Sawtooth-like oscillations and steady states caused by the m/n=2/1 double tearing mode

The sawtooth-like oscillations resulting from the m/n=2/1 double tearing mode (DTM) are numerically investigated through the three-dimensional, toroidal, nonlinear resistive-MHD code (CLT). We find that the nonlinear evolution of the m/n=2/1 DTM can lead to sawtooth-like oscillations, which are similar to those driven by the kink mode. The perpendicular thermal conductivity and the external heating rate can significantly alter the behaviors of the DTM driven sawtooth-like oscillations. With a high perpendicular thermal conductivity, the system quickly evolves into a steady state with m/n=2/1 magnetic islands and helical flow. However, with a low perpendicular thermal conductivity, the system tends to exhibit sawtooth-like oscillations. With a sufficiently high or low heating rate, the system exhibits sawtooth-like oscillations, while with an intermediate heating rate, the system quickly evolves into a steady state. At the steady state, there exist the non-axisymmetric magnetic field and strong radial flow, and both are with helicity of m/n=2/1. Like the steady state with m/n=1/1 radial flow, which is beneficial for preventing the Helium ash accumulation in the core, the steady state with m/n=2/1 radial flow might also be a good candidate for the advanced steady-state operations in future fusion reactors. We also find that the behaviors of the sawtooth-like oscillations are almost independent of Tokamak geometry, which implies that the steady state with saturated m/n=2/1 islands might exist in different Tokamaks.

Beta-induced Alfvén eigenmodes and geodesic acoustic modes in presence of strong tearing activity during the current ramp-down on JET

The analysis of the current ramp-down phase of JET plasmas has revealed the occurrence of additional magnetic oscillations in pulses characterized by large magnetic islands. The frequencies of these oscillations range from 5 kHz to 20 kHz, being well below the toroidal gap in the Alfven continuum and of the same order of the low-frequency gap opened by plasma compressibility. The additional oscillations only appear when the magnetic island width exceeds a critical threshold, suggesting that the oscillations could tap their energy from the tearing mode (TM) by a non-linear coupling mechanism. A possible role of fast ions in the excitation process can be excluded, being the pulse phase considered characterized by very low additional heating. The calculation of the coupled Alfven-acoustic continuum in toroidal geometry suggests the possibility of beta-induced Alfven eigenmodes (BAE) rather than beta-induced Alfven acoustic eigenmodes (BAAE). As a main novelty compared to previous works, the analysis of the electron temperature profiles from electron cyclotron emission has shown the simultaneous presence of magnetic islands on different rational surfaces in pulses with multiple magnetic oscillations in the low-frequency gap of the Alfven continuum. This observation supports the hypothesis of different BAE with toroidal mode number n = 1 associated with different magnetic islands. As another novelty, the observation of magnetic oscillations with n = 2 in the BAE range is reported for the first time in this work. Some pulses, characterized by slowly rotating tearing modes, exhibit additional oscillations with n = 0, likely associated with geodesic acoustic modes (GAM), and a cross-spectral bicoherence analysis has confirmed a non-linear interaction among TM, BAE and GAM, with the novelty of the observation of multiple triplets (twin BAEs plus GAM), due to the simultaneous presence of several magnetic islands in the plasma.

Analysis of hydrogen fueling, recycling, and confinement at Wendelstein 7-X via a single-reservoir particle balance

A single-reservoir particle balance for the main plasma species hydrogen has been established for Wendelstein 7-X (W7-X). This has enabled the quantitative characterization of the particle sources in the standard island divertor configuration for the first time. Findings from attached scenarios with two different island sizes with a boronized wall and turbo molecular pumping are presented. Fueling efficiencies, particle flows and source locations were measured and used to infer the total particle confinement time $\tau_{\rm{p}}$. Perturbative gas injection experiments served to measure the effective particle confinement time $\tau_{\rm{p}}^*$. Combining both confinement times provides access to the global recycling coefficient $\bar{R}$. Hydrogen particle inventories have been addressed and the knowledge of particle sources and sinks reveals the core fueling distribution and provides insight into the capability of the magnetic islands to control exhaust features. Measurements of hydrogen fueling efficiencies were sensitive to the precise fueling location and measured between 12~\% and 31~\% with the recycling fueling at the strike line modeled at only 6~\%, due to much higher densities. 15~\% of the total \SI{5.2E+22}{a/s} recycling flow ionizes far away from the recycling surfaces in the main chamber. It was shown that 60~\% of recycled particles ionize above the horizontal and 18~\% above the vertical divertor target, while the remainder of the recycling flow ionizes above the baffle (7~\%). Combining these source terms with their individual fueling efficiencies resolves the core fueling distribution. Due to the higher fueling efficiency in the main chamber, up to 51~\% of the total \SI{5.1E+21}{1/s} core fueling particles are entering the confined plasma from the main chamber. $\tau_{\rm{p}}$ values in the range of 260 ms were extracted for these discharges. Together with $\tau_{\rm{p}}$, the global recycling coefficient $\bar{R}$ was resolved for every $\tau_{\rm{p}}^*$ measurement and a typical value close to unity was obtained. An increase of the island size, resulted in no change of $\tau_{\rm{p}}$, but doubled $\tau_{\rm{p}}^*$, indicating the feasibility of the control coils as an actuator to control exhaust features without affecting core confinement properties.

Influence of low-Z impurity on the stabilization of m/n = 2/1 tearing/locked modes in EAST

The impact of the low-Z impurity concentration on the modes stabilization has been investigated in the EAST tokamak. Series of tearing modes (TMs) with multiple helicities are excited by the concentration of low-Z (carbon) impurity, and the dominant mode structure is featured by m/n = 2/1 magnetic islands that propagate in electron diamagnetic drift direction (m and n are poloidal and toroidal mode numbers respectively). The m/n = 2/1 locked modes (LMs) can be formed by the redistribution of low-Z impurity concentration, which is unlocked spontaneously for the decreasing of impurity concentration, where the width of magnetic islands can reach w ≅ 5 cm (w/a ≅ 0.1, a is minor radius). The increasing of electromagnetic brake torque is the primary reason for the mode locking, and the 'O'-point of m/n = 2/1 magnetic islands is locked by the tungsten protector limiter (toroidal position: -0.4π ≦ φ ≦ -0.3π) with separation of Δφ ≅ 0. The 3D asymmetric structure of m/n = 2/1 magnetic islands is formed for the interaction with the tungsten protector limiter, and the electromagnetic interaction decreases dramatically for the separation of Δφ ≧ 0.2π. The mechanisms for the mode excitation and locking can be illustrated by the "hysteresis effect" between the low-Z impurity concentration and the width of m/n = 2/1 magnetic islands, namely the growth of magnetic islands is modulated by the low-Z impurity concentration, and the rotation velocity is decelerated accordingly. However, the intrinsic mechanism for the unlocking of m/n = 2/1 LMs is complicated by considering the concentration of the low-Z impurity, and the possible unlocking mechanism is discussed. Therefore, understanding of the relationship between the impurities and magnetic islands is more important for optimizing the control techniques (RMP→LMs, ECRH→NTM, impurity seeding→major collapse, et al).

Statistical description of coalescing magnetic islands via magnetic reconnection

The physical picture of interacting magnetic islands provides a useful paradigm for certain plasma dynamics in a variety of physical environments, such as the solar corona, the heliosheath and the Earth's magnetosphere. In this work, we derive an island kinetic equation to describe the evolution of the island distribution function (in area and in flux of islands) subject to a collisional integral designed to account for the role of magnetic reconnection during island mergers. This equation is used to study the inverse transfer of magnetic energy through the coalescence of magnetic islands in two dimensions. We solve our island kinetic equation numerically for three different types of initial distribution: Dirac delta, Gaussian and power-law distributions. The time evolution of several key quantities is found to agree well with our analytical predictions: magnetic energy decays as $\tilde {t}^{-1}$ , the number of islands decreases as $\tilde {t}^{-1}$ and the averaged area of islands grows as $\tilde {t}$ , where $\tilde {t}$ is the time normalised to the characteristic reconnection time scale of islands. General properties of the distribution function and the magnetic energy spectrum are also studied. Finally, we discuss the underlying connection of our island-merger models to the (self-similar) decay of magnetohydrodynamic turbulence.

Annihilation of Magnetic Islands at the Top of Solar Flare Loops

The dynamics of magnetic reconnection in the solar current sheet (CS) is studied by high-resolution 2.5-dimensional MHD simulation. With the commencing of magnetic reconnection, a number of magnetic islands are formed intermittently and move quickly upward and downward along the CS. Upon collision with the semi-closed flux of the flare loops, the downflow islands cause a second reconnection with a rate comparable with that in the main CS. Though the time-integrated magnetic energy release is still dominated by the reconnection in the main CS, the second reconnection can release substantial magnetic energy, annihilating the main islands and generating secondary islands with various scales at the flare loop top. The distribution function of the flux of the secondary islands is found to follow a power law varying from f ψ ∼ ψ − 1 (small scale) to ψ −2 (large scale), which seems to be independent to background plasma β and thermal conduction (TC). However, the spatial scale and the strength of the termination shocks driven by the main reconnection outflows or islands decrease if β increases or if TC is included. We suggest that the annihilation of magnetic islands at the flare loop top, which is not included in the standard flare model, plays a nonnegligible role in releasing magnetic energy to heat flare plasma and accelerate particles.

Interaction between Multiple Current Sheets and a Shock Wave: 2D Hybrid Kinetic Simulations

Particle acceleration behind a shock wave due to interactions between magnetic islands in the heliosphere has attracted attention in recent years. The downstream acceleration may yield a continuous increase of particle flux downstream of the shock wave. Although it is not obvious how the downstream magnetic islands are produced, it has been suggested that current sheets are involved in the generation of magnetic islands due to their interaction with a shock wave. We perform 2D hybrid kinetic simulations to investigate the interaction between multiple current sheets and a shock wave. In the simulation, current sheets are compressed by the shock wave and a tearing instability develops at the compressed current sheets downstream of the shock. As the result of this instability, the electromagnetic fields become turbulent and magnetic islands form well downstream of the shock wave. We find a “post-cursor” region in which the downstream flow speed normal to the shock wave in the downstream rest frame is decelerated to ∼ 1V A immediately behind the shock wave, where V A is the upstream Alfvén speed. The flow speed then gradually decelerates to 0 accompanied by the development of the tearing instability. We also observe an efficient production of energetic particles above 100 E 0 during the development of the instability some distance downstream of the shock wave, where E 0 = m p V A 2 and m p is the proton mass. This feature corresponds to Voyager observations showing that the anomalous cosmic-ray intensity increase begins some distance downstream of the heliospheric termination shock.

Kinetic Plasma Turbulence Generated in a 3D Current Sheet With Magnetic Islands

In this article we aim to investigate the kinetic turbulence in a reconnecting current sheet (RCS) with X- and O-nullpoints and to explore its link to the features of accelerated particles. We carry out simulations of magnetic reconnection in a thin current sheet with 3D magnetic field topology affected by tearing instability until the formation of two large magnetic islands using particle-in-cell (PIC) approach. The model utilizes a strong guiding field that leads to the separation of the particles of opposite charges, the generation of a strong polarization electric field across the RCS, and suppression of kink instability in the “out-of-plane” direction. The accelerated particles of the same charge entering an RCS from the opposite edges are shown accelerated to different energies forming the “bump-in-tail” velocity distributions that, in turn, can generate plasma turbulence in different locations. The turbulence-generated waves produced by either electron or proton beams can be identified from the energy spectra of electromagnetic field fluctuations in the phase and frequency domains. From the phase space analysis we gather that the kinetic turbulence may be generated by accelerated particle beams, which are later found to evolve into a phase-space hole indicating the beam breakage. This happens at some distance from the particle entrance into an RCS, e.g. about 7di (ion inertial depth) for the electron beam and 12di for the proton beam. In a wavenumber space the spectral index of the power spectrum of the turbulent magnetic field near the ion inertial length is found to be −2.7 that is consistent with other estimations. The collective turbulence power spectra are consistent with the high-frequency fluctuations of perpendicular electric field, or upper hybrid waves, to occur in a vicinity of X-nullpoints, where the Langmuir (LW) can be generated by accelerated electrons with high growth rates, while further from X-nullponts or on the edges of magnetic islands, where electrons become ejected and start moving across the magnetic field lines, Bernstein waves can be generated. The frequency spectra of high- and low-frequency waves are explored in the kinetic turbulence in the parallel and perpendicular directions to the local magnetic field, showing noticeable lower hybrid turbulence occurring between the electron’s gyro- and plasma frequencies seen also in the wavelet spectra. Fluctuation of the perpendicular electric field component of turbulence can be consistent with the oblique whistler waves generated on the ambient density fluctuations by intense electron beams. This study brings attention to a key role of particle acceleration in generation kinetic turbulence inside current sheets.

Progress of HL-2A experiments and HL-2M program

Since the last IAEA Fusion Energy Conference in 2018, significant progress of the experimental program of HL-2A has been achieved on developing advanced plasma physics, edge localized mode (ELM) control physics and technology. Optimization of plasma confinement has been performed. In particular, high-N H-mode plasmas exhibiting an internal transport barrier have been obtained (normalized plasma pressure N reached up to 3). Injection of impurity improved the plasma confinement. ELM control using resonance magnetic perturbation (RMP) or impurity injection has been achieved in a wide parameter regime, including Types I and III. In addition, the impurity seeding with supersonic molecular beam injection (SMBI) or laser blow-off (LBO) techniques has been successfully applied to actively control the plasma confinement and instabilities, as well as the plasma disruption with the aid of disruption prediction. Disruption prediction algorithms based on deep learning are developed. A prediction accuracy of 96.8% can be reached by assembling convolutional neural network (CNN). Furthermore, transport resulted from a wide variety of phenomena such as energetic particles and magnetic islands have been investigated. In parallel with the HL-2A experiments, the HL-2M mega-ampere class tokamak was commissioned in 2020 with its first plasma. Key features and capabilities of HL-2M are briefly presented.

Development of a reduced model for energetic particle transport by sawteeth in tokamaks

The sawtooth instability is known for inducing transport and loss of energetic particles (EP), and for generating seed magnetic islands that can trigger tearing modes. Both effects degrade the overall plasma performance. Several theories and numerical models have been previously developed to quantify the expected EP transport caused by sawteeth, with various degrees of sophistication to differentiate the response of EPs at different energies and on different orbits (e.g. passing vs. trapped), although the analysis is frequently limited to a single time slice during a tokamak discharge. This work describes the development and initial benchmark of a framework that enables a reduced model for EP transport by sawteeth retaining the full EP phase-space information. The model, implemented in the ORBIT hamiltonian particle-following code, can be used either as a standalone post-processor taking input data from codes such as TRANSP, or as a preprocessor to compute transport coefficients that can be fed back to TRANSP for time-dependent simulations including the effects of sawteeth on energetic particles. The advantage of the latter approach is that the evolution of the EP distribution can be simulated quantitatively for sawtoothing discharges, thus enabling a more accurate modeling of sources, sinks and overall transport properties of EP and thermal plasma species for comprehensive physics studies that require detailed information of the fast ion distribution function and its evolution over time.