C. Di Troia

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.

An extended hybrid magnetohydrodynamics gyrokinetic model for numerical simulation of shear Alfvén waves in burning plasmas

Adopting the theoretical framework for the generalized fishbonelike dispersion relation, an extended hybrid magnetohydrodynamics gyrokinetic simulation model has been derived analytically by taking into account both thermal ion compressibility and diamagnetic effects in addition to energetic particle kinetic behaviors. The extended model has been used for implementing an extended version of hybrid magnetohydrodynamics gyrokinetic code (XHMGC) to study thermal ion kinetic effects on Alfvenic modes driven by energetic particles, such as kinetic beta induced Alfven eigenmodes in tokamak fusion plasmas. The XHMGC nonlinear model can be used to address a number of problems, where kinetic treatments of both thermal and supra-thermal plasma components are necessary, as theoretically predicted, or where it is desirable to investigate the phenomena connected with the presence of two supra-thermal particle species with different radial profiles and velocity space distributions.

Particle simulation of energetic particle driven Alfvén modes in NBI heated DIII-D experiments

The mutual nonlinear interactions of shear Alfv´ en modes and alpha particles can enhance their transport in burning plasmas. Theoretical and numerical works have shown that rapid transport of energetic ions can take place because of fast growing Alfvmodes (e.g. energetic particle driven modes, EPMs). This kind of transport has been observed in experiments as well as in numerical simulations. Hybrid MHD-gyrokinetic codes can investigate linear and nonlinear dynamics of energetic particle (EP) driven modes, retaining the mutual interaction between waves and EPs self- consistently. Self-consistent nonlinear wave-particle interactions (both in configuration and velocity space) are crucial for a correct description of the mode dynamics in the case of strongly driven modes; thus, a non-perturbative approach is mandatory. The knowledge of the threshold characterizing the transition from weakly to strongly driven regimes is of primary importance for burning plasma operations (e.g. for ITER), in order to avoid EPM enhanced EP transport regimes. The hybrid MHD-gyrokinetic code (HMGC) has been applied to the interpretation of phenomena observed in present experiments with neutral beam (NB) heating. In reversed-shear beam-heated DIII-D discharges, a large discrepancy between the expected and measured EP radial density profiles has been observed in the presence of large Alfvactivity. HMGC simulations with EP radial profiles expected from classical NB deposition as input give rise to strong EPM activity, resulting in relaxed EP radial profiles at saturation level close to experimental measurements. The frequency spectra obtained from several simulations with different toroidal mode numbers, as calculated during the saturated phase when the strong EPMs transform in weak reversed-shear Alfv´ en modes, are quite close to experimental observations both in absolute frequency and in radial localization. In this work, we discuss in particular the effects of nonlinear coupling between different toroidal mode numbers.

Analysis of the nonlinear behavior of shear-Alfvén modes in tokamaks based on Hamiltonian mapping techniques

We present a series of numerical simulation experiments set up to illustrate the fundamental physics processes underlying the nonlinear dynamics of Alfvenic 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 prod...

Kinetic structures of shear Alfvén and acoustic wave spectra in burning plasmas

We present a general theoretical framework for discussing the physics of low frequency fluctuation spectra of shear Alfven and acoustic waves in toroidal plasmas of fusion interest. This framework helps identifying the relevant dynamics and, thus, interpreting experimental observations. We also discuss the roles of such general theoretical framework for verification and validation of numerical simulation codes vs. analytic predictions and experimental results.

From the orbit theory to a guiding center parametric equilibrium distribution function

This work proposes a parametric equilibrium distribution function to be applied to the gyrokinetic studies of the finite orbit width behavior of guiding centers representing several species encountered in axisymmetric tokamak plasmas, such as fusion products, thermal bulk and energetic particles from ion cyclotron radiation heating and negative neutral beam injections. can be used to fit experimental profiles and it could provide a useful tool for experimental and numerical data analysis. Moreover, it could help one to develop analytical computations for facilitating data interpretation in the light of theoretical models. This distribution function can be easily implemented in gyrokinetic codes, where it could be used to simulate plasma also in the presence of external heating sources.

Orbit-based representation of equilibrium distribution functions for low-noise initialization of kinetic simulations of toroidal plasmas

Abstract This work deals with the initial loading of phase space markers for global gyrokinetic particle-in-cell (PIC) simulations of plasmas that are magnetically confined in a toroidally axisymmetric configuration. A method is presented, which allows to prepare a marker distribution that is independent of time. This is achieved by discretizing the phase space along lines of constants of motion, which allows to load markers on the toroidal surfaces of unperturbed guiding center orbits. On each orbit surface, markers are distributed uniformly in time, so their distribution represents the compressible motion of physical particles. This method allows to initialize global PIC codes with an accurate equilibrium distribution function for charged particles, taking into account prompt losses to the wall. It facilitates simulations with lower noise levels and minimal noise–signal correlation; especially, in the linear regime. The problem considered is the representation of energetic ions in tokamaks, which are characterized by large drifts across magnetic surfaces.

Minority heating by ICRH: a tool for investigating burning plasma physics in FAST

A combined Fokker–Planck numerical analysis of the quasi-linear plasma–ion-cyclotron (IC) wave interaction and collisional relaxation of minority ion tails created by IC absorption was performed in order to determine the characteristic fast-ion parameters that are necessary for addressing some of the main ITER burning plasma physics issues, e.g. fast-ion transport due to collective mode excitations, cross-scale couplings of micro-turbulence with meso-scale fluctuations due to energetic particles, etc. These investigations refer to actual scenarios of the Fusion Advanced Studies Torus (FAST), a conceptual tokamak design operating with deuterium plasmas in a dimensionless parameter range similar to that of ITER and equipped with IC resonance heating (ICRH) as a main heating scheme. The destabilization and saturation of fast-ion driven Alfvenic modes below and above the energetic particle modes stability threshold are investigated by numerical simulations with the HMGC code, which assumes the anisotropic energetic particle distribution function accelerated by ICRH as input. The results of this study, obtained by integration of different numerical simulation analyses aimed at investigating the various relevant physics, are presented and discussed.

Nonlinear interplay of Alfvén instabilities and energetic particles in tokamaks

The confinement of energetic particles (EP) is crucial for an efficient heating of tokamak plasmas. Plasma instabilities such as Alfven Eigenmodes (AE) can redistribute the EP population making the plasma heating less effective, and leading to additional loads on the walls. The nonlinear dynamics of toroidicity induced AE (TAE) is investigated by means of the global gyrokinetic particle-in-cell code ORB5, within the NEMORB project. The nonperturbative nonlinear interplay of TAEs and EP due to the wave-particle nonlinearity is studied. In particular, we focus on the nonlinear modification of the frequency, growth rate and radial structure of the TAE, depending on the evolution of the EP distribution in phase space. For the ITPA benchmark case, we find that the frequency increases when the growth rate decreases, and the mode shrinks radially. This nonlinear evolution is found to be correctly reproduced by means of a quasilinear model, namely a model where the linear effects of the nonlinearly modified EP distribution function are retained.