The area of energetic particle (EP) physics in fusion research has been actively and extensively researched in recent decades. The progress achieved in advancing and understanding EP physics has been substantial since the last comprehensive review on this topic by Heidbrink and Sadler (1994 Nucl. Fusion 34 535). That review coincided with the start of deuterium?tritium (DT) experiments on the Tokamak Fusion Test Reactor (TFTR) and full scale fusion alphas physics studies.Fusion research in recent years has been influenced by EP physics in many ways including the limitations imposed by the ?sea? of Alfv?n eigenmodes (AEs), in particular by the toroidicity-induced AE (TAE) modes and reversed shear AEs (RSAEs). In the present paper we attempt a broad review of the progress that has been made in EP physics in tokamaks and spherical tori since the first DT experiments on TFTR and JET (Joint European Torus), including stellarator/helical devices. Introductory discussions on the basic ingredients of EP physics, i.e., particle orbits in STs, fundamental diagnostic techniques of EPs and instabilities, wave particle resonances and others, are given to help understanding of the advanced topics of EP physics. At the end we cover important and interesting physics issues related to the burning plasma experiments such as ITER (International Thermonuclear Experimental Reactor).

Energetic particle physics in fusion research in preparation for burning plasma experiments

This paper presents a complete theoretical framework for studying turbulence and transport in rapidly rotating tokamak plasmas. The fundamental scale separations present in plasma turbulence are codified as an asymptotic expansion in the ratio ϵ = ρi/a of the gyroradius to the equilibrium scale length. Proceeding order by order in this expansion, a set of coupled multiscale equations is developed. They describe an instantaneous equilibrium, the fluctuations driven by gradients in the equilibrium quantities, and the transport-timescale evolution of mean profiles of these quantities driven by the interplay between the equilibrium and the fluctuations. The equilibrium distribution functions are local Maxwellians with each flux surface rotating toroidally as a rigid body. The magnetic equilibrium is obtained from the generalized Grad–Shafranov equation for a rotating plasma, determining the magnetic flux function from the mean pressure and velocity profiles of the plasma. The slow (resistive-timescale) evolution of the magnetic field is given by an evolution equation for the safety factor q. Large-scale deviations of the distribution function from a Maxwellian are given by neoclassical theory. The fluctuations are determined by the ‘high-flow’ gyrokinetic equation, from which we derive the governing principle for gyrokinetic turbulence in tokamaks: the conservation and local (in space) cascade of the free energy of the fluctuations (i.e. there is no turbulence spreading). Transport equations for the evolution of the mean density, temperature and flow velocity profiles are derived. These transport equations show how the neoclassical and fluctuating corrections to the equilibrium Maxwellian act back upon the mean profiles through fluxes and heating. The energy and entropy conservation laws for the mean profiles are derived from the transport equations. Total energy, thermal, kinetic and magnetic, is conserved and there is no net turbulent heating. Entropy is produced by the action of fluxes flattening gradients, Ohmic heating and the equilibration of interspecies temperature differences. This equilibration is found to include both turbulent and collisional contributions. Finally, this framework is condensed, in the low-Mach-number limit, to a more concise set of equations suitable for numerical implementation.

https://iopscience.iop.org/article/10.1088/0034-4885/76/11/116201/pdf

Multiscale gyrokinetics for rotating tokamak plasmas: fluctuations, transport and energy flows

High frequency modes (150-300 kHz) are found in several magnetic configurations of TJ-II plasmas heated by neutral beam injection (NBI). The clear dependence of mode frequency on plasma density and mass species suggests them to be Alfveigenmodes. The appearance of these modes is linked to the presence of low order rational surfaces close to the rotational transform profile. They can exhibit steady or chirping behaviour depending on the plasma profiles. Frequency chirping is observed in NBI plasmas with broad temperature profiles, but rarely observed with relatively peaked profiles. The Alfvactivity has been characterized in detail with magnetic coils for the standard configuration. Cross analyses with heavy ion beam probe and reflectometer signals have yielded spatial resolution and radial profiles of the perturbation. Correlation between magnetic coil signals and signals from diagnostics sensitive to edge ion losses, namely Langmuir probes and a fast ion loss detector, has been observed in some cases and characterized taking advantage of the chirping nature of the observed Alfvactivity. (Some figures in this article are in colour only in the electronic version)

https://iopscience.iop.org/article/10.1088/0029-5515/51/3/033001/pdf

Alfvén eigenmodes measured in the TJ-II stellarator

Zonal flows and their high-frequency counterpart, the geodesic acoustic modes (GAMs) are considered as a possible mechanism of the plasma turbulence self-regulation. In the T-10 tokamak GAMs have been studied by the heavy ion beam probing and multipin Langmuir probes. The wide range of the regimes with Ohmic, on-axis and off-axis electron cyclotron resonance heating (ECRH) were studied (Bt = 1.5–2.4 T, Ip = 140–300 kA, , PEC < 1.2 MW). It was shown that GAM has radially homogeneous structure and poloidal m = 0 for potential perturbations. The local theory predicts that , that means the frequency increases with the decrease of the minor radius. In contrast, the radial distribution of experimental frequency of the plasma potential and density oscillations, associated to GAM, is almost uniform over the whole plasma radius, suggesting the features of the nonlocal (global) eigenmodes. The GAM amplitude in the plasma potential also tends to be uniform along the radius. GAMs are more pronounced during ECRH, when the typical frequencies are seen in the narrow band from 22 to 27 kHz for the main peak and 25–30 kHz for the higher frequency satellite. GAM characteristics and the range of GAM existence are presented as functions of Te, density, magnetic field and PEC.

The features of the global GAM in OH and ECRH plasmas in the T-10 tokamak

A direct comparison of the electric potential and its fluctuations in the T-10 tokamak and the TJ-II stellarator is presented for similar plasma conditions in the two machines, using the heavy ion beam probe diagnostic. We observed the following similarities: (i) plasma potentials of several hundred volts, resulting in a radial electric field Er of several tens of V?cm?1; (ii) a negative sign for the plasma potential at central line-averaged electron densities larger than 1\times 10^{19}\,{\rm m}^{-3} SRC=http://ej.iop.org/images/0029-5515/51/8/083043/nf381326in001.gif/>, with comparable values in both machines, even when using different heating methods; (iii) with increasing electron density ne or energy confinement time ?E, the potential evolves in the negative direction; (iv) with electron cyclotron resonance heating and associated increase in the electron temperature Te, ?E degrades and the plasma potential evolves in the positive direction. We generally find that the more negative potential and Er values correspond to higher values of ?E. Modelling indicates that basic neoclassical mechanisms contribute significantly to the formation of the electric potential in the core. Broadband turbulence is suppressed at spontaneous and biased transitions to improved confinement regimes and is always accompanied by characteristic changes in plasma potential profiles. Various types of quasi-coherent potential oscillations are observed, among them geodesic acoustic modes in T-10 and Alfv?n eigenmodes in TJ-II.

Plasma potential and turbulence dynamics in toroidal devices (survey of T-10 and TJ-II experiments)

Energetic ion driven Alfven eigenmodes (AEs) are believed to be an important element disturbing the transport in a future fusion reactor. The studies of the AE properties in modern toroidal devices have made crucial contributions to the reactor relevant physics. AEs are conventionally studied by magnetic probes (MPs), which provide the poloidal m and toroidal n mode numbers and their spectral characteristics. Heavy ion beam probing (HIBP) has become a new tool to study AEs with high spatial and frequency resolution. HIBP in the TJ-II heliac observes locally (~1 cm) resolved AEs over the whole radial interval. The set of low-m (m < 8) modes, detected with the high-frequency resolution (<5 kHz), present different types of AEs. AEs are pronounced in the local density, electric potential and poloidal magnetic field oscillations, detected simultaneously by HIBP in the frequency range 50 kHz < fAE < 300 kHz. Various AE modes are visible in the neutral beam injector (NBI)-heated plasma for co-NBI (<450 kW), counter- (<450 kW) and balanced NBI (<900 kW) from the plasma centre to the edge. A high coherence between MP and HIBP data was found for specific AEs. When the density rises, AE frequency decreases, , and the cross-phase between the plasma density, poloidal magnetic field and potential remains constant. The amplitude of the AE potential oscillations δAE ~ 10 V was estimated. Poloidally resolved density and potential measurements may provide information about the AE poloidal wavelength and the AE contribution to the poloidal electric field Epol and the turbulent particle flux ΓE×B. The typical range of Epol oscillations for AEs is . Depending on the δne and δEpol amplitudes and cross-phase, AEs may make a small or a significant contribution to the turbulent particle flux ΓE×B for the observed wavenumbers kθ < 3 cm−1.

I.A. Krasilnikov

Papers

Internal measurements of Alfvén eigenmodes with heavy ion beam probing in toroidal plasmas

Plasma potential and turbulence dynamics in toroidal devices (survey of T-10 and TJ-II experiments)