Table of contents

Coherent losses of neutral beam ions are observed at frequencies corresponding to toroidal and reversed-shear Alfvén eigenmodes (RSAEs) in DIII-D. Reversed-shear profiles are created by injecting beam power during the plasma current ramp. Beam ion losses stemming from Alfvén eigenmode activity contribute to flattening of the energetic ion density profile in such discharges. This is the first observation of convective beam ion losses due to RSAEs. The energies and pitch angles of lost ions are measured and found to exist within a well-defined region of phase space. Loss flux signals decrease in time as current penetrates and Alfvén eigenmode activity becomes more core localized. Preliminary Monte Carlo simulations of energetic ion interactions with measured mode structures show the dominant loss mechanism is a transition from a counter-passing orbit to a trapped orbit that is lost to the wall.

A finite-mass fluid electron model has been developed for simulating low-frequency electromagnetic waves in finite-β magnetized plasmas. Here, β is the ratio between plasma and magnetic pressures. It is demonstrated in slab geometry that the model successfully exhibits the linear properties of both the kinetic and inertial Alfvén waves as well as the theoretically predicted collisionless tearing-mode instability.

The profile effect of shear flows on double tearing modes is investigated in a two-dimensional resistive magnetohydrodynamics model. It is found that the flow shear between the resonant surfaces rather than the flow shear on an individual resonant surface is the dominant effect on island suppression.

This work addresses the transport of neutral particles (atoms, molecules) in magnetized fusion plasmas, in the presence of density fluctuations with given statistics. The latter are described by a multivariate gamma distribution. The geometry is a 2D slab and turbulence is assumed to be statistically homogeneous. The average neutral density and ionization source, which are the quantities relevant for integrated simulations and diagnostic applications, are calculated analytically in the scattering free case. The boundary conditions and the ratio of the turbulence correlation length to the neutral mean free path are identified as the main control parameters in the problem. The non-trivial relationship between the average neutral density and the ionization source is investigated. Monte Carlo calculations including scattering are then presented, and the main trends obtained in the scattering free case are shown to be conserved.

Using the retarding field analyzer technique, ion energies carried by edge localized mode (ELM) filaments have been measured for the first time in the far scrape-off layer (SOL) of the ASDEX Upgrade tokamak. Energies, E_i ELM, exceeding 160 eV have been found, 5–6 cm outside the separatrix, with a decay length of about 2 cm. The measured ELM particle ion temperature in the far SOL is in the range T_i ELM ≈ 50–80 eV, in good agreement with the predictions from two simple collisionless models of ELM parallel transport. In between ELMs, T_i ≈ T_e ≈ 10 eV is observed in the far SOL, consistent with relatively strong ion–electron thermal coupling in this region.

The path-integrated gain of whistler-mode chorus is evaluated by the incorporation of a kappa distribution of energetic electrons and a realistic field-aligned density model of background electrons. Variations of temperature anisotropy and number density of energetic electrons along the magnetic latitude are derived based on the conservation of the first adiabatic invariant. Numerical simulation shows that a lower-band chorus has a much higher path-integrated gain than an upper-band chorus under the same conditions. During propagation towards higher latitudes, chorus waves grow to large amplitudes in the early stage but ultimately attenuate due to wave damping. The path-integrated gain is higher with the initial wave vector pointing toward lower L shells than toward higher L shells. Moreover, the energetic electron population has a significant influence on the path-integrated gain, and the wave gain is larger as the temperature anisotropy or the density of energetic electrons is enhanced. This result provides further understanding of the chorus wave propagation characteristics in space plasmas.

The one-dimensional fluid code SOLF1D has been used for modelling of plasma transport in the scrape-off layer (SOL) along magnetic field lines, both in steady state and under transient conditions that arise due to plasma turbulence. The presented work summarizes results of SOLF1D with attention given to transient parallel transport which reveals two distinct time scales due to the transport mechanisms of convection and diffusion. Time-dependent modelling combined with the effect of ballooning shows propagation of particles along the magnetic field line with Mach number up to M ≈ 1 and supersonic transport when plasma–neutral interactions are not present. Asymmetric heat and particle fluxes are analysed for a case with poloidally asymmetric radial outflow (ballooning) and for a radial outflow with parallel momentum (rotation). In addition, parallel damping of the density and electron temperature calculated in SOLF1D is compared with the approximative model used in the turbulence code ESEL both for steady-state and turbulent SOL. Dynamics of the parallel transport are investigated for a simple transient event simulating the propagation of particles and energy to the targets from a blob passing across the flux tube at the outboard midplane and for more complex time-dependent data provided by ESEL.

Guided propagation of whistler waves along cylindrical non-uniformities of a dc magnetic field is studied within the framework of a full-wave approach. Conditions are revealed under which such guiding structures, commonly known as magnetic flux tubes, can support volume and surface eigenmodes in the whistler range. The dispersion properties and field structures of whistler eigenmodes guided by flux tubes with an enhanced magnetic field are calculated and analysed for plasma parameters typical of laboratory experiments. The results obtained are useful in understanding the basic features of whistler wave guidance by magnetic flux tubes and can be applied to interpreting the data of the relevant experiments.

We present particle-in-cell (PIC) simulations of minority energetic protons in deuterium plasmas, which demonstrate a collective instability responsible for emission near the lower hybrid frequency and its harmonics. The simulations capture the lower hybrid drift instability in a parameter regime motivated by tokamak fusion plasma conditions, and show further that the excited electromagnetic fields collectively and collisionlessly couple free energy from the protons to directed electron motion. This results in an asymmetric tail antiparallel to the magnetic field. We focus on obliquely propagating modes excited by energetic ions, whose ring-beam distribution is motivated by population inversions related to ion cyclotron emission, in a background plasma with a temperature similar to that of the core of a large tokamak plasma. A fully self-consistent electromagnetic relativistic PIC code representing all vector field quantities and particle velocities in three dimensions as functions of a single spatial dimension is used to model this situation, by evolving the initial antiparallel travelling ring-beam distribution of 3 MeV protons in a background 10 keV Maxwellian deuterium plasma with realistic ion–electron mass ratio. These simulations provide a proof-of-principle for a key plasma physics process that may be exploited in future alpha channelling scenarios for magnetically confined burning plasmas.

This paper describes the precursor activity observed in the ASDEX Upgrade tokamak before sawtooth crashes in various neutral beam heated plasmas, utilizing the soft x-ray diagnostic. In addition to the well-known (m, n) = (1,1) internal kink mode and its harmonics, a lower frequency mode is studied in detail. Power modulation of this mode is found to correlate with the power modulation of the (1, 1) kink mode in the quasistationary intervals indicating possible nonlinear interaction. Throughout the studied sawtooth crashes, the power of the lower frequency mode rose by several orders of magnitude just before the crash. In addition to its temporal behaviour, its spatial structure was estimated and the most likely value was found to be (1, 1). A possible role of this mode in the mechanism of the sawtooth crash is discussed.

The effect of equilibrium plasma rotation (toroidal and poloidal) on low-frequency, electrostatic modes—the geodesic acoustic modes (GAMs) and the zonal flows (ZFs)—in large aspect ratio tokamaks is studied within the framework of ideal MHD. It is shown that the plasma rotation results in a frequency up-shift of the ordinary GAM. The new branch of continuum modes induced by the poloidal rotation is found. This mode originates from the opposite sign Doppler shift of frequency due to poloidal rotation for m = ±1 poloidal side-band harmonics of the perturbed mass density, pressure and parallel velocity. In the case of slow poloidal rotation (Ω_P ≪ c_s/qR₀) its frequency is close to the sound frequency c_s/qR₀ (Ω_P is the poloidal angular velocity, c_s is the speed of sound, q is the safety factor and R₀ is the major radius of tokamak). The mode can be called the rotation-induced acoustic mode. This mode disappears in the case of purely toroidal plasma rotation. The frequency of the new mode in the case of relatively slow poloidal rotation (Ω_P ⩽ c_s/qR₀) is lower than the frequency of the ordinary GAM modified by plasma rotation. In the case of larger poloidal angular velocities Ω_P (Ω_P ⩾ 2c_s/qR₀) the mode becomes unstable and is identified as the unstable ZF. With a further increase in the poloidal angular velocity at constant toroidal angular velocity the instability is suppressed, and the mode turns again into a marginally stable, oscillating mode.

Taking advantage of the electron Bernstein waves heating system of the TJ–II stellarator, an electron Bernstein emission (EBE) diagnostic was installed. Its purpose is to investigate the B–X–O radiation properties in the zone where optimum theoretical electron Bernstein wave (EBW) coupling is predicted. An internal movable mirror shared by both systems allows us to collect the EBE radiation along the same line of sight that is used for EBW heating. The theoretical EBE has been calculated for different orientations of the internal mirror using the TRUBA code as the ray tracer. A comparison with experimental data obtained in NBI discharges is carried out. The results provide valuable information regarding the experimental O–X-mode conversion window expected in the EBW heating experiments. Furthermore, the characterization of the radiation polarization shows evidence of the underlying B–X–O conversion process.

A fast-ion D-alpha (FIDA) diagnostic has been developed for the fully tungsten coated ASDEX Upgrade (AUG) tokamak using 25 toroidally viewing lines of sight and featuring a temporal resolution of 10 ms. The diagnostic's toroidal geometry determines a well-defined region in velocity space which significantly overlaps with the typical fast-ion distribution in AUG plasmas. Background subtraction without beam modulation is possible because relevant parts of the FIDA spectra are free from impurity line contamination. Thus, the temporal evolution of the confined fast-ion distribution function can be monitored continuously. FIDA profiles during on- and off-axis neutral beam injection (NBI) heating are presented which show changes in the radial fast-ion distribution with the different NBI geometries. Good agreement has been obtained between measured and simulated FIDA radial profiles in MHD-quiescent plasmas using fast-ion distribution functions provided by TRANSP. In addition, a large fast-ion redistribution with a drop of about 50% in the central fast-ion population has been observed in the presence of a q = 2 sawtooth-like crash, demonstrating the capabilities of the diagnostic.

Experiments have been performed on MAST using internal (n = 3) resonant magnetic perturbation (RMP) coils. The application of the RMPs to L-mode discharges has shown a clear density pump-out when the field line pitch angle at the low-field side of the plasma is sufficiently well aligned with the applied field. The application of the RMPs before the L–H transition increases the power required to achieve H-mode by at least 30%. In type I ELMing H-mode discharges, at a particular value of q₉₅, the ELM frequency can be increased by a factor of 5 by the application of the RMPs. This effect on the ELMs and the L-mode density pump-out is not correlated with the width of the region for which the Chirikov parameter, calculated using the vacuum field, is greater than 1 but may be correlated with the size of the resonant component of the applied field in the pedestal region or with the location of the peak plasma displacement when the plasma response is taken into account.

Soliton generation mechanism in a double-plasma device is explored by carrying out diagnostics measurements using a Langmuir probe and laser induced fluorescence. Soliton profiles are investigated for different amplitudes, durations and frequencies of the applied grid signal. Particle-in-cell simulations are also carried out in order to study in detail the evolution and propagation mechanism of solitons. For low temperature ions, the simulation results show similar features as observed in the experiment. However, the simulations with fast ions having larger velocities than the soliton show strong interaction of the fast ions with the soliton and ion burst, producing another soliton through the energy exchange mechanism.

Multi-group radiation hydrodynamics simulations have been performed to investigate the margins of thermonuclear ignition in a 1 : 1 deuterium–tritium (DT) mixture that has been contaminated with an ion species that does not usefully contribute to the burning process. In this paper we examine the effects of a range of contaminant materials that may be associated with the re-entrant cone of the cone-guided fast ignition approach to inertial confinement fusion, specifically contamination by carbon, iron and gold. The effect of contamination on the ρr required for ignition is quantified for each material, for a range of contamination fractions. It is shown that, if uniformly distributed, gold contamination must be limited to values of a few 10⁻⁵ with respect to the fuel ion number density in order that the change in the required ignition hotspot ρr remain on the order of a few percent or less. In similar circumstances, carbon contamination at levels as high as a few 10⁻³ are found to be tolerable, suggesting that schemes which employ a cone tamping layer composed of CH plastic, or similar low-Z material, may offer significant advantages. However, it is further shown that the required ignition ρr is principally a function of the total mass of contaminant in the hotspot, and that quite high localized concentrations of high-Z material can be tolerated.

An energy sweeping technique is developed and applied for charge exchange (CX) neutral particle diagnostics in the URAGAN-3M (U-3M) torsatron. Measurements are performed during low-density (n_e = (0.5–1) × 10¹² cm⁻³) frame antenna radio frequency (RF) plasma discharges in the RF frequency range close to the ion cyclotron frequency (ICRF). The presence of ions with energies up to 4 keV is established experimentally. According to the experimental data the ion energy distribution is close to Maxwellian in the energy range 0.4–2.5 keV and can be described by the ion temperature T_i = 300–600 eV. This is an indication of direct RF energy deposition onto the ions due to the negligible ion–electron energy exchange. The radial dependences of CX neutral flux and ion temperature under consideration are investigated using a set of similar discharges. The radial distribution of the studied temperature has a flat profile in the range ρ = 0.5–1. This is an indication of the ion energy deposition localization close to the plasma edge. The possible mechanisms of ion heating are briefly discussed.

Plasma behavior in the vicinity of strong sources of impurities is considered. A model, based on a fluid description of electrons, main and impurity ions and taking into account the plasma quasi-neutrality, Coulomb collisions of background and impurity charged particles, radiation losses, sinks of particles to bounding material surfaces, is elaborated. Particle, momentum and energy balances are deduced by integrating transport equations within the clouds of neutral and singly charged impurities, both inside and beyond the scrape-off layer of the puffing limiter. These provide algebraic non-linear equations for the characteristic densities and temperatures of the plasma components in the cloud and for the cloud dimension itself. Computations are done for the conditions of impurity seeding experiments in the tokamak TEXTOR. The model allows us to simulate two-dimensional images of radiation losses which can be directly compared with experimental observations.

An analysis of Maxwell's equations valid in a region of an ordinary wave to extraordinary wave conversion in plasmas confined by sheared and curved magnetic fields is carried out to derive an approximate system of wave equations in a three-dimensional (3D) inhomogeneous simplified stellarator-like geometry. The case is considered in which the ordinary wave cut-off surface and extraordinary wave cut-off surface, whose curvature is neglected, intersect at a point corresponding to the maximum of an incoming wave transverse distribution. The set of reduced partial differential wave equations is solved analytically by an integral representation of solutions. The form of the integral representation is justified by identifying the contour of integration. An asymptotic representation of the solution in the WKB domain is obtained that gives conversion coefficients for beams of WKB waves with a finite transverse distribution of rf field.

The effect of a neutral density background on the toroidal angular momentum and kinetic energy profiles has been investigated in JET. Under equivalent conditions but with increasing gas fuelling during the flat top phase, it has been observed that both the edge rotation and temperature decrease. The increase in electron density was not sufficient to compensate the rotation and temperature loss such that both energy and momentum confinement times are significantly reduced. The edge localized mode behaviour is observed to be significantly affected by the increased neutral influx. A simple 1.5D fluid model has been used to qualitative capture the neutral transport response within the plasma, followed by a forward model of the passive charge-exchange (CX) emission of carbon to obtain a corrected radial neutral density profile. It has been found that the neutral density is sharply attenuated over the edge region, with similar edge magnitudes in both the non-fuelled (Γ₀/n_e ∼ 1.2 m s⁻¹) and maximum fuelled case (Γ₀/n_e ∼ 2.5 m s⁻¹). Discharges with reversed-B operation exhibited even higher normalized neutral fluxes related to first orbit effects and increased wall interactions. Over the full neutral influx range, a decrease in pedestal thermal Mach number from 0.25 to 0.14 was observed. Increased neutral penetration up to the pedestal top (r/a ∼ 0.9) due to multiple CX interactions is obtained from the interpretive model. Under these multiple neutral–ion interactions, the impact on the CX loss of angular momentum is larger compared with the CX energy loss. The drag torque was seen to increase up to 10% of the total applied torque, while energy losses appeared to be smaller. The accuracy of this global approach method is unfortunately limited; however, the estimated momentum sink was found comparable to the torque required to explain the discrepancy between observed global energy and momentum confinement.

By combining the lower hybrid current drive (LHCD) and ion Bernstein wave (IBW) heating codes, synergistic simulation of lower hybrid wave (LHW) and IBW is preliminarily done and used to investigate synergistic experiments of LHW and IBW in HT-7, offering an effective tool for analyzing LHW and IBW experiments, particularly separating the contribution of temperature and synergistic effect to driven current due to IBW heating. Results show that IBW can effectively heat plasma and play with LHW, hence modifying the LHW power deposition and plasma current profile. Compared with the LHW plasma, there is an increment in driven current in the case of the LHW + IBW plasma, due to a temperature increase and synergistic effect of LHW and IBW. Studies show that the driven current fraction of temperature contribution and synergistic effect depends significantly on the plasma parameters and the resonant layer. Compared with global IBW heating, localized IBW heating makes localized electron temperature higher, which is helpful in driving a larger off-axis current and benefits the hollow current profile, suggesting that off-axis IBW heating is preferred for a weak or negative magnetic shear plasma and for improving plasma confinement. Although the simulated results are not completely consistent with experimental measurements, they are nearly in agreement qualitatively. More work will be done later for further investigation.

The absorption of an ultra-intense circularly-polarized laser pulse by a near-critical (0.1n_c < n_e < a₀n_c) plasma is studied. Previously two regimes of absorption have been suggested: a 'leading edge depletion' (LED) regime and a 'transverse ponderomotive acceleration' regime. Here we seek to describe these concepts more thoroughly, and determine if two distinct regimes actually exist. New analytic models to describe each regime are derived. These are compared with 1D and 2D particle-in-cell simulations, and good quantitative agreement is found, showing the existence of two separate regimes. The LED regime exhibits very efficient absorption of laser light, which is promising for applications.

For certain scattering geometries collective Thomson scattering (CTS) measurements are sensitive to the composition of magnetically confined fusion plasmas. CTS therefore holds the potential to become a new diagnostic for measurements of the fuel ion ratio—i.e. the tritium to deuterium density ratio. Measurements of the fuel ion ratio will be important for plasma control and machine protection in future experiments with burning fusion plasmas. Here we examine the theoretical basis for fuel ion ratio measurements by CTS. We show that the sensitivity to plasma composition is enhanced by the signatures of ion cyclotron motion and ion Bernstein waves which appear for scattering geometries with resolved wave vectors near perpendicular to the magnetic field. We investigate the origin and properties of these features in CTS spectra and give estimates of their relative importance for fuel ion ratio measurements.

The magnetorotational instability (MRI) is investigated using a two-fluid model. Electrons and singly charged ions are supposed to have the same angular velocity to eliminate the equilibrium current. The linear dispersion relation governing local MRI is derived. The instability criteria in the non-magnetized and weakly magnetized cases differ remarkably from those predicted by the one-fluid model. Based on the general magnetized case, we present the critical conditions for the occurrence of instability. Gyroeffects significantly alter the instability criterion and introduce four unstable regions, one of which is reduced to the magnetohydrodynamic result when the angular frequency is much less than the ion gyrofrequency. When the angular frequency is much less than the electron gyrofrequency, the ion gyroeffect contributes to the instability criterion and induces the Hall term.

Resistive wall mode (RWM) stability limits have been probed by MHD spectroscopy and numerical modelling. MAST plasmas have operated up to β_N = 5.7, well above the predicted ideal kink no-wall limit or measured resonant field amplification limits due to a combination of rotation and kinetic damping. By varying the density, both the rotation and the fast ion distribution function have been changed dramatically. Detailed drift-kinetic modelling shows that whilst the contribution of energetic beam ions to RWM damping does increase at sufficiently high plasma rotation as to allow resonance with the fast ion precession frequency, the thermal ion damping always dominates over the fast ion contribution.

The forces acting on a spherical conducting particle in a transversely flowing magnetized plasma are calculated in the entire range of magnetization and Debye length, using the particle code SCEPTIC3D (Patacchini and Hutchinson 2010 Plasma Phys. Control. Fusion52 035005, 2011 Plasma Phys. Control. Fusion53 025005). In short Debye length (i.e. high density) plasmas, both the ion-drag and Lorentz force arising from currents circulating inside the dust show strong components antiparallel to the convective electric field, suggesting that a free dust particle should gyrate faster than what predicted by its Larmor frequency. In intermediate to large Debye length conditions, by a downstream depletion effect already reported in unmagnetized strongly collisional regimes, the ion-drag in the direction of transverse flow can become negative. The internal Lorentz force, however, remains in the flow direction, and large enough in magnitude so that no spontaneous dust motion should occur.