The divertor biasing technique offers a promising alternative to control the edge localized mode (ELM) as well as the divertor heat load in tokamaks, as compared to the resonant magnetic perturbation (RMP) generated by magnetic coils. The linear resistive MHD code MARS-F [Liu et al. Phys. Plasmas 7, 3681 (2000)] is employed to study the plasma response to the $n=2$ ($n$ is the toroidal mode number) field perturbation in HL-2A, produced by the divertor biasing current filaments flowing in the scrape-off layer (SOL) region. The response field due to biasing currents is compared with the RMP field utilized for ELM control in HL-2A. The strength of the radial resonant field perturbation, produced by the biasing currents of 100 A level, is found to be comparable with RMP generated by several kA of ELM control coil currents for the reference plasma. The plasma normal displacement near the X-point and {the associated neoclassical toroidal viscosity torque are} also computed to be similar between these two techniques. The modeling results thus strongly suggest that the biasing technique can be applied to control ELMs. Moreover, the biasing currents produce field perturbations, including the plasma response, that are localized more near the plasma edge (compared to the RMP counterpart), thus reducing the chance of mode locking associated with core perturbations. Particle orbit tracing also reveals that the biasing current produced magnetic perturbation tends to widen the heat deposition region and induce the strike point splitting of the ion saturation flow on the outer divertor surface, consistent with experimental observations in HL-2A. These toroidal modeling results confirm the possibility of ELM control and plasma exhaust solution by the divertor biasing technique.

The plasma response to the n = 1, 2, 4 (n is the toroidal mode number) resonant magnetic perturbation (RMP) fields, and the consequences on the fast ion confinement, are numerically investigated for a reference high-pressure plasma in HL-2M, by utilizing the linear resistive magnetohydrodynamic code MARS-F (Liu et al 2000 Phys. Plasmas 7 3681). The best coil current configurations, in terms of the coil phasing between the upper and lower rows of coils for controlling type-I edge localized modes (ELMs) in HL-2M, are identified as −130, −30, 180 degrees for the n = 1, 2, 4 fields, respectively, based on the edge peeling-tearing plasma response criterion. The plasma is found to substantially amplify the applied vacuum RMP field with the best coil phasing for the reference HL-2M equilibrium. The overall field amplification factor, defined as the peak-to-peak ratio of the poloidal spectra for the total field perturbation including the plasma response and the vacuum field alone, is about five for all n’s. The amplification, however, does not occur with the worst coil phasing for ELM control. This field amplification due to the high-pressure plasma response, together with the plasma screening of the resonant radial field components in the core region, have several consequences on the fast ion confinement in HL-2M during ELM control with RMP. (i) Three-dimensional fields including the plasma response, and with the best coil phasing, substantially enhance the distortion of fast ion orbits compared to the vacuum field approximation. With the n = 1 RMP, the plasma-response-induced enhancement of the orbit distortion reaches a factor of four when measured in terms of the canonical toroidal angular momentum. (ii) With the best coil phasing, the plasma response widens the stochastic region for the particle orbits on the Poincaré plane. (iii) The orbit islands, including the plasma response, remain as large as the vacuum counterparts in the plasma core where strong screening of the resonant field components occur. All these effects lead to enhanced fast ion transport (and loss) in the high-pressure HL-2M plasma, when the best RMP spectrum is applied to control ELMs.

The artificial neural networks (NNs) are trained, based on the numerical database, to predict the no-wall and ideal-wall βN limits, due to onset of the n = 1 (n is the toroidal mode number) ideal external kink instability, for the HL-2M tokamak. The database is constructed by toroidal computations utilizing both the equilibrium code CHEASE and the stability code MARS-F. The stability results show that (i) the plasma elongation generally enhances both βN limits, for either positive or negative triangularity plasmas; (ii) the effect is more pronounced for positive triangularity plasmas; (iii) the computed no-wall βN limit linearly scales with the plasma internal inductance, with the proportionality coefficient ranging between 1 and 5 for HL-2M; (iv) the no-wall limit substantially decreases with increasing pressure peaking factor. Furthermore, both the Neural Network (NN) model and the Convolutional Neural Networks model (CNN) are trained and tested, resulting in consistent results. The trained NNs predict both the no-wall and ideal-wall limits with as high as 95% accuracy, compared to those directly computed by the stability code. Additional test cases, produced by the Tokamak Simulation Code (TSC), also show reasonable performance of the trained NNs, with the relative error being within 10%. The constructed database provides effective references for the future HL-2M operations. The trained NNs can be used as a real-time monitor for disruption prevention in the HL-2M experiments, or serve as part of the integrated modeling tools for ideal kink stability analysis.

Externally applied resonant magnetic perturbations (RMPs), generated by magnetic coils located outside the plasma (referred to as RMP coils), provide an effective way to control the edge localized mode (ELM) in tokamak devices. Due to the discrete nature of toroidal distribution of these window-frame coils, toroidal sidebands always \bl{exist} together with the fundamental harmonic designed for ELM control. In this work, the MARS-F code (Liu\textit{ et al 2000 Phys. Plasmas} \textbf{7} 3681) is applied to investigate detailed features of the RMP spectra considering both the dominant harmonic (n=2) and the associated sideband (n=6), and the impact of the combinedfields on magnetic footprints as well as on the fast ion losses for a reference double-null scenario in the HL-2M device. It is found that the sum of the $n=2$ and $n=6$ RMP fields splits the footprint and widens the footprint area, as compared to the single-$n$ (n=2) harmonic case. Resistive plasma response breaks the up-down symmetry of the footprint pattern on the outer divertor plates, which is otherwise symmetric assuming vacuum RMP fields. Considering fast ion losses, a threshold value exists for the initially launched radial position of test particles as well as for the RMP coil current, before the loss occurs. As the threshold criterion is satisfied, the combined $n=2$ and $n=6$ RMP fields enhance the fast ion loss rate by $~20\%$, as compared to that of the $n=2$ component alone. These results illustrate the important role of the sideband of RMP fields on the magnetic footprints and fast ion losses in tokamak plasmas.

Transport and loss of beam injected energetic-particles (EPs) due to three-dimensional (3D) perturbations, associated with the external kink (XK) instability and fishbone-like mode (FLM), are numerically investigated utilizing the guiding center following code ORBIT for static toroidal plasmas in HL-2A. The perturbation structure for the XK is computed by the MARS-F code and then mapped to the Boozer coordinates as defined in ORBIT. The simulation shows that the EP profile experiences a significant change in the middle of the plasma column, when the XK-induced radial magnetic field perturbation amplitude, normalized by the equilibrium field, exceeds a threshold value of about 10−2. The EP transport is found to be dominated by a diffusion process instead of convection. Furthermore, by scanning the perturbation frequency as a free parameter while maintaining the XK mode structure (thus mimicking the FLM as observed in DIII-D and JT-60U tokamaks), redistribution and loss of EPs are found to be substantially enhanced due to strong resonances between the FLM and EPs, when the mode frequency exceeds a threshold value of ~2 kHz for the case considered. For either XK or FLM, the response of passing EPs to the perturbation is dominant due to the assumed tangential neutral beam injection. Most lost EPs due to these instabilities are initially passing particles but are eventually lost through trapped orbits.