F. Zonca

Chapter 5: Physics of energetic ions

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 Alfvenic 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 Alfven 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 Alfven 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 Alfven 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.

Radial structures and nonlinear excitation of geodesic acoustic modes

Geodesic acoustic modes (GAM) are shown to constitute a continuous spectrum due to radial inhomogeneities. The importance and theoretical as well as experimental implications of this fact are discussed in this work. The existence of a singular layer causes GAM to mode convert to short-wavelength kinetic GAM (KGAM) via finite ion Larmor radii; analogous to kinetic Alfven waves (KAW). Furthermore, it is shown that KGAM can be nonlinearly excited by drift-wave (DW) turbulence via 3-wave parametric interactions, and the resultant driven-dissipative nonlinear system exhibits typical prey-predator self-regulatory dynamics, consistent with recent experimental observations on HL-2A. The degeneracy of GAM/KGAM with beta-induced Alfven eigenmodes (BAE) is demonstrated and discussed, with emphasis on its important role in the complex self-organized behaviors of burning plasmas.

Kinetic theory of low-frequency Alfvén modes in tokamaks

The kinetic theory of low-frequency Alfven modes in tokamaks is presented. The inclusion of both diamagnetic effects and finite core-plasma ion compressibility generalizes previous theoretical analyses (Tsai S T and Chen L 1993 Phys. Fluids B 5 3284) of kinetic ballooning modes and clarifies their strong connection to beta-induced Alfven eigenmodes. The derivation of an analytic mode dispersion relation allows us to study the linear stability of both types of modes as a function of the parameters characterizing the local plasma equilibrium and to demonstrate that the most unstable regime corresponds to a strong coupling between the two branches due to the finite thermal ion temperature gradient. In addition, we also show that, under certain circumstances, non-collective modes may be present in the plasma, formed as a superposition of local oscillations which are quasi-exponentially growing in time.

The radial structure of the ion‐temperature‐gradient‐driven mode

An analysis of the radial structure of the ion‐temperature‐gradient‐driven mode is presented and the dependence of the radial correlation length Lr on parameters such as magnetic shear is discussed. It is found that Lr decreases algebraically with increasing shear for moderate to large shear values, and it decreases exponentially with decreasing shear for low shear values. These results seem in qualitative agreement with several experiments which observe strong reduction of the transport coefficients close to the magnetic axis.

The Fusion Advanced Studies Torus (FAST): a proposal for an ITER satellite facility in support of the development of fusion energy*

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 = 1.82m, a = 0.64m) with high toroidal field (BT up to 8.5T) and plasma current (Ip up to 8MA). 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; 30MW on the plasma). Moreover, the experiment foresees the use of 6MW of lower hybrid (LHCD), essentially for plasma control and for non-inductive current drive, and of electron cyclotron resonance heating (ECRH, 4MW) for localized electron heating and plasma control. The ports have been designed to accommodate up to 10MW of negative neutral beams (NNBI) in the energy range 0.5‐1MeV. The total power input will be in the 30‐40MW range under different plasma scenarios with a wall power load comparable to that of ITER ( P/ R∼ 22MWm −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 ≈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

Current drive at plasma densities required for thermonuclear reactors

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.

Hybrid magnetohydrodynamic‐gyrokinetic simulation of toroidal Alfvén modes

Resonant energetic particles play a major role in determining the stability of toroidal Alfven eigenmodes (TAE’s) by yielding the well‐known driving mechanism for the instability and by producing an effective dissipation, which removes the singular character of local oscillations of the shear‐Alfven continuum and gives discrete kinetic Alfven waves (KAW’s). Toroidal coupling of two counterpropagating KAW’s generates the kinetic analog of the TAE, the KTAE (kinetic TAE). The nonperturbative character of this phenomenon and of the coupling between TAE and KAW’s, and the relevance of finite drift‐orbit effects limit the effectiveness of the analytical approach to asymptotic regimes, which are difficult to compare with realistic situations. A three‐dimensional hybrid fluid‐particle initial‐value code for the numerical simulation of the linear and nonlinear evolution of toroidal modes of the Alfven branch has been developed. It is shown that for typical parameters the KTAE is, indeed, more unstable than the TAE.

Theory of Alfvén waves and energetic particle physics in burning plasmas

We present an overview on one issue of practical interest for burning plasmas, i.e. whether fast ions and charged fusion products are sufficiently well confined such that they transfer their energy and/or momentum to the thermal plasma without appreciable degradation due to collective modes. In the present work, we address this issue by analysing theoretically the dynamics of shear Alfven waves collectively excited by energetic particles in tokamak plasmas. Both linear physics, such as spectral and stability properties, and key non-linear wave and particle dynamics are identified and considered. We also discuss the investigations of such processes via computer simulations as well as the importance of benchmarking with existing or future experimental observations.

Existence of ion temperature gradient driven shear Alfvén instabilities in tokamaks

The existence of unstable ion temperature gradient driven Alfven eigenmodes (AITG) is demonstrated in tokamak plasmas, which are ideally stable with respect to magnetohydrodynamics (MHD). Conditions for the destabilization of such modes are quantitatively discussed on the basis of numerical solutions of a set of one-dimensional integral equations along the ballooning coordinate (quasi-neutrality and parallel Ampere’s law). Furthermore, theoretical analyses of the eigenmode dispersion relation, which is given in a compact analytical form in the small ion orbit width limit (compared to the radial wavelength), provide a basis for explaining the general properties of the modes. It is emphasized that instability requires both sufficiently strong thermal ion temperature gradients and that the plasma be not too far away from ideal MHD marginal stability.

Theory of toroidal Alfvén modes excited by energetic particles in tokamaks

A general analytical theory for the two‐dimensional eigenmode structures and stability of high toroidal‐mode‐number (high‐n) shear Alfven modes in axisymmetric tokamaks is presented. This theory, thus, further generalizes the previous work on the high‐n toroidal Alfven eigenmode (TAE) [Phys. Fluids B 5, 3668 (1993)] by including, nonperturbatively, plasma kinetic effects and resonant excitations by energetic particles. Specifically, in addition to recovering the known theoretical predictions on TAE, we have derived new results on global radial structures, as well as stability properties of kinetic toroidal Alfven eigenmodes (KTAE) and energetic‐particle modes (EPM).