The isotope dependence of plasma transport will have a significant impact on the performance of future D-T experiments in JET and ITER and eventually on the fusion gain and economics of future reactors. In preparation for future D-T operation on JET, dedicated experiments and comprehensive transport analyses were performed in H, D and H-D mixed plasmas. The analysis of the data has demonstrated an unexpectedly strong and favourable dependence of the global confinement of energy, momentum and particles in ELMy H-mode plasmas on the atomic mass of the main ion species, the energy confinement time scaling as ${\tau _E}\sim {A^{0.5}}$ (Maggi et al., Plasma Phys. Control. Fusion, vol. 60, 2018, 014045; JET Team, Nucl. Fusion, vol. 39, 1999, pp. 1227–1244), i.e. opposite to the expectations based only on local gyro-Bohm (GB) scaling, ${\tau _E}\sim {A^{ - 0.5}}$, and stronger than in the commonly used H-mode scaling for the energy confinement (Saibene et al., Nucl. Fusion, vol. 39, 1999, 1133; ITER Physics Basis, Nucl. Fusion, vol. 39, 1999, 2175). The scaling of momentum transport and particle confinement with isotope mass is very similar to that of energy transport. Nonlinear local GENE gyrokinetic analysis shows that the observed anti-GB heat flux is accounted for if collisions, E × B shear and plasma dilution with low-Z impurities (9Be) are included in the analysis (E and B are, respectively the electric and magnetic fields). For L-mode plasmas a weaker positive isotope scaling ${\tau _E}\sim {A^{0.14}}$ has been found in JET (Maggi et al., Plasma Phys. Control. Fusion, vol. 60, 2018, 014045), similar to ITER97-L scaling (Kaye et al., Nucl. Fusion, vol. 37, 1997, 1303). Flux-driven quasi-linear gyrofluid calculations using JETTO-TGLF in L-mode show that local GB scaling is not followed when stiff transport (as is generally the case for ion temperature gradient modes) is combined with an imposed boundary condition taken from the experiment, in this case predicting no isotope dependence. A dimensionless identity plasma pair in hydrogen and deuterium L-mode plasmas has demonstrated scale invariance, confirming that core transport physics is governed, as expected, by the 4 dimensionless parameters ρ*, ν*, β, q (normalised ion Larmor radius, collisionality, plasma pressure and safety factor) consistently with global quasi-linear gyrokinetic TGLF calculations (Maggi et al., Nucl. Fusion, vol. 59, 2019, 076028). We compare findings in JET with those in different devices and discuss the possible reasons for the different isotope scalings reported from different devices. The diversity of observations suggests that the differences may result not only from differences affecting the core, e.g. heating schemes, but are to a large part due to differences in device-specific edge and wall conditions, pointing to the importance of better understanding and controlling pedestal and edge processes.

A magnetic field configuration of an island divertor for a quasi-axisymmetric stellarator (CFQS) is proposed. The configuration incorporates large islands surrounding the core confinement region. The interface between the core region and the peripheral region of the island divertor is a clear magnetic separatrix similar to a tokamak divertor. The structure of divertor magnetic field lines is very regular without stochasticity and the connection length is sufficiently long for good divertor performance. Such a divertor configuration is produced in the magnetic field configuration for the CFQS device, which is now under construction in China.

It is demonstrated that finite-pressure, approximately quasi-axisymmetric stellarator equilibria can be directly constructed (without numerical optimization) via perturbations of given axisymmetric equilibria. The size of such perturbations is measured in two ways, via the fractional external rotation and, alternatively, via the relative magnetic field strength, i.e. the average size of the perturbed magnetic field, divided by the unperturbed field strength. It is found that significant fractional external rotational transform can be generated by quasi-axisymmetric perturbations, with a similar value of the relative field strength, despite the fact that the former scales more weakly with the perturbation size. High mode number perturbations are identified as a candidate for generating such transform with local current distributions. Implications for the development of a general non-perturbative solver for optimal stellarator equilibria are discussed.

A runaway avalanche can result in a conversion of the initial plasma current into a relativistic electron beam in high-current tokamak disruptions. We investigate the effect of massive material injection of deuterium–noble gas mixtures on the coupled dynamics of runaway generation, resistive diffusion of the electric field and temperature evolution during disruptions in the deuterium–tritium phase of ITER operations. We explore the dynamics over a wide range of injected concentrations and find substantial runaway currents, unless the current quench time is intolerably long. The reason is that the cooling associated with the injected material leads to high induced electric fields that, in combination with a significant recombination of hydrogen isotopes, leads to a large avalanche generation. Balancing Ohmic heating and radiation losses provides qualitative insights into the dynamics; however, an accurate modelling of the temperature evolution based on energy balance appears crucial for quantitative predictions.

A fluid system is derived to describe electrostatic magnetized plasma turbulence at scales somewhat larger than the Larmor radius of a given species. It is related to the Hasegawa–Mima equation, but does not conserve enstrophy, and, as a result, exhibits a forward cascade of energy, to small scales. The inertial-range energy spectrum is argued to be shallower than a $-11/3$ power law, as compared to the $-5$ law of the Hasegawa–Mima enstrophy cascade. This property, confirmed here by direct numerical simulations of the fluid system, may help explain the fluctuation spectrum observed in gyrokinetic simulations of streamer-dominated electron-temperature-gradient driven turbulence (Plunk et al., Phys. Rev. Lett., vol. 122, 2019, 035002), and also possibly some cases of ion-temperature-gradient driven turbulence where zonal flows are suppressed (Plunk et al., Phys. Rev. Lett., vol. 118, 2017, 105002).

Finding coil sets with desirable physics and engineering properties is a crucial step in the design of modern stellarator devices. Existing stellarator coil optimization codes ultimately produce zero-thickness filament coils. However, stellarator coils have finite depth and thickness, which can make the single-filament model a poor approximation, particularly when coil build dimensions are relatively large compared to the coil–plasma distance. In this paper, we present a new method for designing coils with finite builds and present a mechanism to optimize the orientation of the winding pack. We approximate finite-build coils with a multi-filament model. A numerical implementation has been developed, and applications to the Helically Symmetric eXperiment stellarator and a new UW-Madison quasihelically symmetric configuration are shown.

The Dimits shift is the shift between the threshold of the drift-wave primary instability and the actual onset of turbulent transport in a magnetized plasma. It is generally attributed to the suppression of turbulence by zonal flows, but developing a more detailed understanding calls for consideration of specific reduced models. The modified Terry–Horton system has been proposed by St-Onge (J. Plasma Phys., vol. 83, 2017, 905830504) as a minimal model capturing the Dimits shift. Here, we use this model to develop an analytic theory of the Dimits shift and a related theory of the tertiary instability of zonal flows. We show that tertiary modes are localized near extrema of the zonal velocity $U(x)$, where $x$ is the radial coordinate. By approximating $U(x)$ with a parabola, we derive the tertiary-instability growth rate using two different methods and show that the tertiary instability is essentially the primary drift-wave instability modified by the local $U'' \doteq {\rm d}^2 U/{\rm d} x^2 $. Then, depending on $U''$, the tertiary instability can be suppressed or unleashed. The former corresponds to the case when zonal flows are strong enough to suppress turbulence (Dimits regime), while the latter corresponds to the case when zonal flows are unstable and turbulence develops. This understanding is different from the traditional paradigm that turbulence is controlled by the flow shear $| {\rm d} U / {\rm d} x |$. Our analytic predictions are in agreement with direct numerical simulations of the modified Terry–Horton system.

Massive material injection has been proposed as a way to mitigate the formation of a beam of relativistic runaway electrons that may result from a disruption in tokamak plasmas. In this paper we analyse runaway generation observed in eleven ASDEX Upgrade discharges where disruption was triggered using massive gas injection. We present numerical simulations in scenarios characteristic of on-axis plasma conditions, constrained by experimental observations, using a description of the runaway dynamics with a self-consistent electric field and temperature evolution in two-dimensional momentum space and zero-dimensional real space. We describe the evolution of the electron distribution function during the disruption, and show that the runaway seed generation is dominated by hot-tail in all of the simulated discharges. We reproduce the observed dependence of the current dissipation rate on the amount of injected argon during the runaway plateau phase. Our simulations also indicate that above a threshold amount of injected argon, the current density after the current quench depends strongly on the argon densities. This trend is not observed in the experiments, which suggests that effects not captured by zero-dimensional kinetic modelling – such as runaway seed transport – are also important.

We discuss theoretical and numerical aspects of gyrokinetics as a Lagrangian field theory when the field perturbation is introduced into the symplectic part. A consequence is that the field equations and particle equations of motion in general depend on the time derivatives of the field. The most well-known example is when the parallel vector potential is introduced as a perturbation, where a time derivative of the field arises only in the equations of motion, so an explicit equation for the fields may still be written. We will consider the conceptually more problematic case where the time-dependent fields appear in both the field equations and equations of motion, but where the additional term in the field equations is formally small. The conceptual issues were described by Burby (J. Plasma Phys., vol. 82 (3), 2016, 905820304): these terms lead to apparent additional degrees of freedom to the problem, so that the electric field now requires an initial condition, which is not required in low-frequency (Darwin) Vlasov–Maxwell equations. Also, the small terms in the Euler–Lagrange equations are a singular perturbation, and these two issues are interlinked. For well-behaved problems the apparent additional degrees of freedom are spurious, and the physically relevant solution may be directly identified. Because we needed to assume that the system is well behaved for small perturbations when deriving gyrokinetic theory, we must continue to assume that when solving it, and the physical solutions are thus the regular ones. The spurious nature of the singular degrees of freedom may also be seen by changing coordinate systems so the varying field appears only in the Hamiltonian. We then describe how methods appropriate for singular perturbation theory may be used to solve these asymptotic equations numerically. We then describe a proof-of-principle implementation of these methods for an electrostatic strong-flow gyrokinetic system; two basic test cases are presented to illustrate code functionality.

This work presents updates in the diagnostics systems, magnetohydrodynamics (MHD) calculations and simulations of microwave heating scenarios of the small modular Stellarator of Costa Rica 1 (SCR-1). Similarly, the design of a flexible bolometer and magnetic diagnostics (a set of Mirnov coils, Rogowski coils and two diamagnetic loops) are introduced. Furthermore, new MHD equilibrium calculations for the plasma of the SCR-1 device were performed using the VMEC code including the poloidal cross-section of the magnetic flux surfaces at different toroidal positions, profiles of the rotational transform, magnetic well, magnetic shear and total magnetic field norm. Charged particle orbits in vacuum magnetic field were computed by the magnetic field solver BS-SOLCTRA (Vargas et al. In 27th IAEA Fusion Energy Conference (FEC 2018), 2018. IAEA). A visualization framework was implemented using Paraview (Solano-Piedra et al. In 23rd IAEA Technical Meeting on the Research Using Small Fusion Devices (23rd TM RUSFD), 2017) and compared with magnetic mapping results (Coto-Vílchez et al. In 16th Latin American Workshop on Plasma Physics (LAWPP), 2017, pp. 43–46). Additionally, simulations of microwave heating scenarios were performed by the IPF-FDMC full-wave code. These simulations calculate the conversion of the ordinary waves to extraordinary waves and allow us to identify the location where the conversion takes place. Finally, the microwave heating scenarios for the $330^{\circ }$ toroidal position are presented. The microwave heating scenarios showed that the O–X–B mode conversion is around 12–14 %. It was possible to identify the spatial zone where the conversion takes place (upper hybrid frequency).

Recently, the validity range of the approximations commonly used in neoclassical calculation has been reconsidered. One of the primary motivations behind this trend is observation of an impurity hole in LHD (Large Helical Device), i.e. the formation of an extremely hollow density profile of an impurity ion species, such as carbon $\text{C}^{6+}$, in the plasma core region where a negative radial electric field ($E_{r}$) is expected to exist. Recent studies have shown that the variation of electrostatic potential on the flux surface, $\unicode[STIX]{x1D6F7}_{1}$, has significant impact on neoclassical impurity transport. Nevertheless, the effect of $\unicode[STIX]{x1D6F7}_{1}$ has been studied with radially local codes and the necessity of global calculation has been suggested. Thus, we have extended a global neoclassical code, FORTEC-3D, to simulate impurity transport in an impurity hole plasma including $\unicode[STIX]{x1D6F7}_{1}$ globally. Independently of the $\unicode[STIX]{x1D6F7}_{1}$ effect, an electron root of the ambipolar condition for the impurity hole plasma has been found by global simulation. Hence, we have considered two different cases, each with a positive (global) and a negative (local) solution of the ambipolar condition, respectively. Our result provides another support that $\unicode[STIX]{x1D6F7}_{1}$ has non-negligible impact on impurity transport. However, for the ion-root case, the radial $\text{C}^{6+}$ flux is driven further inwardly by $\unicode[STIX]{x1D6F7}_{1}$. For the electron-root case, on the other hand, the radial particle $\text{C}^{6+}$ flux is outwardly enhanced by $\unicode[STIX]{x1D6F7}_{1}$. These results indicate that how $\unicode[STIX]{x1D6F7}_{1}$ affects the radial particle transport crucially depends on the profile of the ambipolar-$E_{r}$, which is found to be susceptible to $\unicode[STIX]{x1D6F7}_{1}$ itself and the global effects.

Numerical simulations of Alfvén modes driven by energetic particles are performed with the gyrokinetic (GK) global particle-in-cell code ORB5. A reversed shear equilibrium magnetic field is adopted. A simplified configuration with circular flux surfaces and large aspect ratio is considered. The nonlinear saturation of beta-induced Alfvén eigenmodes (BAE) is investigated. The roles of the wave–particle nonlinearity of the different species, i.e. thermal ions, electrons and energetic ions are described, in particular for their role in the saturation of the BAE and the generation of zonal flows. The nonlinear redistribution of the electron population is found to be important in increasing the BAE saturation level and the zonal flow amplitude.

Impurity temperature screening is a favourable neoclassical phenomenon involving an outward radial flux of impurity ions from the core of fusion devices. Quasisymmetric magnetic fields lead to intrinsically ambipolar neoclassical fluxes that give rise to temperature screening for low enough $\unicode[STIX]{x1D702}^{-1}\equiv d\ln n/d\ln T$. In contrast, neoclassical fluxes in generic stellarators will depend on the radial electric field, which is predicted to be inward for ion-root plasmas, potentially leading to impurity accumulation. Here, we examine the impurity particle flux in a number of approximately quasisymmetric stellarator configurations and parameter regimes while varying the amount of symmetry breaking in the magnetic field. For the majority of this work, neoclassical fluxes have been obtained using the SFINCS drift-kinetic equation solver with electrostatic potential $\unicode[STIX]{x1D6F7}=\unicode[STIX]{x1D6F7}(r)$, where $r$ is a flux-surface label. Results indicate that achieving temperature screening is possible, but unlikely, at low-collisionality reactor-relevant conditions in the core. Thus, the small departures from symmetry in nominally quasisymmetric stellarators are large enough to significantly alter the neoclassical impurity transport. A further look at the magnitude of these fluxes when compared to a gyro-Bohm turbulence estimate suggests that neoclassical fluxes are small in configurations optimized for quasisymmetry when compared to turbulent fluxes.

The neutral beam (NB) fast ion confinement in the Large Helical Device (LHD) is studied for several full field ($B_{t}\sim 2.75~\text{T}$) magnetic configurations by a combination of neutron measurement and simulations. To investigate the NB fast ion confinement, we have performed a series of short-pulse NB injection experiments. The experiment results are analysed by the integrated code TASK3D-a. From this investigation, the effective particle diffusion coefficients of the tangential and perpendicular NBs are approximately $D^{\text{eff}}\sim 0.1~\text{m}^{2}~\text{s}^{-1}$ and $D^{\text{eff}}\sim 1~\text{m}^{2}~\text{s}^{-1}$ in the standard configuration. It is clarified that the NB fast ion confinement improves when the plasmas are shifted inward. Moreover, it is also found that the simulation, which considers the deuteron dilution effect due to the presence of impurity ions, can describe a neutron emission rate consistent with the measurement.

The linear MHD (magnetohydrodynamic) stability for high beta plasmas in the inward shifted Large Helical Device (LHD) configurations has been investigated for a wide range of magnetic Reynolds numbers $S$ using numerical simulations based on the kinetic MHD model with kinetic thermal ions where the beta is the ratio of the plasma pressure to the magnetic pressure. It is found that the dependence of the linear growth rate of the resistive ballooning modes on the $S$ number changes from $\unicode[STIX]{x1D6FE}\propto S^{-1/3}$ to $\unicode[STIX]{x1D6FE}\propto S^{-1}$ by the kinetic thermal ion effects so that the resistive ballooning modes are significantly suppressed as the $S$ number increases. For a high $S$ number comparable to experimental values, the most unstable modes are interchange modes. The kinetic thermal ion effects change the most unstable interchange mode from the ideal mode to the resistive mode. This transition of the interchange modes by kinetic thermal ion effects is consistent with the shift of the marginal stability boundary for the ideal interchange modes observed in the LHD experiments.

The edge region of quasi-adiabatic plasma is pedagogically simulated by the dynamics between the electric potential $\unicode[STIX]{x1D711}$ and the electron density $n$ whose equilibrium density gradient is negative and held fixed. The zonal flow (ZF) $V$ is either enforced sinusoidally or generated self-consistently from the turbulence. Cross-phase $\unicode[STIX]{x1D6FF}$ between $\unicode[STIX]{x1D711}$ and $n$, which is important in the determination of the turbulence level and the transport, is strongly influenced by the ZF. In the region near $V=0$, $\unicode[STIX]{x1D6FF}$ becomes negative due to the large gradient of the ZF. It is found that the instabilities are quenched there, and the fluctuations decay. The ZF thus works as a transport barrier in the region where the ZF changes direction with large gradient.

The turbulence-induced quasi-linear particle flux of a highly charged, collisional impurity species is calculated from the electrostatic gyrokinetic equation including collisions with the bulk ions and the impurities themselves. The equation is solved by an expansion in powers of the impurity charge number $Z$. In this formalism, the collision operator only affects the impurity flux through the dynamics of the impurities in the direction parallel to the magnetic field. At reactor-relevant collisionality, the parallel dynamics is dominated by the parallel electric field, and collisions have a minor effect on the turbulent particle flux of highly charged, collisional impurities.

Using transport models, the impacts of trapped electrons on zonal flows and turbulence in helical field configurations are studied. The effect of the trapped electrons on the characteristic quantities of the linear response for zonal flows is investigated for two different field configurations in the Large Helical Device. The turbulent potential fluctuation, zonal flow potential fluctuation and ion energy transport are quickly predicted by the reduced models for which the linear and nonlinear simulation results are used to determine dimensionless parameters related to turbulent saturation levels and typical zonal flow wavenumbers. The effects of zonal flows on the turbulent transport for the case of the kinetic electron response are much smaller than or comparable to those in an adiabatic electron condition for the two different field configurations. It is clarified that the effect of zonal flows on the turbulent transport due to the trapped electrons changes, depending on the field configurations.

The modelling of edge carbon transport and emission on EAST tokamak under resonant magnetic perturbation (RMP) fields has been conducted with the three-dimensional edge transport code EMC3-EIRENE. The measured vertical distribution of CVI emission by the extreme ultraviolet spectrometer system for the perturbed case shows a reduction in the CVI emission by 20 % compared to the equilibrium case. The chord-integrated CVI emission can be reconstructed by EMC3-EIRENE modelling, which presents an increase in the CVI emission with RMP fields. The discrepancy between experiments and simulations has been investigated by parameter study to examine the sensitivity of the simulation results on the edge plasma conditions and the impurity perpendicular transport. It is found that the variation of edge plasma conditions for the equilibrium case cannot resolve the discrepancy in the CVI emission between simulations and measurements. The simulations with enhanced impurity perpendicular transport coefficient allows a reasonable agreement with the measured reduction of CVI emission.

The core toroidal plasma intrinsic rotation has been studied by experiments and simulations in the Joint Texas Experimental Tokamak (J-TEXT). The direction of core intrinsic rotation in the J-TEXT plasma is counter-current. As the plasma density ramps up, the rotation velocity increases in the counter-current direction. By comparing four different electron densities, linear local gyrokinetic simulations have been performed by the Gyrokinetic Electromagnetic Numerical Experiment code for the first time on J-TEXT. It is found that the most dominant turbulence is the ion temperature gradient at $0.2a$, where $a$ is the minor radius of the plasma and this is unchanged during the plasma density ramp up. By scanning the radial wave vectors, it is found that the residual stress term reverses from negative to positive when the plasma density exceeds a certain threshold. The pinch term is larger than the residual stress term at all four electron densities, which means that the pinch term is always dominant in the core of a J-TEXT plasma.