important in fusion research because they can result in the degradation of the material. In the present work, we carry out density-functional theory calculations to investigate the clustering of hydrogen and helium atoms at interstitial sites, vacancy and small vacancy clusters (Vac_m, m = 2, 3), and the influence of hydrogen and helium on vacancy evolution in tungsten. We find that hydrogen atoms are extremely difficult to aggregate at interstitial sites to form a stable cluster in tungsten. However, helium atoms are energetically favourable to cluster together in a close-packed arrangement between (1 1 0) planes forming helium monolayer structure, where the helium atoms are not perfectly in one plane. Both hydrogen and helium prefer to aggregate stably in vacancy and small vacancy cluster forming Vac_mX_n (X = H, He). The concentrations of Vac_mH_n (m = 1) clusters relative to temperature are evaluated through the law of mass action. The present calculations also show that the emission of a 〈1 1 1〉 dumbbell self-interstitial atom (SIA) from He_n to form VacHe_n and from VacHe_n to form Vac₂He_n may take place for n > 5 and n > 9, respectively. According to the present results, we predict that a helium monolayer structure could nucleate for He atom platelet lying on (1 1 0) plane in tungsten, and the helium platelet formation on (1 1 0) plane in molybdenum observed by the experiment may be due to the initial monolayer arrangement of He atoms at interstitial sites. Meanwhile, our results contribute to the understanding for nucleation and the development of the voids and blisters in tungsten that are observed in the experiments.

This paper reports on experimental evidence that shows perpendicular electron cyclotron resonance heating (ECRH) can trigger classical tearing modes when deposited near a rational flux surface. The complex evolution of an m = 2 island is followed during current ramp-up in KSTAR plasmas, from its initial onset as the rational surface enters the ECRH resonance layer to its eventual lock on the wall after the rational surface leaves the layer. Stability analysis coupled to a transport calculation of the current profile with ECRH shows that the perpendicular ECRH may play a significant role in triggering and destabilizing classical m = 2 tearing modes, in agreement with our experimental observation.

Dynamics of fast ions and shear Alfvén waves are simulated using MEGA, a global nonlinear hybrid code. The scenario considered is based on JT-60U shot E039672, driven by strong negative-ion-based neutral beams (N-NB), just before the onset of a so-called abrupt large event (ALE). It is found that modes with toroidal mode numbers n = 2, 3, 4 can be destabilized, besides the n = 1 mode studied previously. The properties of the modes with n > 1 are sensitive to the value of the plasma beta and the form of the fast ion distribution, so simulation conditions are set up as realistically as presently possible. When the fast ion drive exceeds a certain threshold, the n = 3 mode is enhanced through a convective amplification process while following fast ions were displaced either by the n = 3 mode itself or by the n = 1 mode. The fast ion transport in several cases, simulated with single- or multiple-n modes, is analysed and implications of the results for the explanation of ALEs are discussed.

Two groups of frequency sweeping modes are observed and interpreted in the HL-2 A plasmas with q_min ∼ 1. The tokamak simulation code calculations indicate the presence of a reversed shear q-profile during the existence of these modes. The mode frequencies lie in between TAE and BAE frequencies, i.e. ω_BAE < ω < ω_TAE, and these modes are highly localized near q_min, i.e. r/a ∼ 0.25. A group of modes characterized by down-sweeping frequency with q_min decrease due to q_min > 1 and nq_min − m > 0, and another group of modes characterized by up-sweeping frequency with q_min drop, owing to q_min < 1 and nq_min − m < 0 before sawtooth crash. The kinetic Alfvén eigenmode code analysis supports that the down-sweeping modes are kinetic reverse shear Alfvén eigenmodes (KRSAEs), and the up-sweeping modes are RSAEs, which exist in the ideal or kinetic MHD limit. In addition, the down- and up-sweeping RSAEs both have fast nonlinear frequency behaviour in the process of slow frequency sweeping, i.e. producing pitch-fork phenomena. These studies provide valuable constraint conditions for the q-profile measurements.

Simulations of gyrokinetic energetic ions interacting with the magneto-hydrodynamic (MHD) Alfvén Eigenmodes are presented. The effect of the finite fast-ion orbit width and the finite fast-ion gyroradius, the role of the equilibrium radial electric field, as well as the effect of anisotropic fast-particle distribution functions (loss-cone and ICRH-type distributions), are studied in Wendelstein 7-X stellarator geometry using a combination of gyrokinetic particle-in-cell and reduced MHD eigenvalue codes. A preliminary stability analysis of a HELIAS reactor configuration is undertaken.

In this paper, we report on a comparison of collisionless simulations on global modes (i.e. low poloidal mode number) with the gyrokinetic particle-in-cell code NEMORB against analytical theory and the gyrokinetic semilagrangian code GYSELA. Only axisymmetric modes, i.e. with toroidal mode number n = 0, are considered, and flat equilibrium profiles. Benchmarks are performed for geodesic acoustic modes against local analytical theory. In the presence of energetic ions, benchmarks of NEMORB are performed against GYSELA. The models of adiabatic versus trapped-kinetic versus fully kinetic-electrons and of electrostatic versus electromagnetic at very low beta are compared. Scalings of Alfvén modes are also presented.

This paper presents results of studies of fast particles (ions and alpha particles) in a steady-state compact fusion neutron source (CFNS) and a compact spherical tokamak (ST) reactor with Monte-Carlo and Fokker–Planck codes. Full-orbit simulations of fast particle physics indicate that a compact high field ST can be optimized for energy production by a reduction of the necessary (for the alpha containment) plasma current compared with predictions made using simple analytic expressions, or using guiding centre approximation in a numerical code. Alpha particle losses may result in significant heating and erosion of the first wall, so such losses for an ST pilot plant have been calculated and total and peak wall loads dependence on the plasma current has been studied. The problem of dilution has been investigated and results for compact and big size devices are compared.

A simple radial transport code for predicting the fusion alpha density profiles in an ITER burning plasma unstable to Alfvén eigenmodes (AEs) is illustrated. This extends earlier work by Angioni et al (2009 Nucl. Fusion49 055013) treating the fusion alpha transport from high-n micro-turbulence to include marginal stability (or 'stiff') transport from alpha-driven low-n AEs. The local alpha density gradient AE thresholds are provided by physically realistic linear gyrokinetic code simulations. The transported alpha density profiles are compared to the alpha classical slowing-down profiles dependent on the birth rate source profiles. The base case thermal plasma (and hence source) profiles are taken from a theory-based core transport and H-mode pedestal prediction of ITER performance by Kinsey et al (2011 Nucl. Fusion51 083001). The distinction between the alpha particle and the much smaller alpha energy transport loss is emphasized. The AE transport is localized to the mid-core radii with the high-n micro-turbulence controlling the transport loss of low energy alphas at the edge. Edge energy loss is about 100-fold smaller than particle loss. Even with the worst case boundary condition, only about 0.1% of net heating is lost and escaping alphas can be characterized as very hot helium.

In order to better understand the behaviour of both neutral beam injected and spontaneously generated fast ions in the Madison Symmetric Torus reversed-field pinch, we have developed the full orbit-following code random ion orbits (RIO). The low magnetic field and relatively large level of MHD activity present in MST require a full orbit code as the guiding centre assumptions are violated even for ions with modest energy. Furthermore, quasi-periodic bursts of MHD activity (sawteeth) generate large transient electric fields and significant modifications to the equilibrium magnetic fields. Understanding the full effect of these sawteeth on the spatial and velocity distribution of the fast ions is of great interest. To this end, RIO now has the ability to take the full 3D, time evolving, magnetic and electric fields produced by the visco-resistive MHD code DEBS as input. In static cases, where broad-spectrum magnetic perturbations from DEBS are input, but fixed in time, beam injected ions are found to be generally well confined with the core fast ion density profile largely unaffected by the magnetic modes while the fast ion density in the mid-radius is substantially reduced. In the dynamic case, the large amplitude magnetic fluctuations that occur at the sawtooth crash produce substantial fast ion loss. Those fast ions that are not lost are accelerated by a large, transient, parallel electric field in the co-current direction. This causes the average energy of the beam ions to increase by ∼20%, consistent with recent experimental measurements.

The new neutron spectrometer time-of-flight enhanced diagnostics (TOFED) for the EAST tokamak is presented and its characteristics are described in terms of simulation results, as well as the interface in the torus hall along with new neutral beam (NB) injectors. The use of TOFED for studies of the slowing down of NB-injected deuterons is illustrated. The implications of measuring the neutron emission on a long pulse machine are discussed together with the experimental challenges and diagnostic possibilities approaching those to be encountered in continuous operation.

Suprathermal ions, created by fusion reactions or by additional heating, will play an important role in burning plasmas such as the ones in ITER or DEMO. Basic plasma experiments, with easy access for diagnostics and well-controlled plasma scenarios, are particularly suitable to investigate the transport of suprathermal ions in plasma waves and turbulence. Experimental measurements and numerical simulations have revealed that the transport of fast ions in the presence of electrostatic turbulence in the basic plasma toroidal experiment TORPEX is generally non-classical. Namely, the mean-squared radial displacement of the ions does not scale linearly with time, but 〈r²(t)〉 ∼ t^γ, with γ ≠ 1 generally, γ > 1 corresponding to superdiffusion and γ < 1 to subdiffusion. A generalization of the classical model of diffusion, the so-called fractional Lévy motion, which encompasses power-law (Lévy) statistics for the displacements and correlated temporal increments, leads to non-classical dynamics such as that observed in the experiments. On a macroscopic scale, this results in fractional differential operators, which are used to model non-Gaussian, non-local anomalous transport in a growing number of applied fields, including plasma physics. In this paper, we show that asymmetric fractional Lévy motion can be described by a diffusion equation using space-fractional differential operator with skewness. Numerical simulations of tracers in TORPEX turbulence are performed. The time evolution of the radial particle position distribution is shown to be described by solutions of the fractional diffusion equation corresponding to asymmetric fractional Lévy motion in sub- and superdiffusive cases.

A detailed description of the 14 MeV neutron emission in plasmas heated by neutral beam injection has been carried out by coupling Monte Carlo calculations of the neutron emission spectrum with TRANSP modelling of the beam ion energy distributions. The model is used to study tritium beam injection experiments of the JET trace tritium campaign for internal transport barrier (ITB) and H-mode discharges. For ITB discharges, the measured neutron emission spectrum is well described by modelling using as input the beam ion distribution calculated with TRANSP. For H mode discharges the neutron spectrum can be reproduced only if high energy tritons are lost from the plasma, suggesting the possible role of low frequency tearing modes on the beam ions. The presented results are of relevance for tritium beam transport studies in trace tritium experiments and, more generally, for deuterium and tritium transport studies in high power experiments using neutron emission spectroscopy.

Experiments aiming to study the loss of energetic ions carried out in JET using low density plasmas and on-axis minority ion cyclotron resonance heating (ICRH) have been reported in Nabais et al (2010 Nucl. Fusion50 115006). Though the fast ions accelerated by on-axis ICRH have a distribution in the normalized magnetic moment centred at Λ = 1, experimental measurements have shown that the fast ions whose loss is triggered by tornado modes (toroidal Alfvén eigenmodes (TAE) localized inside the q = 1 surface) reach the scintillator cup with an average Λ significantly higher than one (Λ = 1.1). On the other hand, the losses associated with the presence of TAE localized on the plasma boundary reach the scintillator cup with an average Λ slightly below unity. Since Λ increases while the fast ions drift radially outward due to resonant interaction with the Alfvénic modes, the high values of Λ characterizing the losses triggered by tornado modes indicate these ions have experienced a large radial displacement before being lost, i.e. they were originally localized in the plasma core. These experimental results corroborate the conclusion from Nabais et al (2012 Nucl. Fusion52 083021) that the combined action of modes localized at different radial locations can lead to large radial transport and loss of ions originally localized in the plasma core. The results presented here also show that measurements of the pitch angle may be used to extract information about the original location of the ions reaching the scintillator cup.

A multi-phase simulation that is a combination of classical simulation and hybrid simulation for energetic particles interacting with a magnetohydrodynamic (MHD) fluid is developed to simulate the nonlinear dynamics on the slowing down time scale of the energetic particles. The hybrid simulation code is extended with realistic beam deposition profile, collisions and losses, and is used for both the classical and hybrid phases. The code is run without MHD perturbations in the classical phase, while the interaction between the energetic particles and the MHD fluid is simulated in the hybrid phase. In a multi-phase simulation of DIII-D discharge #142111, the stored beam ion energy is saturated due to Alfvén eigenmodes (AE modes) at a level lower than in the classical simulation. After the stored fast ion energy is saturated, the hybrid simulation is run continuously. It is demonstrated that the fast ion spatial profile is significantly flattened due to the interaction with the multiple AE modes with amplitude v/v_A ∼ δB/B ∼ O(10⁻⁴). The dominant AE modes are toroidal Alfvén eigenmodes (TAE modes), which is consistent with the experimental observation at the simulated moment. The amplitude of the temperature fluctuations brought about by the TAE modes is of the order of 1% of the equilibrium temperature. This is also comparable with electron cyclotron emission measurements in the experiment.

In a tokamak-based fusion power plant, possible scenarios may include regulated sawtooth oscillations to remove thermalized helium from the core of the plasma. During a sawtooth crash, the helium ash and other impurities trapped in the core are driven by the instability to an outer region. However, in a fusion plasma, high energy ions will represent a significant population. We thus study the behaviour of these energetic particles during a sawtooth. This paper presents the modelling of the redistribution of fast ions during a sawtooth reconnection event in a tokamak plasma. Along the lines of the model for the evolution of the flux surfaces during a sawtooth collapse described in Ya.I. Kolesnichenko and Yu.V. Yakovenko 1996 Nucl. Fusion36 159, we have built a time-dependent electromagnetic model of a sawtooth reconnection. The trajectories of the ions are described by a complete gyro-orbit integration. The fast particles were evolved from specific initial parameters (given energy and uniform spread in pitch) or distributed initially according to a slowing-down distribution created by fusion reactions. Our modelling is used to understand the main equilibrium parameters driving the motions during the collapse and to determine the evolution of the distribution function of energetic ions when different geometries of reconnection are considered.