A second-order semi-implicit time integration method has been developed for solving the linearized collision operator in multi-species plasmas. A key feature of this method is that it treats the collision operator as a single entity, avoiding the operator splitting between its test particle and field particle components. This scheme employs an implicit trapezoidal time integration scheme for the isothermal test particle part (including pitch-angle scattering and energy diffusion) with a finite volume discretization in (v parallel to, j) velocity coordinates, while the non-isothermal model term and field particle part are treated explicitly. This approach avoids the species cross-coupling required by fully implicit schemes, enabling the collision term to be computed efficiently with a banded/sparse-matrix solver. The method has been implemented in the gyrokinetic semi-Lagrangian code NLT and verified through multi-species relaxation tests and neoclassical transport simulations. Numerical benchmarks against explicit methods confirm its robustness, achieving order-of-magnitude improvements in the allowable time-step size, particularly in simulations of electron-ion collisions. Furthermore, the numerical discretization rigorously preserves particle number, momentum, and energy conservation, maintains the self-adjoint property of the collision operator, and satisfies Boltzmann's H-theorem.

This study investigates chaotic diffusion in multi-scale turbulence driven by nonlinear wave-particle resonance coupling. Turbulent waves with distinct characteristic wavelengths across scales coherently interact with charged particles when their phase velocities match the particles' velocities. A multi-wavenumber mapping framework is developed to model chaotic transport under multi-scale turbulence. By analytically deriving velocity correlation functions, we quantify the diffusion coefficient under conditions of cross-scale wave intensity parity. A critical analysis reveals that chaotic dynamics at smaller scales prove insufficient to completely erase phase-space correlations established by large-scale turbulent components. The largest-scale turbulence components dominate deviations from quasi-linear (QL) theory predictions, establishing a scale-dependent hierarchy in chaotic transport. Mere reduction of inter-wave phase velocity spacing for small-scale components cannot recover QL diffusion at finite wave amplitudes in multi-scale turbulence. Incorporating a larger-scale component into a small-scale-driven strong chaotic system can induce deviation from QL diffusion. Specifically, for two-scale turbulence, the QL approximation systematically underestimates transport. Increasing the number of smaller-scale components with strong overlap parameters drives convergence toward the QL approximation. This framework establishes a methodology, which may inspire the analysis of more general resonance-driven turbulence in laboratory and astrophysical plasmas.

Parasitic absorption of lower hybrid waves (LHWs) by fusion-born alpha particles can significantly impair lower-hybrid current-drive (LHCD) efficiency and modify the alpha-particle phase-space distribution in burning plasma. This study develops a linear analytical model to quantify alpha-particle parasitic absorption of LHWs for the China fusion engineering test reactor (CFETR). Analysis reveals that the absorption is highly sensitive to the edge plasma density, edge electron temperature, and wave frequency. The model predictions agree well with GENRAY simulations, as the shift of the parallel refractive index n parallel to along the ray trajectory is small. For waves launched from the low-field side, which reach the electron damping region in a single pass, alpha-particle parasitic absorption may account for up to approximately 26% of the input power. In contrast, in top-launch scenarios, where waves undergo multiple passes through the edge plasma before entering the electron-damping region, parasitic absorption by alpha particles may exceed that by electrons. This model provides a fast and efficient tool for optimizing CFETR operation scenarios to mitigate deleterious alpha-particle parasitic absorption.

A local neoclassical transport module has been developed and validated in the semi-Lagrangian gyrokinetic code NLT for multi-species collisional plasmas. The module incorporates a linearized multi-species Sugama collision operator and provides two complementary solution strategies. In the initial-value formulation, a composite substep source-integration scheme is introduced to accurately evaluate the neoclassical drive along unperturbed particle trajectories while retaining large macroscopic time steps. A direct steady-state solver is also implemented to obtain the stationary neoclassical response without long-time relaxation. The two approaches are benchmarked against the Eulerian neoclassical code NEO for electron-ion plasmas and three-species plasmas with carbon impurities. The NLT results reproduce the NEO particle and heat fluxes, parallel flows, and bootstrap current over a broad collisionality range. As representative applications, the validated framework is applied to EAST-relevant tungsten impurity transport and core trapped-electron-mode stability. The results show that tungsten neoclassical transport is sensitive to local profile gradients, while the increased effective collisionality associated with larger Z_ eff can reduce the linear TEM growth rate under the considered EAST-relevant conditions. These developments extend NLT toward realistic multi-species collisional transport simulations.

An ad hoc calculation is presented to evaluate the growth rate of ion cyclotron emission (ICE) driven by ionized atoms from neutral beam injection (NBI). The distribution function of ionized NBI atoms is modeled with a power-law dependence on particle speed (v) with a power-law index alpha and a Gaussian distribution in pitch angle (mu) with a standard deviation. The growth rate of nearly perpendicular propagating fast magnetosonic waves is then calculated in uniform plasma to study the effects of the velocity gradient and the pitch-angle anisotropy on the excitation of ICE. In the limit of mu s -> 0, the contribution to the growth rate (gamma) arising from the velocity gradient satisfies gamma proportional to alpha and the contribution due to the pitch-angle anisotropy satisfies gamma proportional to mu s-1. The dependence of gamma on the injection direction of NBI and the speed of NBI atoms is examined in the limit of mu s -> 0. The growth rate of ICE on EAST and ASDEX Upgrade is analyzed using TRANSP-calculated distribution of ionized NBI atoms. The fast decrease in the signals of core ICE in discharge #100 126 on EAST is attributed to the increase of mu s and the decrease of alpha of the distribution of NBI ions at the core. The core ICE found on ASDEX Upgrade is, however, primarily caused by the velocity gradient, since ionized NBI atoms at the core of ASDEX Upgrade have a much softer distribution in v than ionized NBI atoms at the core of EAST. The possibility of pitch-angle scattering of NBI ions on self-generated fast magnetosonic waves through quasi-linear interaction is examined in uniform plasma, assuming that the excited waves only propagate at a specified angle. The results, though idealized and heuristic, indicate that nearly perpendicular propagating ICE at the second and third harmonic frequencies may be more efficient in scattering resonant particles in pitch-angle space.

Abstract Synergistic interactions between radio-frequency (RF) sheaths and fast electrons (FEs) pose a critical plasma-material interaction challenge in tokamaks utilizing combined ion cyclotron range of frequencies (ICRF) heating and lower hybrid wave (LHW) injection. This regime is investigated via one-dimensional particle-in-cell simulations of an RF sheath interacting with an LHW-generated FE distribution. Our simulations reveal two nonlinear, coupled mechanisms that amplify heat loads, with the magnitude of the impact strongly dependent on the LHW power $P_{\mathrm{LHW}}$ and the RF voltage amplitude $V_0$. First, intense FE fluxes at high $P_{\mathrm{LHW}}$ ($>5$~MW) introduce an FE-driven rectification that elevates the time-averaged sheath potential. This potential ``clamping'' effect doubles the average ion heat flux $\langle q_i \rangle$ to 5.0~MW/m$^2$, while the superimposed RF voltage swing ($\sim 2V_0$) drives the instantaneous peak $q_i^{\max}$ to 9.2~MW/m$^2$, nearly 40\% above the thermal baseline. In contrast, low-$P_{\mathrm{LHW}}$ FEs exert a negligible effect on $\langle q_i \rangle$. Second, FEs open a direct deposition channel, boosting $\langle q_e \rangle$ by over an order of magnitude. Notably, this electron heat flux is mitigated by $V_0$. Increasing $V_0$ from 100~V to 400~V suppresses $\langle q_e \rangle$ (from 3.9 to 2.7~MW/m$^2$) via an RF shielding mechanism, yet counter-intuitively intensifies $q_e^{\max}$ to 4.8~MW/m$^2$ by compressing transmission into a brief, deep sheath collapse. Crucially, although $V_0$ governs $q_{\mathrm{tot}}^{\max}$ ($\approx q_{i}^{\max}$) in high-voltage regimes, the FE population continues to drive $\langle q_{\mathrm{tot}} \rangle$, amplifying it more than threefold to $7.7~\mathrm{MW/m^2}$ at $V_0=400~\mathrm{V}$. These findings indicate that standard Maxwellian-based sheath models may severely underpredict heat loads, especially the critical instantaneous thermal stresses masked by time-averaged metrics, in the presence of FEs. The observed kinetic coupling thus emerges as a vital factor for accurate predictive modeling in next-step devices such as ITER and CFETR.

The fast electrons induced by plasma-lower hybrid wave (LHW) interactions near the guard limiter of the LHW antenna on the EAST tokamak not only enhance the limiter corrosion and dust production, but also alter the dust transport. Based on the shifted orbital motion limited model accounting for a flowing Maxwellian background plasma, this work investigates the tungsten dust transport in the sheath in front of the guard limiter of the LHW antenna, after the sheath structure is obtained using the one-dimensional particle-in-cell code, in which the fast electron component and electron emission from the tungsten material surface are included. It is shown that the fast electron concentration has a substantial impact on the dynamic characteristics of dust in the sheath, since the presence of the fast electrons enhances the heat flux to the dust, and the enhancement is stronger at higher fast electron concentrations. When the fast electron concentration is small, the dust can survive or survive partially in the sheath and then enter the edge plasma region, although it may lose part of its mass while crossing the sheath. Conversely, the dust quickly reaches the boiling temperature, and then melts and disappears in the sheath at high fast electron concentrations. The results indicate that the dust is accelerated to melt by the fast electrons and potentially mitigates the degradation of the plasma performance, compared to when it transits the sheath of Maxwellian plasma. Furthermore, the dust survival probability in the sheath of plasma containing fast electrons is also determined by the dust size and injection velocity. Large-radius dust with a high injection velocity is more likely to survive and cross the sheath, while dust with a small injection velocity may redeposit easily on the material surface due to the stronger electric force when the fast electron component is presented.

A nonlinear gyrokinetic simulation, which incorporates both the reversed shear Alfv & eacute;n eigenmode (RSAE) and the ion temperature gradient (ITG) turbulence, has been performed using the electromagnetic gyrokinetic Particle-In-Cell (PIC) code GEM. Strong nonlinear wave coupling and energy transfer between RSAE and ITG turbulence have been observed. Specific analyses show that the n = 4 Alfv & eacute;n eigenmode primarily interacts with the ITG harmonics with long wavelength (n <= 16). It is found that a background ITG turbulence can suppress the saturation level of RSAE and change the energetic particle transport. The frequency up-shift of RSAE and the frequency modulation on ITG components by RSAE are also observed. The impacts of the initial condition on the RSAE-ITG turbulence simulation are also discussed.

Parametric instabilities (PIs), including resonant type (involving two resonant daughter waves) and non-resonant type (where at least one daughter wave is a quasi-mode), are widely observed in plasma physics. In this work, we present a novel approach to solving the governing equations for both types of PI. The method involves first decoupling the wave equations and then solving the amplitude equation using an iterative characteristic root approach. By recalculating the amplification factors for both types of PI, we clarify two unclear physical aspects: (i) The wave number of the quasi-mode is established as a complex root of its linear dispersion equation. Using the determined wave number, we derive a unified amplification factor formula encompassing all PI types, with a minor modification to the non-resonant PI formula found in previous literature. (ii) The physical gap between the two types is bridged. Taking backward scattering as an example, there exists an intermediate stage between the resonant type, which exhibits no convective amplification, and the non-resonant type, which undergoes normal amplification. In this stage, the amplification factor increases sharply as the damping rate rises. Furthermore, our approach incorporates the effects of local parameter gradients, extending the applicability of analytical methods to higher inhomogeneity levels. The theoretical predictions are validated through numerical examples, providing insights for future refinements in PI modeling.

Lower hybrid wave (LHW) current drive plays a crucial role in sustaining steady-state (SS) discharges on the Experimental Advanced Superconducting Tokamak (EAST). Hotspots frequently form on the wave antenna and guard limiters during SS operations. Although both experimental and theoretical studies suggest that fast electrons could be responsible for these hotspots, the underlying mechanisms of fast electron generation under typical EAST operational parameters and their impact on the hotspots remain unresolved. In this work, particle-in-cell simulations are used to investigate the interactions between LHWs and electrons in front of the antenna, taking into account the realistic incident power spectra and localized field effects. The results show that, due to resonance overlap, fast electrons are produced through resonant interactions between electrons and LHW components with a high parallel refractive index (N parallel to). The velocity distribution function in velocity space is found to significantly depend on plasma parameters near the antenna, such as q95, electron temperature, and input power. These fast electrons notably enhance the sheath potential on the guard limiters and increase the heat flux to the wall.

In ion cyclotron range of frequencies (ICRFs) heating experiments on tokamaks, the observation of hot spots on the first wall and increased impurities at the plasma boundary in specific parameter regimes has prompted investigations into the underlying mechanisms. While previous studies have highlighted the role of fast ions generated by radio frequency sheaths in contributing to heat flux and impurity production, the influence of electrons has been overlooked. This study addresses this gap by exploring the impact of the localized electric fields induced by ICRF antennas on electron dynamics in the scrape-off layer of the EAST tokamak through test-particle simulations. Simulation results reveal two primary mechanisms through which the ICRF electrostatic wave packet affects electrons. For thermal electrons, low-power ICRF injection leads to a notable decrease of approximately 20% in electron density near the wave packet center due to ponderomotive reflection of low-speed electrons. Consequently, increasing electron temperature can mitigate this effect to some extent. As for fast electrons with velocities in the vicinity of the central phase velocity of the wave packet, significant acceleration occurs upon their quasi-trapping by the wave packet. Specifically, under 2 MW ICRF injection, some initial 1.5 keV fast electrons undergo substantial acceleration, reaching energies of 20 keV, with the average energy flux amplified 7 times. As power levels rise to 8 MW, the trapping velocity range widens, enabling the direct capture and acceleration of even thermal electrons by the ICRF localized field. Furthermore, a higher electron temperature of 80 eV can reduce the power demand to 5 MW. This study will qualitatively assess the impact of localized fields on electron acceleration and parameter dependence across various ICRF power levels, offering insights for controlling ICRF operation parameters in future fusion reactors.

Since the last IAEA-FEC in 2021, significant progress on the development of long pulse steady state scenario and its related key physics and technologies have been achieved, including the reproducible 403 s long-pulse steady-state H-mode plasma with pure radio frequency (RF) power heating. A thousand-second time scale (similar to 1056 s) fully non-inductive plasma with high injected energy up to 1.73 GJ has also been achieved. The EAST operational regime of high beta(P) has been significantly extended (H-98y2 > 1.3, beta(P) similar to 4.0, beta(N) similar to 2.4 and n(e)/n(GW) similar to 1.0) using RF and neutral beam injection (NBI). The full edge localized mode suppression using the n = 4 resonant magnetic perturbations has been achieved in ITER-like standard type-I ELMy H-mode plasmas with q(95) approximate to 3.1 on EAST, extrapolating favorably to the ITER baseline scenario. The sustained large ELM control and stable partial detachment have been achieved with Ne seeding. The underlying physics of plasma-beta effect for error field penetration, where toroidal effect dominates, is disclosed by comparing the results in cylindrical theory and MARS-Q simulation in EAST. Breakdown and plasma initiation at low toroidal electric fields (<0.3 V m(-1)) with EC pre-ionization is developed. A beneficial role on the lower hybrid wave injection to control the tungsten concentration in the NBI discharge is observed for the first time in EAST suggesting a potential way toward steady-state H-mode NBI operation.

The attainment of a reliable equilibrium is a critical aspect of tokamak experiments and physics analysis. A common method for establishing a reliable equilibrium current involves reconstructing it from indirect measurements, such as those obtained from polarimeter-interferometers (POINT) and motional Stark effect (MSE) systems. However, uncertainties still exist in the reconstruction results. For the equilibrium reconstruction on the EAST tokamak, which is based on the POINT system, the primary sources of uncertainty are the limited scope of measurements and the sensitivity of the reconstruction process. This paper proposes an enhanced approach that utilizes current simulation as a constraint to maintain consistency between the initial equilibrium and the simulated results. The radio frequency waves driven current is identified as a particularly influential component due to its interaction with the q profiles of the equilibrium and the deposition region of the waves. Two specific discharges are presented to illustrate how a new equilibrium can be achieved, which enhances consistency between the equilibrium and the simulated current, taking into account the dependencies of various components.

The mechanisms by which media inhomogeneity affects the three wave parametric instability (PI), including the wave number mismatch and the parameter gradients, are investigated using an approach based on the Wentzel-Kramers-Brillouin-Jeffreys (WKBJ) approximation. This approach transforms the coupling wave equations into an amplitude equation and iteratively solves its characteristic polynomials. By analyzing the solutions, we proposed that the wave number of the quasi-mode, a key term in the wave number mismatch of non-resonant type PI, should be a complex root of the quasi-mode's linear dispersion equation. Based on this, we derive a unified amplification factor formula that covers the resonant and non-resonant, the forward-scattered and backward-scattered types of PI. The impact of parameter gradients on the local spatial growth rate becomes significant when the inhomogeneity exceeds 10^-3. Considering parameter gradients extends our approach's validity to an inhomogeneity of about 10^-2. This approach holds promise for more specific PI modeling in the future.

Due to the complexity, chaotic behavior, and non-linear nature of tokamak plasma dynamics, modeling tokamak discharges poses a formidable challenge. This modeling task necessitates the accurate prediction of the evolution of tokamak diagnostic signals, entailing the resolution of a sequence-to-sequence time series prediction problem. In this study, we propose a novel framework for tokamak discharge modeling, termed the PCC-Trans framework, which integrates a time series feature selection method based on the Pearson correlation coefficient (PCC) and Transformer, and enhances the predictive accuracy of the model. Specifically, PCC is employed for signals correlation analysis and the selection of relevant, non-redundant features to augment the Transformer. Through analysis and modeling of experimental data from the Experimental Advanced Superconducting Tokamak (EAST), the proposed framework demonstrates superior performance across four case studies compared to five other machine learning approaches, including Multi-layer Perceptron (MLP), Long Short-Term Memory (LSTM), Bi-directional Long Short-Term Memory (BiLSTM), Convolutional Neural Network (CNN), and Transformer. Additionally, we validate the efficacy of the feature selection method by assessing the necessity of each element within the feature set and its influence on modeling performance.

An ad hoc calculation is presented to interpret the growth of sideband waves during lower hybrid current drive (LHCD) experiments on Experimental Advanced Superconducting Tokamak (EAST). We adopt the solution of the non-linear dispersion relation for parametric instabilities to describe the growth rate of ion cyclotron quasi-modes (ICQMs) in the peripheral plasma, and use the WKB solution of the propagation of electrostatic waves in two dimensions to model the variation of the electric field in the scrape-off-layer (SOL). We then calculate the growth rates and amplification factors of the sideband waves associated with ICQM in the parallel and perpendicular coupling limits. The onset and substantial growth of the first down-shifted sideband of lower hybrid waves (LHWs) are associated with elevation of the plasma density in the outer SOL where the growth rate of ICQM in the parallel coupling limit increases sharply after the density is elevated. The peak frequencies associated with the first harmonic of ICQM obtained from calculating the amplification factors in the parallel coupling limit ( Apara) agree very well with the observed frequencies of the first down-shifted sideband of 2.45 GHz LHWs in EAST pulse 43 772 and 86 521. The consistency between the calculation and the observation indicates that the sideband waves are associated with parametric decay instability of ICQM excited in the outer SOL through parallel coupling. The amplitude of Apara obtained from a single pass of LHWs through the SOL of EAST is, however, one order of magnitude smaller than unity, meaning that it remains elusive whether the substantial growth of sideband waves mainly occurs in front of the antenna or requires multiple passes of LHWs across the SOL region.

The compressional magnetic component δB|| has been implemented in the gyrokinetic Particle-in-Cell (PIC) code GEM for the fully electromagnetic simulation of microscopic instabilities in high-β tokamak plasmas. The simulation model is formulated for the split-weight scheme that is based on the canonical momentum formulation of the gyrokinetic equation. A pseudo-spectral method is used to solve the coupled gyrokinetic field equations while preserving all finite-Larmor-radius (FLR) effects. The algorithm is verified by the method of manufactured solutions. Simulations of the ion-temperature-gradient-driven (ITG) mode, the kinetic balloon mode (KBM) and the trapped electron mode (TEM) are presented.

Over the decades, the integrated modeling (IM) environment for magnetically confined fusion has evolved from a single, isolated, proprietary numerical computing software to an open, flexible platform emphasizing sharing, communication, and workflow. This development direction is consistent with the FAIR4RS principles put forward by the scientific community in recent years. In this article, we describe how the FAIR4RS principles were put into practice during the development of the IM management tool FyDev for the Experimental Advanced Superconducting Tokamak (EAST). FyDev integrates the process of building, deploying, and invoking research software, automating the entire process. FyDev can also assign a unique ID for each software, convert the software ID to a Python module, and encapsulate a package management tool to enhance the software building process, ensuring consistency throughout the entire phase of the research software find, access, use, and invocation in a uniform contextual environment.

A deep neural network is developed and trained on magnetic measurements (input) and EFIT poloidal magnetic flux (output) on the EAST tokamak. In optimizing the network architecture, we use automatic optimization in searching for the best hyperparameters, which helps the model generalize better. We compare the inner magnetic surfaces and last-closed-flux surfaces (LCFSs) with those from EFIT. We also calculated the normalized internal inductance, which is completely determined by the poloidal magnetic flux and can further reflect the accuracy of the prediction. The time evolution of the internal inductance in full discharges is compared with that provided by EFIT. All of the comparisons show good agreement, demonstrating the accuracy of the machine learning model, which has the high spatial resolution as the off-line EFIT while still meets the time constraint of real-time control.