Table of contents

This special section brings together much of what is currently at the forefront of ion cyclotron resonance frequency (ICRF) research. Which theories are people working on? Where is progress being made? What results are being obtained?

The present Nuclear Fusion section on ICRF is not—and was explicitly meant not to be—an overview or review of ICRF systems, research achievements or theories. It is more a snapshot of the leading edge of the investigations. It is based, in part, on presentations to the 16th Topical Conference on RF Power in Plasmas, Park City, Utah, USA, April 2005.

The forefront of ICRF research currently being actively pursued covers a wide range of topics: theoretical, experimental and technological.

As can be expected, most of the papers in this section have direct relevance to ITER. Elements that will be important in ITER, and that are being addressed and developed in the papers, are the presence of fast particles with their influence on wave propagation and damping, the non-linear mechanisms in the edge—in particular close to the wave launcher—and steady-state aspects. Specific ITER components as well as RF scenarios are studied.

Continued efforts to improve the analytical description of wave damping and absorption and the availability of gradually more powerful computers led to significant progress in incorporating the effect of particles with non-thermal velocity distributions—the presence of which has already become significant in present-day machines due to massive RF and/or NBI heating which forces the particles away from thermo-dynamical equilibrium (Brambilla et al, Jaeger et al).

The exact role that RF-created and fusion-born fast particles will play is still a matter of lively debate. As shown in the papers by Choi et al and Pinsker et al, the presence of energetic particles is a significant factor in the wave absorption, even at high harmonics.

Accounting for the actual magnetic topology allows the capture of RF induced effects which were treated in less detail in earlier modelling. Murakami et al present a wave–particle description that accounts for the complex geometry of the Large Helical Device (LHD). Finite Larmor radius effects and changes to the guiding centre orbits are addressed theoretically in the papers by Johnson et al and Hellsten et al.

In the edge, the plasma is not fully ionized, the machine walls and protruding objects are close-by, and the magnetic topology can be complicated. Despite these difficulties an understanding and appropriate modelling of the plasma edge is imperative as the plasma edge is an essential feature in ICRF coupling and RF-plasma interaction. The full richness of the antenna near-field plasma dynamics and the non-linear plasma–wave interaction close to the launchers is addressed by Myra et al, while Bobkov et al present experimental evidence of some key players in the area of wave coupling.

Advances are being made in treating increasingly realistic and detailed antenna geometries with plasma in coupling computations (Lancellotti et al) and on describing the presence and effect of the plasma in front of the antenna box.

The role of edge interactions becomes of greater consequence as the pulse length grows towards steady state conditions. Colas et al provide evidence gathered during the long pulses in Tore Supra.

Proper design and tuning of the wave launcher is essential to ensure coupling to a variety of experimental conditions. Messiaen et al and Bosia et al focus on specific technological elements of the ICRF system foreseen for ITER: the antenna and the matching system.

In the initial phase of ITER, where H will be used as the majority ion species, special non-fusion ICRF scenarios will need to be used. Such scenarios are explored by Mayoral et al in JET.

We hope that this special section will give you a flavour of the ongoing research in the ICRF area and that it will contribute to advancing ICRF in particular for ITER.

The code TORIC solving Maxwell equations in toroidal axisymmetric plasmas in the ion cyclotron (IC) frequency range has proved to be a useful tool for the simulation of IC heating and current drive in tokamak plasmas. TORIC has now been integrated in a package which includes, among other features, an interface to the experimental data (Grad–Shafranov MHD configuration, density and temperature profiles), interfaces to quasilinear Fokker–Planck solvers for the electrons and ions and a subroutine which allows us to estimate the effects of suprathermal anisotropic minority ions populations on wave propagation and absorption. This package allows somewhat simplified but essentially self-consistent simulations of heating and current drive in this frequency domain. In this paper we summarize the physics included in TORIC, with particular emphasis on the most recent extensions, and present an example of the application of the package to the analysis of two IC heating experiments in ASDEX Upgrade and in JET.

Global wave solutions with self-consistent velocity distributions are calculated for ion cyclotron heating in non-Maxwellian plasmas. The all-orders spectral algorithm (AORSA) global wave solver is generalized to treat non-thermal velocity distributions arising from fusion reactions, neutral beam injection and wave driven diffusion in velocity space. Quasi-linear diffusion coefficients are derived directly from the wave electric field and used to calculate ion velocity distribution functions with the CQL3D Fokker–Planck code. Alternatively, the quasi-linear coefficients can be calculated numerically by integrating the Lorentz force equations along particle orbits. Self-consistency between the wave electric field and resonant ion distribution function is achieved by iterating between the global-wave and Fokker–Planck solutions.

To study fast Alfvén wave damping on fast ions, a Monte-Carlo code, ORBIT-RF, has been coupled with a 2D full wave code, TORIC4. The ORBIT-RF/TORIC4 combination has been applied to DIII-D experimental conditions to investigate fast wave (FW) heating of injected beam ions over a range of ion cyclotron harmonics. ORBIT-RF using a single dominant toroidal and poloidal Fourier wave number qualitatively reproduces the strong FW–beam interaction at 60 MHz (4Ω_D and 5Ω_D) and the much weaker interaction at 116 MHz (8Ω_D) in DIII-D L-mode plasmas, consistent with experimental observations. The result at 8Ω_D differs from linear theory prediction using a Maxwellian to model the fast ion distribution function, suggesting the importance of finite orbit effect, Coulomb collisions for transport across flux surfaces and details of the non-Maxwellian fast ion distribution.

The absorption of fast Alfvén waves (FW) by ion cyclotron harmonic damping in the range of harmonics from 4th to 8th is studied theoretically and with experiments in the DIII-D tokamak. A formula for linear ion cyclotron absorption on ions with an arbitrary distribution function which is symmetric about the magnetic field is used to estimate the single-pass damping for various cases of experimental interest. It is found that damping on fast ions from neutral beam injection can be significant even at the 8th harmonic if the fast ion beta, the beam injection energy and the background plasma density are high enough and the beam injection geometry is appropriate. The predictions are tested in several L-mode experiments in DIII-D with FW power at 60 MHz and at 116 MHz. It is found that 4th and 5th harmonic absorption of the 60 MHz power on the beam ions can be quite strong, but 8th harmonic absorption of the 116 MHz power appears to be weaker than expected. The linear modelling predicts a strong dependence of the 8th harmonic absorption on the initial pitch-angle of the injected beam, which is not observed in the experiment. Possible explanations of the discrepancy are discussed.

ICRF heating in the Large Helical Device is studied applying two global simulation codes; a drift kinetic equation solver, GNET, and a wave field solver, TASK/WM. Characteristics of energetic ion distributions in the phase space are investigated changing the resonance heating position; i.e. the on-axis and off-axis heating cases. A clear peak of the energetic ion distribution can be seen in the off-axis heating case because of the stable orbit of resonant energetic ions. The simulation results are also compared with experimental results evaluating the count number of the neutral particle analyzer and a relatively good agreement is obtained.

An orbit averaged quasilinear operator for resonant ion cyclotron interactions is analysed. The regions in phase space where the interactions are strong and the boundaries between regions with resonant and non-resonant ion orbits are identified. At these boundaries the quasilinear diffusion coefficient becomes discontinuous, causing the standard Monte Carlo scheme to induce an unphysical flow of test particles into the region with lower diffusion coefficient. A new Monte Carlo scheme that balances the flows across discontinuities is proposed. Moreover, the quasilinear diffusion coefficient is shown to deviate significantly from the lowest order Larmor radius scaling , where δH is the perturbed Hamiltonian. This is not only caused by the finite Larmor radius effects, but also by the inhomogeneous electric field polarization and by the changes to the guiding centre orbits during the wave-particle interactions.

A detailed study of ion cyclotron interactions in a toroidal plasma has been carried out in order to elucidate the role of toroidal effects on ion cyclotron emission. It is well known that non-relaxed distribution functions can give rise to excitation of magnetosonic waves by ion cyclotron interactions when the distribution function increases with respect to the perpendicular velocity. We have extended and clarified the conditions under which even collisionally relaxed distribution function can destabilize magnetosonic eigenmodes. In a toroidal plasma, cyclotron interactions at the plasma boundary with ions having barely co-current passing orbits and marginally trapped orbits can cause destabilisation by the strong inversion of the distribution function along the characteristics of cyclotron interaction by neo-classical effects. The unstable interactions can further be enhanced by tangential interactions, which can also prevent the interactions from reaching the stable part of the characteristics, where they interact with trapped orbits. Conditions on the localization of the magnetosonic eigenmodes for unstable excitation are analysed by studying the anti-Hermitian part of the susceptibility tensor of thermonuclear alpha-particles. The pattern of positive and negative regions of the anti-Hermitian part of the susceptibility tensor of thermonuclear alpha-particles is, in general, consistent with the excitation of edge localized magnetosonic eigenmodes, even though the eigenmodes are usually not localized in the major radius and for distribution functions that have relaxed to steady state.

Nonlinear interactions of ion cyclotron range of frequency (ICRF) waves with fusion plasmas are reviewed. Although the linear theory of ICRF waves, including fast waves (FWs), high-harmonic fast waves and ion Bernstein waves (IBWs), is widely applicable, nonlinear effects can still be important, especially in the edge plasma or for novel core applications. Here the topics of flow drive, ponderomotive forces, radiofrequency (rf) sheaths, parametric decay and related interactions with the edge plasma are considered. Primary emphasis is placed on the basic underlying physics and tokamak applications. For FW antennas, the parallel electric field near launching structures is known to drive rf sheaths which can give rise to convective cells, interaction with plasma 'blobs', impurity production and edge power dissipation. In addition to sheaths, IBW waves in the edge plasma are subject to strong ponderomotive effects and parametric decay. In the core plasma, slow waves can sometimes induce nonlinear effects. Mechanisms by which these waves can influence the radial electric field and its shear are summarized and related to the general (reactive-ponderomotive and dissipative) force on a plasma from rf waves. Standard ICRF codes have begun to incorporate the nonlinear topics described here. Further progress in integrated simulation should allow new predictive modelling capabilities.

The relative impact of edge localized modes (ELM) size and plasma shape on the antenna coupling in ASDEX Upgrade discharges is studied. A strong dependence of relative change in the ion cyclotron range of frequencies antenna coupling during ELMs on the ELM size is observed. The changes in the coupling also show some dependence on the plasma triangularity; the latter generally influences the ELM size. At high plasma density and small antenna–plasma distance, however, there is a strong residual correlation of the antenna coupling on the plasma triangularity which appears not to be connected with the ELM size. A possible explanation of this correlation is given in terms of the connection lengths of the magnetic field lines at the antenna. This hypothesis is substantiated by the investigation of L-mode discharges, which are better diagnosed than the ELM phases of the H-mode ones.

The demand for a predictive tool to help in designing ion-cyclotron radio frequency (ICRF) antenna systems for today's fusion experiments has driven the development of codes such as ICANT, RANT3D, and the early development of TOPICA (TOrino Polytechnic Ion Cyclotron Antenna) code. This paper describes the substantive evolution of TOPICA formulation and implementation that presently allow it to handle the actual geometry of ICRF antennas (with curved, solid straps, a general-shape housing, Faraday screen, etc) as well as an accurate plasma description, accounting for density and temperature profiles and finite Larmor radius effects. The antenna is assumed to be housed in a recess-like enclosure. Both goals have been attained by formally separating the problem into two parts: the vacuum region around the antenna and the plasma region inside the toroidal chamber. Field continuity and boundary conditions allow formulating of a set of two coupled integral equations for the unknown equivalent (current) sources; then the equations are reduced to a linear system by a method of moments solution scheme employing 2D finite elements defined over a 3D non-planar surface triangular-cell mesh. In the vacuum region calculations are done in the spatial (configuration) domain, whereas in the plasma region a spectral (wavenumber) representation of fields and currents is adopted, thus permitting a description of the plasma by a surface impedance matrix. Owing to this approach, any plasma model can be used in principle, and at present the FELICE code has been employed. The natural outcomes of TOPICA are the induced currents on the conductors (antenna, housing, etc) and the electric field in front of the plasma, whence the antenna circuit parameters (impedance/scattering matrices), the radiated power and the fields (at locations other than the chamber aperture) are then obtained. An accurate model of the feeding coaxial lines is also included. The theoretical model and its TOPICA implementation have been fully validated against measured data both in vacuo and in plasma-facing conditions for real-life structures.

Long pulse operation on the Tore Supra tokamak has entered a new phase, characterized by the use of heating power level in excess of 10 MW, during pulses lasting several tens of resistive times. This has been made possible by the use of ion cyclotron range of frequency (ICRF) heating (9 MW coupled to the plasma at 57 MHz), combined with lower hybrid current drive (LHCD: 3 MW at 3.7 GHz) and efficient fuelling techniques (supersonic gas injection, pellets). This paper addresses key technological, operational and physics issues related to the long pulse operation of the Tore Supra ICRF system and required for a reactor: R&D on the ICRF plant, real-time control and safety procedures, integration with other tokamak subsystems, experimental investigation and theoretical modelling of the edge ICRF physics (wave coupling, heat loads on antenna front faces). As far as possible lessons are drawn from the experience gained on Tore Supra for the design and operation of a next-step device.

A mock-up of the complete antenna array (24 straps grouped in 8 triplets) of the ICRH system with external matching for ITER has been constructed with a length reduction factor of 5. At a frequency increased by the same factor the electrical properties of the full-scale system can be measured in the presence of non-dispersive medium. A movable water tank in front of the array simulates variable plasma loading. Measurements of the matching performances of various external circuit configurations and of the scattering matrix of the system show (i) the non-negligible effect of mutual coupling on load resilient matching by Conjugate T (CT) or hybrid leading to coupling between the matching actuators and the generators and asymmetry in power distribution, (ii) good load resilience of a single CT for the right choice of configuration and number of matching parameters, (iii) the large number of matching solutions for coupled CTs and (iv) the benefit of passive power distribution to the straps. This has been successfully tested in the case of the complete array. The power is passively distributed among the upper half and the bottom half of the 24 radiating straps of the antenna plug. The 4 top and 4 bottom triplets are, respectively, set in parallel outside the antenna plug near a voltage anti-node by means of T junctions. The load resilient matching (VSWR <1.3 for an antenna loading variation of about 1–8 Ω m⁻¹) is then obtained by a 4-parameters single CT configuration or a hybrid. The maximum voltage along the line remains equal to the one in the antenna plug and there is a fair power share between the straps. A straightforward robust matching procedure of the complete array is described.

The effective radiation resistance of different toroidal and poloidal phasing conditions is measured and compared. The paper also underlines the significant influence of the presence of the electrostatic screen and the resulting increase in the recess of the straps on the reduction of the coupling to the load and of the mutual coupling between the straps.

In ITER, the ion cyclotron heating (ICH) system should routinely and reliably operate at a power level close to the installed power (20 MW) in quasi-continuous operation. The operation will be efficient and reliable only if plasma coupling and absorption of the fast wave on the plasma bulk are optimized, parasitic power losses in the plasma edge minimized, and the RF power flow, from the wave launching structure to the absorption layer, efficiently maintained against the effects of significant load variations. In this paper the ion cyclotron launcher proposed in the ITER Final Design Report (FDR) is briefly reviewed and a number of design changes are proposed, without any modification of the basic layout, in order to simplify construction and maintenance and to improve the performance and reliability of operation.

During the initial operation of the International Thermonuclear Experimental Reactor (ITER), it is envisaged that activation will be minimized by using hydrogen (H) plasmas where the reference ion cyclotron resonance frequency (ICRF) heating scenarios rely on minority species such as helium (³He) or deuterium (D). This paper firstly describes experiments dedicated to the study of ³He heating in H plasmas with a sequence of discharges in which 5 MW of ICRF power was reliably coupled and the ³He concentration, controlled in real-time, was varied from below 1% up to 10%. The minority heating (MH) regime was observed at low concentrations (up to 2%). Energetic tails in the ³He ion distributions were observed with effective temperatures up to 300 keV and bulk electron temperatures up to 6 keV. At around 2%, a sudden transition was reproducibly observed to the mode conversion regime, in which the ICRF fast wave couples to short wavelength modes, leading to efficient direct electron heating and bulk electron temperatures up to 8 keV. Secondly, experiments performed to study D minority ion heating in H plasmas are presented. This MH scheme proved much more difficult since modest quantities of carbon (C) impurity ions, which have the same charge to mass ratio as the D ions, led directly to the mode conversion regime. Finally, numerical simulations to interpret these two sets of experiments are under way and preliminary results are shown.

A formulation of the anisotropic pressure magnetohydrodynamic equilibrium problem for three-dimensional plasmas with imposed nested magnetic surfaces is developed based on a bi-Maxwellian model of the distribution function for the energetic particle species. The hot particle distribution function satisfies the constraint . Large parallel and perpendicular anisotropy factors can be explored within the model through the choice of the hot particle perpendicular to parallel temperature ratio T_⊥/T_||. A fixed boundary version of the VMEC code has been adapted to numerically compute three-dimensional anisotropic pressure equilibria. Applications to a 10-field period Heliotron device and a 2-field quasiaxisymmetric stellarator demonstrate that the pressures do not vary significantly around the magnetic surfaces when the total parallel pressure p_|| is larger than its perpendicular counterpart p_⊥. For off-axis hot particle deposition with p_⊥ > p_||, p_⊥ concentrates in the region where the energetic particles are generated. On the other hand, p_|| is distributed roughly uniformly around the flux surfaces in the Heliotron but is localized on the low field side in the quasiaxisymmetric machine. The hot particle density structure correlates more closely with the corresponding perpendicular rather than with parallel pressure. The specific form for the definition of β that best correlates with the Shafranov shift is identified.

In this paper, different pattern recognition techniques have been tested in order to implement an automatic tool for disruption classification in a tokamak experiment. The methods considered refer to clustering and classification techniques. In particular, the investigated clustering techniques are self-organizing maps and K-means, while the classification techniques are multi-layer perceptrons, support vector machines, and k- nearest neighbours. Training and testing data have been collected selecting suitable diagnostic signals recorded over 4 years of EFDA-JET experiments. Multi-layer perceptron classifiers exhibited the best performance in classifying mode lock, density limit/high radiated power, H-mode/L-mode transition and internal transport barrier plasma disruptions. This classification performance can be increased using multiple classifiers. In particular the outputs of five multi-layer perceptron classifiers have been combined using multiple classifier techniques in order to obtain a more robust and reliable classification tool, that is presently implemented at JET.

Plasma start-up and sustainment without an inductive field have been studied in the TST-2@K spherical tokamak using high power RF sources (8.2 GHz/up to 170 kW). Steady state discharges with a plasma current of 4 kA were achieved. The line integrated density was about 3 × 10¹⁷ m⁻² and the electron temperature was 160 eV. A truncated equilibrium was introduced to reproduce magnetic measurements. It was found that a positive Pfirsch–Schlüter current in the open field line region at the outboard boundary makes a significant contribution to the current. Insensitivity of the current to variations in the vertical field and RF power variation was also found.

Steady state divertor operation with high performance plasmas (n_e ∼ 0.7 × 10¹⁹ cm⁻³, T_i ∼ 2 keV) was demonstrated for half an hour in the Large Helical Device (LHD), the superconducting helical device (R = 3.6–3.9 m, a = 0.6 m, B = 3 T, l/m = 2/10). The high performance plasmas have been sustained with an averaged heating power of 680 kW and achieved an injected energy of 1.3 GJ. This required both advanced technological integration of heating systems and divertor heat flux control. In particular, optimization of divertor heat flux distribution along the divertor leg trace on divertor plates and real-time magnetic axis sweeping (R = 3.67–3.7 m) have allowed LHD to access a steady state regime with a margin of safety for the actively cooled divertor plates. The distribution of divertor heat load along the traces was investigated with calorimetric measurements and it was found that there was a localized heat load connected with the loss of high-energy ions produced by ion cyclotron radio frequency near-fields. Orbit analysis shows that the behaviour of high-energy ions is qualitatively in good agreement with the experimental result. Long-pulse discharges were terminated by radiation collapse due to penetration of metallic flakes into the plasma.

Two-dimensional (2D) spatial profile and the temporal evolution of the 14 and 2.5 MeV neutron emissivities from D–D and D–T fusion reactions were studied using the measurements of the upgraded neutron profile monitor during the last trace tritium experiments in JET. The JET neutron profile monitor provides unique capability for 2.5 and 14 MeV neutrons line-integrated measurements simultaneously. A systematic comparison of D–D and D–T neutron emissivity was performed. The tritium concentration or fuel ratio (n_T/n_D) was analysed for a set of 34 ELMy-H mode discharges with tritium puff. Tritium concentration is deduced with a method based on the ratio of D–T 14 MeV and D–D 2.5 MeV neutron emissivities in order to exploit the maximum information available from neutron data. With the help of a tomography algorithm recently developed at JET, 2D spatial profiles of the tritium concentration in the plasma were obtained. These profiles can be used to perform transport studies. Tritium core confinement is clearly seen to increase with plasma density for the set of discharges studied. Differences in the shape of these profiles are also found between low and high density plasmas. Shortly after tritium puffing, 2D spatial profiles of the tritium concentration exhibit typical hollow profiles and in some cases transient poloidal asymmetric features have been observed in 2D images.

The role of stochastization of magnetic field lines is analysed in fast reconnection phenomena occurring in magnetized fusion plasma during various conditions in the ASDEX Upgrade tokamak. The mapping technique is applied to trace the field lines of toroidally confined plasma where perturbation parameters are expressed in terms of experimental perturbation amplitudes determined from the ASDEX Upgrade tokamak. It is found that fast reconnection observed during amplitude drops of the neoclassical tearing mode instability in the frequently interrupted regime can be related to stochastization. It is also shown that stochastization can explain the fast loss of confinement during the minor disruption. This demonstrates that stochastization can be regarded as a possible cause for different MHD events in the ASDEX Upgrade.