Summary of the 10th Conference on Magnetically Confined Fusion Theory and Simulation (CMCFTS)

1.   Introduction

The 10th Conference on Magnetically Confined Fusion Theory and Simulation (CMCFTS) was successfully held at the Kingsoft Industry Park (KIP), Zhuhai, China, from 28th to 31st October 2022. This is a series of CMCFTS started in Beijing in 2013 that has been held annually in China. The conference focuses on the latest achievements and progress in the research field of magnetically confined fusion plasma theory and the large-scale numerical simulation in the past years. The 10th CMCFTS is co-sponsored by the Theory and Simulation Project Group of the National Magnetic Confinement Fusion Energy Research and Development Program of China, the Plasma Physics Branch of the Chinese Physical Society, and the Nuclear Fusion and Plasma Physics Branch of the Chinese Nuclear Society. The conference was locally hosted by the Sino-French Institute of Nuclear Engineering and Technology (Sun Yat-sen University). The Materials Research Institute (China Academy of Engineering Physics) is the joint organizer.

Chinese research teams on the theory and simulation of magnetically confined fusion plasma have made remarkable progress with the support of the ITER Program, the National Magnetic Confinement Fusion Energy Research and Development Program of China, and the National Natural Science Foundation of China. In order to enhance the communication and cooperation among scientific researchers and further promote the theory and simulation development of magnetically confined fusion, it is decided to organize a seminar on the theory and simulation of magnetically confined fusion once a year. The 1st to 7th symposiums were held in Beijing, Chengdu, Hefei, Hangzhou, Beijing, Dalian, and Wuhan, respectively, from 2013 to 2019. The influence of the conferences gradually expanded and the scale of the conference is increasing year by year. The conference was renamed the Conference on Magnetic Confined Fusion Theory and Simulation (CMCFTS) in 2020. Since then, the 8th and 9th sessions were successfully held in Nanchang (Jiangxi Province), and Nanning (Guangxi Province), respectively.

There were four sections at this conference, namely the plenary lectures, the invited talks, the oral reports, and the poster section. Five plenary lectures were delivered, with two reviews of the latest experimental progress of the major tokamak facilities at the Southwestern Institute of Physics (SWIP) and the Institute of Plasma Physics in the Chinese Academy of Sciences (ASIPP), to encourage the collaboration between theory and experiments. Jiansheng Hu from ASIPP and Wulyu Zhong from SWIP presented the recent results of the EAST and HL-2 A/M experiments, respectively. Significant progress has been achieved, notably, the realization of a thousand-second improved confinement plasma in the EAST experiment, the Mega-Ampere plasma current in HL-2M operation [1, 2], and inputs from theories and simulations to understand these results were encouraged. The ongoing upgrades to the devices and plans for next-step campaigns were also introduced.

As magnetic fusion research is entering the era of burning plasmas, three plenary talks on tritium cycle research, alpha particle physics, and the transport and confinement for the plasma turbulence expected in fusion plasma were delivered. The conference received over one hundred oral report submissions, and finally, a total of fifty-nine oral presentations were selected. The oral presentations were divided into two sub-venues, namely the live sub-venue and the online sub-venue. A poster session of 120 min was arranged on the evening of 30th October, which is very popular at the living conference.

At this conference, there were 180 contributed abstracts and 110 onsite participants from 18 domestic universities and research institutes (https://ifcen.sysu.edu.cn/news/1861), including Zhejiang University, Dalian University of Technology, Southwestern Institute of Physics, etc More than 100 participants from the Institute of Plasma Physics of the Chinese Academy of Sciences, the University of Science and Technology of China, and other institutions could not attend the live conference because of the epidemic situation at that time. Therefore, the conference was held in a combination of both live and online ways, and it was broadcast on the academic online platform. According to the statistical data collected from the online platform of the conference, each parallel session was watched by over 10 000 viewers per day.

The topics of this conference include (1) equilibrium and magnetohydrodynamic (MHD) instability, (2) micro-turbulence and transport, (3) energetic particle physics, (4) edge physics, and (5) other topics covering radio-frequency (RF) wave heating and current drive, fusion reactor physics, integrated modeling, the fusion fuel cycle, the new concept design, as well as the large-scale numerical simulation and high-performance computation.

In this report, sections 2–6 described the technical summaries of oral presentations at this conference, which indicated the significant progress and some major challenges in the theory and simulation research fields of magnetically confined fusion. The poster section was briefly introduced in section 7. Finally, a summary and future perspectives of the CMCFTS were given in section 8.

2.   Equilibrium and MHD instability

Equilibrium and MHD instability are crucial for any magnetically confined fusion devices. At this conference, five papers were presented on this topic. Wei Zhang from Zhejiang University systematically investigated the explosive growth of the electron diamagnetic drift during sawtooth crashes, which caused the sudden stop of the reconnection process. During the nonlinear evolution of the resistive-kink mode, the pressure gradient at the X-point of the 1/1 island becomes larger and larger, and so as the local electron diamagnetic frequency. This can significantly reduce the nonlinear growth rate of the resistive kink mode and cause incomplete reconnection. This mechanism is verified in CLT simulations, and a series of incomplete-reconnection sawtooth oscillations is stimulated [3]. This novel mechanism is also applied to interpret the observations from EAST, showing good agreement between the theoretical predictions, simulations, and experimental observations.

Yemin Hu reported a numerical code that is developed by using the improved Von Hagenow method to simulate the current reversal balance at the free boundary. The numerical results show that the zero plasma current equilibrium configuration can be achieved under the condition of the equivalent magnitude of the conventional coil equilibrium control current [4]. Simultaneously, it is found that under the appropriate current profile conditions, the equilibrium configuration can achieve the same or even better confinement efficiency, and the plasma parameters are the same as the conventional equilibrium configuration.

Tong Liu reported the successful application of multi-mode three-dimensional MHD spectroscopy (M3DS) to identify the multi-mode eigenvalues in EAST, DIII-D, and KSTAR tokamak experiments with stable plasmas [5]. Real-time M3DS has been implemented in a DIII-D plasma control system (PCS) and the real-time detection of plasma stability has been achieved in live DIII-D experiments. The real-time M3DS is expected to be significant for the prediction of MHD stabilities and therefore the avoidance of severe disruptions in ITER and future fusion reactors.

Xuexi Zhang modified the EFIT (Equilibrium Fitting) code, and it was reported that the edge-localized current density information can be obtained from the external magnetic measurements. A full reconstruction of the current profile including the edge-localized current profile and the internal current profile can be achieved by the external magnetic measurements and the motional-Stark Effect (MSE) measurements [6].

Shiyong Zeng extensively investigated the growth of the tearing mode induced by impurity radiation using the single-fluid three-dimensional (3D) resistive MHD code NIMROD incorporated with an impurity radiation module KPRAD [7]. The MHD simulations reproduced the observed events of the tearing mode growth triggered by impurity radiation during the impurity penetration process in EAST.

3.   Micro-turbulence and transport

Micro-turbulence and transport is another issue discussed at this conference, which is crucial for understanding the core plasma confinement in magnetically confined fusion devices. Fourteen papers reported new theory findings and simulation results on some issues of micro-turbulence and transport. Jiquan Li gave a plenary talk on perspectives of turbulence and transport expected in burning plasma parameter regimes, due to multiple spatiotemporal scale nonlinear wave-particle as well as wave-wave interactions. Several key issues expected were discussed, including (1) effects of multiple species, including impurity, isotope, and helium ash contribution; (2) interaction between energetic particles and turbulence including electromagnetic effects expected in reactor finite-β plasmas; (3) cross-scale interaction between shear Alfvén wave (SAW) instabilities, macroscopic MHD and drift wave (DW) turbulences.

Zhibin Guo presented the turbulence-driven inward particle pinch, where turbulent particle transport was investigated in the presence of differential rotation flow in magnetized plasmas [8]. It is shown that the turbulent vorticity transport drives a particle pinch with a velocity equal to the normalized vorticity flux. Thus, by injecting vorticity to the plasma, i.e. spinning up the plasma rotation, an inward particle pinch would be induced. This new particle transport mechanism has potential application in resolving the challenging problem of how the fuels, fueled at the rapidly rotating edge layer, penetrate the burning core region of the fusion reactor.

Haotian Chen presented the electron temperature gradient (ETG) turbulence and its saturation by zonal flow (ZF) generation. Since observed numerically in the early 2000 s, radially elongated streamers have been proposed to significantly enhance the electron heat transport driven by ETG turbulence [9]. Haotian Chen et al developed a nonlinear gyrokinetic theory for the ZF excitation in intermediate-scale (shorter than ion gyroradius but longer than electron gyroradius) ETG turbulence [10], which was connected with long-time saturation. It is found that the resultant Schrödinger equation for ETG is characterized by a Navier–Stokes type nonlinearity, which is typically stronger than the Hasegawa–Mima type nonlinearity for the short wavelength ETG in fluid limit [11]. A novel ETG saturation picture is thus proposed that, in the early nonlinear phase, strongly unstable short wavelength ETG is saturated by inverse cascading, with streamers being well preserved; as spectrum downshifts, the ZF excitation becomes more important, and will ultimately break up streamers, leading to isotropic eddies. Therefore, streamers cannot exist in realistic experimental devices. Contrary to the ion temperature gradient (ITG), ETG turbulence is truly kinetic and multi-scale in nature, which has been verified in detail by gyrokinetic simulations [12].

Yi Zhang presented a novel mechanism of turbulence spreading into the magnetic island. By combining experimental and numerical analysis, it is found that the coherent convective cells (named quasi-coherent modes in the experiment) on both sides of the O-point boundary are accumulated during the island formation. The phase entrainment of the convective cells on the turbulence both in the inner and the outer regions of the magnetic island sets up a new transport channel and leads to the fast spreading of the outer turbulence into the magnetic island by conquering the flow shear at the O-point boundary [13].

The global gyrokinetic code GKNET with the heating term was used by Wei Wang to study the evolution characteristics of the stepped shear flow excited by the ITG turbulence under different heating powers and system sizes, and the distribution of transport structure changed with power and the system size [14]. The energy transfer path of ITG turbulence in the nonlinear phase under L-mode steady-state operation was reported.

Hongwei Yang showed that a particular electrostatic instability was driven by a steep ETG with a characteristic time scale around electron transit time while the spatial scale falling in the range of ion gyro-radius was dominant in the Ⅰ-mode regime, and can account for experimentally observed weekly coherent modes (WCMs) turbulence and the so-called transport decoupling between heat and particle in tokamak edge plasmas [15].

Ningfei Chen reported the latest work on the derivation of the fully nonlinear two-field model for drift wave (DW) and energetic particle-induced geodesic acoustic mode (EGAM) interaction based on first-principle nonlinear gyrokinetic theory and focused on how linear energetic particles (EPs) drive to EGAM affects soliton propagation and nonlinear energy transfer [16]. The velocity of solitons is slightly enhanced by linear EPs drive, resulting from the evolution to higher-k_r region. The energy of DW, EGAM, and nonlinear interaction is decomposed from the total energy, with the energy of DW always decreasing and that of EGAM always increasing.

Qinghao Yan and P H Diamond found a formation mechanism of the E× B staircase. Starting from the kinetic equation, they constructed evolution equations of a system including equilibrium profile and turbulence intensity [17]. The wave-particle interaction in the system is modulated by the E× B mean flow, which results in two types of transport states, i.e. resonant and non-resonant. Different transport states can lead to different temperature profiles, which in turn modulates the profile of E× B mean flow. Finally, the system forms a quasi-periodic staircase through a feedback loop [18].

Jianqiang Xu et al investigated the characteristics of geodesic acoustic mode (GAM) and its causal impact on turbulent transport in deuterium (D) and hydrogen (H) dominated ohmic plasmas in the edge region of HL-2A tokamak utilizing the direct causality analysis method [19]. It is shown that the nonlinear coupling between GAM and ambient turbulence as well as the information transfer from the radial electric field fluctuation of GAM to the particle flux and turbulence energy is also shown to be larger in the deuterium regime in comparison with hydrogen, implying that the regulation of turbulent transport by GAM ZF in D plasma is stronger than that in H isotope. The reduction of particle transport in D-dominated plasmas is mainly caused by the strong suppression of density fluctuations. Linear gyrokinetic simulations based on the experimental measurements have indicated that the destabilization of long-wavelength resistive ballooning modes and medium-wavelength trapped electron modes are responsible for the degradation of confinement in H-majority plasmas. Furthermore, the damping rate of GAMs in D-majority plasma is smaller than that in the H isotope, leading to an enhanced suppression effect on the background turbulence due to their longer survival time, which is in qualitative agreement with gyrokinetic predictions of the GAMs. These findings will promote the understanding of the isotope effect on zonal flows and their nonlinear interactions between ambient turbulence in the edge of fusion plasmas.

Weixin Guo et al presented the helium ash transport driven by collisionless trapped electron mode (CTEM) turbulence in the presence of alpha (α) particles. They found that although D_He/χ_eff < 1, which was less efficient for the removal of helium ash as compared with ITG mode [20], D_He/χ_eff could be increased by 50% with the presence of 3% α particles with their density gradient being twice that of electrons [21]. This is mainly because the destabilizing effect of α particles [22] on helium ash diffusivity is stronger than that on electron thermal conductivity. Moreover, the higher concentration as well as the steeper profile of α particles are, the stronger enhancement of D_He/χ_eff gets. Finally, it is also found that both the diffusivities of deuterium and tritium ions are still smaller than that of helium ash even with α particles, which is similar to the case without α particles [23]. These results might be favorable for more accurate prediction of helium ash profile and efficient removal of helium ash in the fusion reactor burning plasmas.

Jiayan Liu presented the effects of impurity on micro-instabilities in tokamak deuterium and tritium plasmas. It is found that the impurity ions with inwardly peaked density profile and high charge concentration have strong stabilizing effects on the trapped electron (TE)-ITG mode in both deuterium and tritium plasmas [24, 25]. Besides, the increasing charge number of impurities tends to decouple the hybrid mode into coexisting or dominating trapped electron mode (TEM)/ITG mode in different parameter regions. These highly desirable results will provide considerable experimental significance to their model.

Kaibang Wu et al analyzed anomalous transport based on the radial fractional diffusion equation. If the particles sit in strong turbulence with large fluctuation amplitude, the particles are trapped, and the average of their square of displacement is not proportional to time anymore, which can be described by the radial fractional transport model [26]. It is shown that for fractional transport models, hollow density profiles are formed and uphill transports can be observed regardless of whether the fractional diffusion coefficients (FDCs) are radially dependent or not. Further, it is found that when FDCs at the positions of source injections increase, the peak values of density profiles decrease. The non-local effect becomes significant as the order of fractional derivatives approaches 1 and causes uphill transport. However, as approaches 2, the fractional diffusion model returns to the standard model governed by Fick's law.

Min Jiang presented the experimental investigation of the impact of the magnetic island on plasma flows and turbulence levels on HL-2A plasmas. She showed that the rotating island (X-/O-point) could modulate density and temperature fluctuations and quasi-coherent modes due to changes in gradient-driven dynamics [13]. Strong flow shear can be formed at the island boundary, which may explain the link between the island and the transport barrier.

Jingchun Li presented the experimental observation of the nonlinear interactions among turbulence, geodesic acoustic mode, and tearing mode in HL-2A edge plasmas. It is found that the nonlinear interaction between GAM and background turbulence decreases with the magnetic island width, while the interaction between the magnetic island and the density perturbation-associated turbulence increases [19]. A special observation is that magnetic island (MI) can significantly reduce turbulence levels, with a non-monotonic dependence of the suppression effect on MI width.

4.   Energetic particle physics

Energetic particle physics is expected to play important role in the burning plasmas of future reactors and has drawn much research attention in the past decades as magnetically confined fusion (MCF) research is approaching the era of burning plasmas. At this conference, sixteen presentations focused on the issues of energetic particle physics. Guoyong Fu gave a plenary presentation on the general physics of alpha particles and shear Alfvén wave instabilities, including the SAW continuum and existence of discrete Alfvén eigenmodes, wave-particle interaction, toroidal Alfvén eigenmode (TAE) nonlinear frequency chirping due to phase space hole and clump formation. In particular, the experimental condition for TAE excitation in TFTR deuterium-tritium discharges was reviewed.

Zhiyong Qiu presented the nonlinear saturation of reversed shear Alfvén eigenmode (RSAE), which was expected to be important in future reactors with reversed shear configurations. The saturation is achieved via nonlinear excitation of low-frequency Alfvén eigenmode, which will heat thermal ions via collisionless Landau damping, leading to core localized fuel ion heating [27]. The heating power is estimated and shown to be comparable to collisional heating.

Feng Wang reported the application of a high-order guiding center with a synchrotron radiation approach (HGSA) in PTC code for runaway electrons (REs) [28]. The collisionless pitch-angle scattering and energy saturation of REs are reproduced numerically for realistic tokamak plasmas, which proves that the HGSA model is suitable for REs' phase space calculation.

Wanling Ge presented the simulational interpretation of fishbone effects on internal transport barrier formation in EAST experiments. It is found that the zonal electric field can be induced in the nonlinear stage of the fishbone, leading to a relatively large E× B zonal flow that is sufficient to suppress the dominant microinstability before ITB formation, which should account for the trigger of ITB. After the ITB is triggered, both the increased reversed shear of q-profile and the broadening energetic ion distribution can stabilize the fishbone [29].

Xingyuan Xu et al explored the generation of the radial electric field by the charge separation between neutral beam-induced electrons and beam ions, which had distinct magnetic drift orbits. The generation and steady-state distributions of neutral beam injection (NBI) fast ions were numerically computed by the orbit code GYCAVA and the NBI code TGCO. The simulation results show that NBI ions can produce a significant radial electric field in the core region. The dependence of the radial electric field on the injection direction and the beam energy has been investigated [30].

Lulu Zhang reported the simulation study of the circulating EP-induced chirping modes in KSTAR experiments. Fishbone and beta-induced Alfvén eigenmode (BAE) was observed in the linear simulations, while nonlinear frequency chirping and jumping to high-frequency branches were observed in the nonlinear simulation. Results indicated that toroidal plasma rotation may substantially affect the mode structure, frequency, and nonlinear evolution.

Based on the experimental parameters, Sizhe Duan reported the systematical investigations on the interactions between BAE (m/n = 2/1), tearing mode (TM) (m/n = 2/1), and the energetic particles, using the hybrid simulation code M3D-K [31]. Due to the redistribution of the energetic particles produced by TM, the radial distribution gradient of the energetic particles near the magnetic island separation line will increase, which can excite the BAE that is originally linearly stable.

Gengxian Li discussed the elongation effect on the growth rate of BAE and its physical mechanism. It is discovered that the BAE growth rate first increases with elongation factor κ, reaches a maximum, and then decreases [32]. The growth rate change is caused by MHD and kinetic effects respectively in the different stages. The equilibrium model and the eigenvalue code (DAEPS) used were also introduced in this report.

Xihui Wang reported the simulation of Alfvén eigenmode (AE) destabilization in EAST low B_t discharge using FAR3d code. The trigger of the AE is successfully explained, and the optimization trend to suppress the AE activity is simulated, which can be crucial in the future experiment to improve the heating efficiency.

Runzhe Zhang reported the analysis of ECRH on ion fishbone stability. It is found that the on/off-axis ECRH may lead to the change in fishbone frequency, of which the off-axis may significantly stabilize the fishbone. Further analysis indicated that the stabilization is achieved via the ECRH-induced trapped electron effects on processional frequency via modification of the pressure profile, while effects associated with increased electron temperature are negligible.

Yanxu Sun reported the application of the first-order Tikhonov regularization method to reconstruct the fast-ion velocity-space distributions from two-view fast-ion D-alpha (FIDA) measurements on EAST. With non-negativity, null measurements, and positions of neutral beam injection peaks as prior information, improved reconstructions have been achieved to investigate the difference in fast ions distribution function after the neutral beam upgrade on EAST [33]. The reconstructions show that after the counter-current neutral beam is upgraded to the co-current beam, the fast ion density increases and the fast ion loss decreases, the heating efficiency is improved, and in the velocity space, fast ions are mainly distributed in positive pitch region.

Jian Bao et al developed a new global eigenvalue code, MAS (Multi-scale Analysis for plasma Stabilities), for studying plasma problems based on a five-field Landau-fluid description of thermal plasmas and gyrokinetic model description of energetic particles. By implementing the physics model into a general tokamak geometry represented in Boozer coordinates, the MAS multi-scale physics capabilities were demonstrated, including low-n MHD modes, mediate-n Alfvén eigenmodes, and high-n drift wave instabilities by carrying out a series of benchmarks, which showed good agreements with theory and other fusion codes. With respect to the key progress contributed to the community, MAS has the advantage of combining rich physics ingredients, realistic geometry, and high computation efficiency for plasma stability analysis in linear regimes [34].

Youjun Hu presented the simulation of α particle heating in a fusion reactor. The steady-state α particle distribution and the resulting heating in a tokamak fusion reactor with a strong magnetic field were simulated by using a Monte-Carlo orbit following code. The results indicate that the heating power to the electron is dominant, as expected. The steady-state α particle distribution is found to carry a small bootstrap current (about 0.4% of the total plasma current) that is in the same direction as the plasma current.

Xiaolong Zhu presented the hybrid simulation of the avalanche transport of energetic particles observed in National Spherical Torus eXperiment (NSTX), which was believed to be a strong nonlinear process, leading to significant EP transport. It is found that the existence of multiple modes and the overlapping of their phase-space wave-particle resonance region are crucial for the onset of avalanche EP transport [35].

Liming Yu presented a systematic investigation of EP-induced low-frequency instabilities including fishbones and tearing modes, in particular the resonant TM instability observed after the strong sawtooth crash, probably excited by the re-distribution of EPs due to fishbone and sawtooth activities. Numerical simulation using M3D-k code suggested this mode was resonantly excited by counter-circulating EPs. These investigations may provide a potential mechanism for ash removal in future reactors [36].

Ming Xu presented the analysis results of the EAST experiment, and it is obtained that (1) the low-frequency modes can be divided into two categories, and the frequency of the modes will sweep up or hop up with the decrease of q_min; (2) the modulus of low-frequency mode is m/n = 4/2, 6/3, …; (3) the radial structure of low-frequency mode is characterized by 'spiral dart' structure; (4) the excitation conditions of the low-frequency modes on EAST are given in detail with the help of the numerical solution of GFLDR. In addition, the frequency sweep or hopping characteristics of such low-frequency modes strongly depend on the change of the q profile, so they can be used for MHD spectroscopy [37].

5.   Edge physics

Eighteen presentations focus on edge physics including core-edge couplings. Guosheng Xu reported that in the EAST experiments in 2022, the EAST group used a multi-pulse of the supersonic molecular beam (~1 ms pulse width) to inject the pure neon gas in the midplane of the low field side, so as to transform the large ELM of ~200 Hz into the small ELM of ~500 Hz, under the conditions of q₉₅ = 4.0, Greenwald density ratio n_e/n_GW ~ 0.7, single null configuration (dR_sep = 2 cm), unfavorable B_t direction, 7.4 MW heating power (including 5 MW neutral beam, 1 MW 4.6 GHz low hybrid wave, 1.4 MW electron cyclotron wave). At the same time, the electron temperature on the surface of the internal and external target plates of the divertor is lower than 5 eV, showing the characteristics of the detached divertor. This experiment has confirmed that under the lower value of q₉₅, at high density, with the single zero configuration and high power heating conditions required by the future fusion reactors (such as ITER and Basic Experimental Superconducting Tokamak (BEST)), both the small ELM and the detached divertor can be operated in a compatible manner [38].

Youwen Sun presented a new model for intrinsic toroidal rotation reversal during density ramping [39], based on changing of dominant roots of neoclassical toroidal plasma viscosity (NTV) induced torque in different collisional regimes [40]. The scaling of the density threshold for rotation reversal is proposed for cross-machine comparison and is verified numerically on different machines [41].

Huihui Wang reported the experimental and numerical investigation of the n = 1 error field penetration in EAST tokamak, with the experiment, carried out using pure RF heating power scanning. The scaling index between the mode penetration threshold and plasma β_N is close to b_r∝β_N^−1.0 based on the experimental results [42]. The numerical results using the MARS-Q code indicated that the influence of NTV torque on field penetration helps to clarify the reduction in error field tolerance as the normalized plasma beta β_N rises in toroidal geometry.

Lu Wang presented the effects of 3D magnetic perturbation (MP) on turbulence. The presence of 3D MP is ubiquitous in tokamak plasmas, which can be induced by MHD instabilities, such as tearing mode and ideal kink mode and may degrade the confinement and modify the stability of the tokamak plasmas. Lu Wang et al investigated both effects of the magnetic island (MI) and the flux surface displacement induced by the ideal kink mode on the micro-instability [43, 44]. It is found that the short-wavelength toroidal ITG mode in Fourier-ballooning representation considers both the flattening effects of MI on plasma pressure and MI-scale E× B shear flow [43]. It is found that when only considering the flattening effects of MI, the ITG mode can be stabilized compared to the case without MI. Meanwhile, the effective toroidal ITG mode drive can be enhanced by including MI-scale E× B flow, which indicates the dominant destabilizing by MI-scale E× B flow over the stabilizing by flattening profile, which results in a higher growth rate than the case without MI. It is also found that the total flow shearing may prevent the ITG turbulence from spreading from the X-point of MI but is not strong enough to prevent spreading from the separatrix across the O-point of larger MI via a comparison between the flow shearing rate and the linear growth rate. Moreover, Zhangsheng Huang reported that 3D effects induced by the ideal kink mode can either stabilize or destabilize CTEM instability, which depended on the poloidal and toroidal mode numbers as well as the phase of 3D MP [44]. Especially, for the destabilizing phase of MPs, the stabilizing effect of finite β (ratio of the thermal pressure to the magnetic pressure) on CTEM can be even reversed when the displacement of the magnetic flux surface exceeds a critical value. Moreover, the synergetic effects of 3D MPs with stabilizing phase and finite β can further reduce the required absolute value of negative magnetic shear to completely stabilize CTEM instability. This indicated that 3D MPs might be used as an actuator for lowing the level of anomalous electron heat transport, and thus facilitated the formation of an electron internal transport barrier.

The resonant magnetic perturbation (RMP) fields are extensively applied in order to actively control the edge localized modes (ELMs), which can also induce 3D MP. Neng Zhang presented the effects of RMP on toroidal flow. Neng Zhang et al investigated that resistive plasma response to the n = 1 (n is the toroidal mode number) RMP field was systematically investigated for a high-beta hybrid discharge on ASDEX Upgrade and ELMs mitigation on HL-2A, by utilizing the MARS-Q code [45, 46]. It is found that the neoclassical toroidal viscous (NTV) torque offers a tool to control the plasma toroidal rotation profile. The results of this work will be helpful in the ITER's future RMP experiments.

Hua Yang presented the dependence of ELM suppression windows and strike point movement on resonant 3D magnetic topology change induced by equilibria scan with n = 4 RMP in EAST. It is found that RMP ELM suppression exists in multi-resonant windows and the movement of the stationary heat flux deposition accompanying q₉₅ is another exciting result that could be used to avoid target heat accumulation locally, thus, may provide a further understanding of divertor heat and particle fluxes control.

Manni Jia presented the effect of plasma response on the boundary transport, and steady-state heat load distribution of the diverter in a 3D field is reported. The simulation results show that the heat flow at the major striking point of the divertor decreases while it increases at the minor striking point [47].

The process of ELM suppression by ICRH on EAST has been presented by Yanlong Li in detail by combining both the experiments and the simulations. It is indicated that the key factor for ELM suppression by ICRH is the RF sheath, rather than the structural changes of the pedestal [48].

Chaofeng Sang showed the development of a new two-dimensional (2D) kinetic tungsten (W) impurity transport code based on the guiding center approximation. The code is verified by benchmarking against the DIVIMP code and is coupled to edge plasma code SOLPS to study W core accumulation in EAST. It is found the competition between friction force and ion temperature gradient force significantly affects the penetration of W impurity to the core region and the enhancement of anomalous diffusion suppresses W core accumulation [49].

Huicong Ma presented impurity transport and screening behavior with the closed divertor in HL-2A. Impurity poloidal transport is mainly dominated by the pressure gradient force, ion temperature gradient force, and friction force [50]. The friction force is dominant and the screening capacity is strong during divertor detachment. Increasing the upstream electron density and seeding rate enhances the screening ability, whereas increasing the heating power weakens it. During divertor detachment, the screening effect of N⁺ and Ar⁺ ions is stronger than that of Ne⁺ ions. For HL-2A, seeding N₂ or Ar gas and consequent divertor detachment are an effective scheme to achieve impurity screening, which has a meaningful suggestion for future fusion devices.

Hui Wang presented the W transport and screening in the edge plasma of EAST under high dissipative divertor conditions. By combining the 0D theoretical analysis and 2D simulations of W erosion and transport carried out by using the SOLPS-DIVIMP, W screening is proved to be enhanced for high upstream plasma density conditions, mainly because the impurity temperature gradient velocity decreases with the increase of the upstream plasma density. Moreover, 2D simulations suggest that the impurity pressure gradient force cannot be neglected for edge W transport analysis, especially for the detached divertor conditions [51].

Jianbin Liu presented the characteristics of the new lower tungsten divertor. It is reported that the new lower tungsten divertor has a strong particle removal ability, which can better realize the compatibility of the detached plasma and the core plasma [52]. In addition, EAST uses the impurity injection of the divertor to feedback control the electron temperature of the target plate and successfully achieves about 30 s operation of the detached highly confined plasma, and good compatibility among the divertor, the boundary plasma, and the core plasma, is obtained.

Chao Dong presented the particle transport induced by weakly coherent mode (WCM) in Ⅰ-mode plasmas. The physical mechanisms behind the WCM and its produced transport in the Ⅰ-mode edge plasmas have been investigated through two-fluid simulations by using the BOUT++ code [53]. The turbulence from simulations is identified to be the WCM from its good agreement with the experimental observations on the poloidal and radial distributions as well as the frequency and wavenumber spectra of the WCM. Linear simulations show that the WCM is driven by the electron pressure gradient and exhibits many features of the drift Alfvén instability. Due to modulation of the E × B drift on the cross-phases between the electric potential fluctuation and the density and temperature fluctuations, the radial particle and heat fluxes induced by the simulated WCM are found to be unchanged across the whole outer shear layer of the E_r well. Comparing the simulated particle and heat fluxes with the experimental values indicated that the WCM is an important particle transport channel but not an important energy transport channel in the Ⅰ-mode regime. The above findings will promote the understanding of the physical mechanism of WCM and the formation of Ⅰ-mode.

Maolin Mou presented the effects of pedestal density on the formation of small edge localized modes. By analyzing two sets of density profiles, one with a fixed separatrix density and the other with a fixed pedestal top density, Maolin Mou et al obtained some new results to interpret the role of high separatrix density and large R_ne (R_ne = n_{e, sep}/n_{e, ped}, the ratio of separatrix density to pedestal top density) on small edge localized modes (ELMs) as follows: (1) there exists a threshold pedestal top density for fixed separatrix density, which indicates the competition between ion inertia and diamagnetic effects; (2) for a fixed pedestal top density, larger separatrix density results in a wider mode spectrum with a smaller growth rate of the most unstable mode, the peeling-ballooning mode is likely to be transferred to resistive ballooning mode, thus ELM energy loss is reduced. Further analyses showed that both high pedestal top density and high R_ne are necessary conditions to achieve small ELMs. The research results provide a new mechanism to interpret the experimental findings in high pedestal density operations.

Linming Shao presented the effects of RMP on the L–H/H–L transitions. By switching on the RMP coils in L-mode plasmas, ELMs-mitigation is achieved after the plasmas enter the H-modes. In low q₉₅ (q₉₅ ~ 3.7) plasmas, the L–H transition power threshold is nonlinearly dependent on the RMP current. By applying the effect of simultaneous particle density and kinetic energy dissipation of RMP coils, 'soft-landing' H–L transitions are achieved at low plasma density and stored energy. These 'soft-landing' H–L transitions are not sensitive to the neutral beam injection power but very sensitive to the fueling rate and the increasing rate of the RMP coil current.

Ting Wu developed a physics model in order to study the mechanism of turbulent transport influencing the scrape-off layer (SOL) width [54]. A new parameter R_a, the ratio of edge turbulence spreading across LCFS into the SOL to the turbulence production term via interchange mechanism in the SOL, is defined for the first time. Combining the experimental analysis, it is found that when turbulence intensity is low, SOL turbulence is dominated by local production; when turbulence intensity is medium and high, SOL turbulence is governed by edge turbulence spreading. Meanwhile, the SOL width increases with R_a and the edge turbulence spreading term, which indicates the significant impact of edge turbulence spreading on the SOL width.

Jin Guo presented the simulation results of the tungsten transport in the boundary plasma using SOLPS-ITER and DIVIMP codes. The result shows that the E× B drift will lead to an increase in the tungsten impurity flow and the tungsten impurity density in the confined plasma will increase by an order of magnitude [55]. Therefore, it is necessary to pay more attention to the influence of E× B drift on the transport of tungsten impurities for the pollution of the confined plasma in the future physical design of the fusion reactor divertor.

6.   Other topics

In addition to the topics mentioned above, there were other topics presented at the conference, including the RF wave heating and current drive, the fusion reactor physics, the integrated modeling, the fusion fuel cycle, the new concept design, as well as the large-scale numerical simulation and high-performance computation. Eighteen presentations focusing on such topics were given at this conference. Jun Ma introduced the application of symbolic computing technology in the simulation of the eigenvalue of the MHD instability. A complete MHD eigenvalue simulation program, SCELT (Symbolic Computation aided Eigenvalue and Linear code for Tokamaks), has been developed based on C++ language under the ring configuration, and the verification of the results obtained by this method has been taken [56].

Wenjin Chen reported the simulation of dynamic magnetic island effects on bootstrap current in toroidal plasmas, based on the first principles of kinetic particle simulation. Kinetic simulation results indicate that the bootstrap current has an asymmetry in the poloidal direction [57]. If the bootstrap current turns on when the tearing mode saturates, the widths of the magnetic islands ascend rapidly and saturate again for both static and dynamic cases. But the saturated island width of the dynamic case is smaller than that of the static case because the magnetic islands in the dynamic case are rotated due to the strong asymmetric distribution of the bootstrap current in the vicinity of the X-points.

Ion cyclotron range of radio-frequency (ICRF) heating and NBI can have synergy due to the acceleration of NBI beam ions by ICRF wave fields near the harmonic resonance layers. In the talk by Wei Zhang from the ASIPP, it was shown by the EAST experiments and the corresponding TRANSP simulation that ICRF-NBI synergy not only significantly improved the plasma performance by increasing the plasma stored energy, plasma temperature, poloidal beta, and neutron yield, but also generated fast deuterium ion tail with energy larger than 300 keV and fast neutron tail with energy larger than 3 MeV [58]. The ICRF-NBI synergy can be enhanced by decreasing the minority ion concentration, increasing the ICRF or NBI power, and optimizing the ICRF resonance position and NBI injection angle.

Yifeng Zheng reported the simulation of the orbit loss and the resulting heat load power deposition distribution of ICRF-NBI synergy-induced fast ions on the limiters in EAST using the full-orbit-following program ISSDE. The dynamic behaviors of these fast ions are under the synergistic effect of ripple field and collision. The fraction of fast ion loss on each limiter is related to the different distances of each limiter from the major plasma and the parallel direction of the fast ions [59].

Pingwei Zheng reported the simulation of m/n = 2/1 neoclassical tearing mode suppression by Ohkawa mechanism-dominated electron cyclotron current drive (OKCD) and the comparison with that of conventional Fisch–Boozer-dominated electron cyclotron current drive (ECCD). It is found that, in the low aspect-ratio tokamaks, OKCD will yield a localized current profile and larger current, leading to stabilization of the m/n = 2/1 neoclassical tearing mode (NTM) [60]. The condition for optimized NTM stabilization was also discussed.

Jiahui Zhang reported the effects of edge density perturbation on the ICRF wave propagation and heating of core plasmas. It is found that, as the scale of density perturbation is comparable to the ICRF wavelength, it may significantly affect the core plasma heating by ICRF [61]. A positive correlation of ICRF scattering to the amplitude and perpendicular scale of the density perturbation was also observed.

Huasheng Xie reported the ENN Group's efforts on the physics design of a spheromak-based machine, which aimed at Q = 10 operation using P and ¹¹B fuels, of which the fusion products were all charged particles. Based on the fusion cross-section of P-¹¹B interactions, the required parameter range of a P-¹¹B-based fusion reactor, including temperature, density, and energy confinement time, is derived, on which a spheromak-based reactor is designed, aiming at Q = 10 operation. The roadmap of the ENN fusion program was also introduced.

Ge Dong reported that the compact tokamak device with the strong magnetic field produced by the high-temperature superconductor can reduce the construction and operation cost of the fusion device and improve the safety and reliability of the device operation [62]. Therefore, the commercialization process of fusion energy can be accelerated.

The implementation of integrated data analysis (IDA) for the evaluation of plasma parameter profiles in HL-2A significantly leads to better utilization of experimental data. Jiahong Chen reported the IDA on the plasma diagnostics of HL-2A, and it is demonstrated that more accurate profile reconstruction with less inferred uncertainty can be achieved by the IDA diagnosis [63, 64].

Yao Zhou et al developed and validated the capability of M3D-C¹ code to model the nonlinear MHD evolution of stellarator plasmas. Based on this, the nonlinear MHD simulations were performed to unravel the mechanism of the current-drive-induced sawtooth-like core crashes in W7-X experiments. Two consecutive (1, 1) internal kink modes are observed, which are produced due to the two ι = 1 resonance in the rotational transform profile. A small-amplitude crash takes place at the inner resonance and then a bigger crash at the outer resonance follows, semi-quantitatively agreeing with the experimental measurements [65].

Jie Huang introduced the Chinese First Quasi-axisymmetric Stellarator (CFQS) which is built by the Southwest Jiaotong University and the National Institute of Nuclear Fusion Science of Japan. The basic characteristics of the electrostatic and electromagnetic micro instabilities in CFQS are given by scanning the density gradient and temperature gradient with a gyro kinetic code [66]. It is found that the turbulent transport level of CFQS is lower than the equivalent tokamak through nonlinear simulations.

Caoxiang Zhu introduced several calculation methods at the conference. The third-order and above algebraic accuracy can be achieved through simple treatment of the tangent vector of the coil with these methods, and the calculation speed can be improved with the same accuracy by using fewer data points [67].

Mingyuan Wang reported that the whistler waves (30–120 MHz) driven by the temperature anisotropy of the energetic electron were observed in the steady state plasma maintained by electron cyclotron wave (ECW) of the ENN Xuanlong-50 (EXL-50). The intensity of whistler waves can be reduced by increasing the electron density or decreasing the temperature anisotropy of the energetic electrons [68]. The frequency chirp phenomenon is also found in the experiment, which is consistent with the instability characteristics driven by the energetic particle beams.

Lingfeng Lu presented the physics design of the 6 MW ICRF heating system for the HL-2M tokamak. ICRF heating schemes for ion heating and energetic ion generations were predicted and the main plasma parameters as well as the antenna setup to achieve these schemes were proposed [69].

Hui Li presented the multi-scale multi-mode interaction based on machine learning (ML). ML is becoming a practical approach in model construction. This method opens new options for addressing current issues in fusion plasma. Therefore, based on ML, they put forth a framework for turbulence prediction with multi-scale multi-mode physics. Two prediction models have been constructed, namely the ExFC-NN and LLF5-NN [70, 71]. Results showed that the characteristics of turbulent transport can be successfully predicted with the NN-based model.

Jie Zhang proposed a 2D Gaussian deposition model [72] for pellet fueling particle sources and benchmarked it against the widely used pellet code HPI2 [73]. The pellet deposition density predicted by the new 2D Gaussian deposition model has an overall good agreement with the HPI2 code. The 2D Gaussian deposition model based on scaling laws for both the pellet ablation rate and the grad-B induced drift of the ablation cloud [73], is employed in the newly developed pellet ablation module (PAM) [74], which runs much faster than the first-principle HPI2 code. The time-efficient simulations make the new model a promising candidate for real-time control of the density profile. The model is then used to make a systematic scan of pellet injection parameters on EAST to numerically optimize the pellet fueling depth, which provides some reference for the future update of the EAST pellet fueling system. The PAM code employing the new model is also incorporated into the integrated modeling workflow [74] under the OMFIT framework to provide a self-consistent pellet fueling particle source for the TGYRO transport code.

Dehong Chen presented the analysis of D-³He fusion for a high-field tokamak. High-field and low aspect ratio tokamak reactors can improve the fusion triple products and fusion power density. Using a self-developed 0D system analysis code, analysis of the ignition parameters regime of D-³He fusion based on tokamak showed that a D-³He fusion reactor can be self-sustained and full-bootstrapped in a compact size, e.g. its major radius can be reduced to 4.8 m in case of B_t = 6.9 T and A = 1.8. For reducing the auxiliary power demand during the start-up and ignition process as lower as possible, a concept of shielding solenoid, which is a water-cooled conductor center solenoid installed instead of an inboard shielding blanket behind the vacuum vessel for inductive start-up, and a D–T fusion power assisting ignition method were proposed. The parameters evolution analysis based on power and the current balance showed that the D–T fusion can be ignited with ohmic heating power alone and the α power from D–T fusion is sufficient to heat the plasma to D-³He fusion ignition condition when the ³He is gradually substituted for the T in the plasma. These concepts and analysis results provide a potential scheme of a D-³He fusion reactor with compact size and low auxiliary power, which facilitates reducing the cost of a D-³He fusion reactor.

Rongbin Zhu presented the anomalous heating and current drive on EXL-50, which is a type of reversed field pinch (RFP) device. Rongbin Zhu et al found that the anomalous current drive on EXL-50 which was insensitive to the injection angle of RF waves and the produced energetic electrons. They proposed the stochastics field acceleration theory to explain anomalous experiments. Electrons can interact with the stochastic fields continually and are raised to high energy just like Fermi acceleration.

7.   Poster section

The poster section was welcomed by the participants of the conference, and in-depth discussions on the contents of the posters were included in this section. The conference set up the outstanding poster award for the students. The selection committee examined the poster of the students who participated in the live poster section (20 students), and five outstanding poster awards for the students (live section) were given. Xiaoran Zhang and Zhanhong Lin from the Dalian University of Technology, Yue Zhou and Miao Xue from the Southwestern Institute of Physics, and Guangyu Wei from Zhejiang University won outstanding poster awards for the students in the live section. An online poster session was organized on 6th November, for the participants who cannot participate in the live conference, where 13 student poster presentations were given. Yuehao Ma from the University of Science and Technology of China, Hanhui Li from Huazhong University of Science and Technology, and Yunchan Hu from the Institute of Plasma Physics of the Chinese Academy of Sciences won outstanding poster awards for the students of the online section.

8.   Summary and prospect

The 10th CMCFTS was held both online and offline in Zhuhai, China, from 28th to 31st October 2022. There were 110 participants from 18 organizations at the live conference. The statistical data from the online broadcasting platform indicated that the participation of the online conference was over 20 000 views per day during the conference.

In the plenary session, five plenary lectures on the latest experimental progress of HL-2 AM, EAST, and the tritium cycle research, as well as the review of alpha particle physics in fusion plasma and the issues of the transport and confinement for the plasma turbulence in a fusion reactor, were reported at the conference. Ten invited talks were given in the main hall and fifty-nine orals were reported in two parallel sessions both live and online. The poster section (43 live posters and 13 online posters) was welcomed by the participants, and eight outstanding poster awards for the students were given. These sessions provided an opportunity to deeply discuss the development to date on the progress of the magnetically confined fusion theory and simulations.

In conclusion, the 10th CMCFTS provided a place for fruitful discussions among scientists in the fields of (1) equilibrium and MHD instability, (2) micro-turbulence and transport, (3) energetic particle physics, (4) edge physics, (5) others topics covering RF wave heating and current drive, fusion reactor physics, integrated modeling, the fusion fuel cycle, the new concept design, as well as the large-scale numerical simulation and high-performance computation. The issues discussed during the plenary lectures, the invited talks, the oral reports, and the poster sections, can be served as a guide for a possible extension of the workshop topics in the future.

The next conference of CMCFTS (namely the 11th Conference on Magnetically Confined Fusion Theory and Simulation) will be held at Tianfu New Area in the city of Chengdu, Sichuan Province, and the organizer will be the Southwestern Institute of Physics (SWIP) of China National Nuclear Corporation (CNNC).