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Radio frequency (RF) sheaths occur under a wide variety of conditions when RF waves, material surfaces and plasma coexist. RF sheaths are of special importance in describing the interaction of ion cyclotron range of frequency (ICRF) waves with the boundary plasma in tokamaks, stellarators and other magnetic confinement devices. In this article the basic physics of RF sheaths is discussed in the context of magnetic fusion research. Techniques for modelling RF sheaths, their interaction with RF wave fields and the resulting consequences are highlighted. The article is intended as a guide for the early-career ICRF researcher, but it may equally well serve to provide an overview of basic RF sheath concepts and modelling directions for any interested fusion scientist.

In this paper we review some theoretical aspects of the dynamics of the mesoscale filaments extending along the magnetic field lines in the edge plasma, which are often called ‘blobs’. We start with a brief historical survey of experimental data and the main ideas on edge and SOL plasma transport, which finally evolved into the modern paradigm of convective very-intermittent cross-field edge plasma transport. We show that both extensive analytic treatments and numerical simulations demonstrate that plasma blobs with enhanced pressure can be convected coherently towards the wall. The mechanism of convection is related to an effective gravity force (e.g. owing to magnetic curvature effects), which causes plasma polarization and a corresponding E× B convection. The impacts of different effects (e.g. X-point magnetic geometry, plasma collisionality, plasma beta, etc.) on blob dynamics are considered. Theory and simulation predict, both for current tokamaks and for ITER, blob propagation speeds and cross-field sizes to be of the order of a few hundred meters per second and a centimeter, respectively, which are in reasonable agreement with available experimental data. Moreover, the concept of blobs as a fundamental entity of convective transport in the scrape-off layer provides explanations for observed outwards convective transport, intermittency and non-Gaussian statistics in edge plasmas, and enhanced wall recycling in both toroidal and linear machines.

Resonant filament-assisted mode conversion (FAMC) scattering of high harmonic fast waves (HHFW) by cylindrical field-aligned density inhomogeneities can efficiently redirect a fraction of the launched HHFW power flux into the parallel direction. Within a simplified analytic approach, this contribution compares the parallel propagation, reflection and dissipation of nearly resonant FAMC modes for three magnetic field line geometries in the scrape-off layer, in the presence of radio-frequency (RF) sheaths at field line extremities and phenomenological wave damping in the plasma volume. When a FAMC mode, excited at the HHFW antenna parallel location and guided along the open magnetic field lines, impinges onto a boundary at normal incidence, we show that it can excite sheath RF oscillations, even toroidally far away from the HHFW launcher. The RF sheaths then dissipate part of the power flux carried by the incident mode, while another part reflects into the FAMC mode with the opposite wave vector parallel to the magnetic field. The reflected FAMC mode in turn propagates and can possibly interact with the sheath at the opposite field line boundary. The two counter-propagating modes then form in the bounded magnetic flux tube a lossy cavity excited by the HHFW scattering. We investigate how the presence of field line boundaries affects the total HHFW power redirected into the filament, and its splitting between sheath and volume losses, as a function of relevant parameters in the model.

Sheared flows perpendicular to the magnetic field can be driven by the Reynolds stress or ion pressure gradient effects and can potentially influence the stability and turbulent saturation level of edge plasma modes. On the other hand, such flows are subject to the transverse Kelvin–Helmholtz (KH) instability. Here, the linear theory of KH instabilities is first addressed with an analytic model in the asymptotic limit of long wavelengths compared with the flow scale length. The analytic model treats sheared $\\boldsymbol{E}\\times \\boldsymbol{B}$ flows, ion diamagnetism (including gyro-viscous terms), density gradients and parallel currents in a slab geometry, enabling a unified summary that encompasses and extends previous results. In particular, while ion diamagnetism, density gradients and parallel currents each individually reduce KH growth rates, the combined effect of density and ion pressure gradients is more complicated and partially counteracting. Secondly, the important role of realistic toroidal geometry is explored numerically using an invariant scaling analysis together with the 2DX eigenvalue code to examine KH modes in both closed and open field line regions. For a typical spherical torus magnetic geometry, it is found that KH modes are more unstable at, and just outside of, the separatrix as a result of the distribution of magnetic shear. Finally implications for reduced edge turbulence modelling codes are discussed.

Progress is reviewed on the simulation of wave-particle interactions in the ion cyclotron range of frequencies (ICRF). Two important aspects of this problem are described. First, mode conversion from a long wavelength fast magnetosonic wave to short wavelength ion Bernstein waves (IBW) and ion cyclotron waves (ICW) is simulated and validation tests of the simulations against experiment are presented. Second, simulations of the quasilinear evolution of nonthermal ion tails during the minority heating are reviewed and experimental validation tests are also discussed. In this paper we describe how access to teraflop computing capability has made it possible to advance the state of the art in this area. We also discuss two aspects of the wave-particle interaction where future work is needed and where in particular access to sub-petaflop and petaflop computing capability would be highly desirable. This work involves the interaction of ICRF waves with energetic neutral beam ions at high ion cyclotron harmonic number and addresses the inclusion of finite ion drift orbit effects in the nonthermal ion tail evolution and the inclusion of nonlinear effects such as RF sheaths in the antenna – edge plasma coupling.

Resonant filament-assisted mode conversion (FAMC) scattering of high harmonic fast waves (HHFW) by cylindrical field-aligned density inhomogeneities can efficiently redirect a fraction of the launched HHFW power flux into the parallel direction. Within a simplified analytic approach, this contribution compares the parallel propagation, reflection and dissipation of nearly resonant FAMC modes for three magnetic field line geometries in the scrape-off layer, in the presence of radio-frequency (RF) sheaths at field line extremities and phenomenological wave damping in the plasma volume. When a FAMC mode, excited at the HHFW antenna parallel location and guided along the open magnetic field lines, impinges onto a boundary at normal incidence, we show that it can excite sheath RF oscillations, even toroidally far away from the HHFW launcher. The RF sheaths then dissipate part of the power flux carried by the incident mode, while another part reflects into the FAMC mode with the opposite wave vector parallel to the magnetic field. The reflected FAMC mode in turn propagates and can possibly interact with the sheath at the opposite field line boundary. The two counter-propagating modes then form in the bounded magnetic flux tube a lossy cavity excited by the HHFW scattering. We investigate how the presence of field line boundaries affects the total HHFW power redirected into the filament, and its splitting between sheath and volume losses, as a function of relevant parameters in the model.

Blob-filaments (or simply 'blobs') are coherent structures formed by turbulence and sustained by nonlinear processes in the edge and scrape-off layer (SOL) of tokamaks and other magnetically confined plasmas. The dynamics of these blob-filaments, in particular their radial motion, can influence the scrape-off layer width and plasma interactions with both the divertor target and with the main chamber walls. Motivated by recent results from the XGC1 gyrokinetic simulation code reported on elsewhere [J. Cheng et al. submitted to Nucl. Fusion and available at arXiv:2302.02877v1], a theory of rapidly spinning blob-filaments has been developed. The theory treats blob filaments in the closed flux surface region or the region that is disconnected from sheaths in the SOL. It extends previous work by treating blob spin, arising from partially or fully adiabatic electrons, as the leading order effect and retaining inertial (ion charge polarization) physics in next order. Spin helps to maintain blob coherency and affects the blob's propagation speed. Dipole charge polarization, treated perturbatively, gives rise to blob-filaments with relatively slow radial velocity, comparable to that observed in the simulations. The theory also treats the interaction of rapidly spinning blob filaments with a zonal flow layer. It is shown analytically that the flow layer can act like a transport barrier for these structures. Finally parallel electron kinetic effects are incorporated into the theory. Various asymptotic parameter regimes are discussed and asymptotic expressions for the radial and poloidal motion of the blob-filaments are obtained.

The physical processes taking place at the edge region are crucial for the operation of tokamaks as they govern the interaction of hot plasma with the vessel walls. Numerical modeling of the edge with state-of-the-art codes attempts to elucidate interactions between neoclassical drifts, turbulence, poloidal and parallel flows that control the physical set-up of the SOL region. Here, we present post-processing analysis of simulations from the gyrokinetic code XGC1, comparing edge turbulence characteristics from a simulation of DIII-D against one of C-Mod. We find that the equilibrium \\(E \\times B\\) flux across the separatrix has a similar poloidal pattern in both discharges which can be explained by magnetic drifts and trapped ion excursions. However, collisionality is noted to play a major role in that it prevents local charge accumulations from having global effects in C-Mod. In both cases, turbulent electron heat flux is higher than the ion one. This seems to be a universal characteristic of the tokamak edge. We identify turbulent frequencies and growth rates of the dominant mode in both simulations. In C-Mod, these numbers point to the presence of a drift wave. In DIII-D, linear simulations with Gene reveal a trapped electron mode. Furthermore, we present the amplitude and size distributions of the blobs from both simulations. Amplitude distributions are in qualitative agreement with experimental observations while size distributions are consistent with the fact that most blobs are not connecting to the divertor plates and suggest that they are generated by the shearing of the turbulent modes.

Sheared flows perpendicular to the magnetic field can be driven by the Reynolds stress or ion pressure gradient effects and can potentially influence the stability and turbulent saturation level of edge plasma modes. On the other hand, such flows are subject to the transverse Kelvin–Helmholtz (KH) instability. Here, the linear theory of KH instabilities is first addressed with an analytic model in the asymptotic limit of long wavelengths compared with the flow scale length. The analytic model treats sheared $\\boldsymbol{E}\\times \\boldsymbol{B}$ flows, ion diamagnetism (including gyro-viscous terms), density gradients and parallel currents in a slab geometry, enabling a unified summary that encompasses and extends previous results. In particular, while ion diamagnetism, density gradients and parallel currents each individually reduce KH growth rates, the combined effect of density and ion pressure gradients is more complicated and partially counteracting. Secondly, the important role of realistic toroidal geometry is explored numerically using an invariant scaling analysis together with the 2DX eigenvalue code to examine KH modes in both closed and open field line regions. For a typical spherical torus magnetic geometry, it is found that KH modes are more unstable at, and just outside of, the separatrix as a result of the distribution of magnetic shear. Finally implications for reduced edge turbulence modelling codes are discussed.

The SOL width is a parameter of paramount importance in modern tokamaks as it controls the power density deposited at the divertor plates, critical for plasma-facing material survivability. An understanding of the parameters controlling it has consequently long been sought (Connor et al. 1999 NF 39 2). Prior to Chang et al.(2017 NF 57 11), studies of the tokamak edge have been mostly confined to reduced fluid models and simplified geometries, leaving out important pieces of physics. Here, we analyze the results of a DIII-D simulation performed with the full-f gyrokinetic code XGC1 which includes both turbulence and neoclassical effects in realistic divertor geometry. More specifically, we calculate the particle and heat ExB fluxes along the separatrix, discriminating between equilibrium and turbulent contributions. We find that the density SOL width is impacted almost exclusively by the turbulent electron flux. In this simulation, the level of edge turbulence is regulated by a mechanism we are only beginning to understand: \\(\\nabla B\\)-drifts and ion X-point losses at the top and bottom of the machine, along with ion banana orbits at the low field side (LFS), result in a complex poloidal potential structure at the separatrix which is the cause of the ExB drift pattern that we observe. Turbulence is being suppressed by the shear flows that this potential generates. At the same time, turbulence, along with increased edge collisionality and electron inertia, can influence the shape of the potential structure by making the electrons non-adiabatic. Moreover, being the only means through which the electrons can lose confinement, it needs to be in a balance with the original direct ion orbit losses to maintain charge neutrality.