Search

The divertor heat flux footprint is modeled for the HL-2A discharge, in the presence of the resonant magnetic perturbation (RMP) applied to control the edge-localized mode. Both the magnetic field lines and the guiding-center drift orbits of test thermal ions are traced, based on the computed plasma response to the RMP. Toroidal modeling identifies a reason—a vertical shift of the plasma separatrix—for the observed upper shift of the heat flux footprint during the initial phase of the RMP application in the experiment. While both the field-line tracing and particle orbit tracing replicate the experimental observation reasonably well, the latter approach is found to produce results that better align with the measured heat flux peaking along the divertor leg. A sensitivity investigation of the simulated footprint location and width against the assumed plasma response models—the conventional fluid model, the fluid model with strong parallel sound wave damping (SWD), and magnetohydrodynamic-kinetic hybrid mode—reveals that the fluid model with SWD yields the best agreement with the experiment, due to the fact that this model produces a stronger field response inside the plasma. These toroidal modeling results, while helping explain and interpret the experimental observations in HL-2A, provide physics insight to guide divertor footprint control via RMP in the future high-performance experiments in devices such as HL-3.

Nonlinear modeling of mitigation of the edge localized mode (ELM) with resonant magnetic perturbation (RMP) is performed for the HL-2A tokamak, utilizing the three-dimensional (3D) magnetohydrodynamic code JOREK. Based on the 3D equilibrium established after application of the $n = 1$ ( $n$ is the toroidal mode number) RMP at $4.9\,\,{\text{kAt}}$ coil current with odd parity, ELM mitigation is successfully simulated consistent with the experimental result. Nonlinear simulations show strong mode coupling among toroidal Fourier harmonics, allowing redistribution of the magnetic energy such that the most unstable toroidal mode saturates at a lower level. This magnetic energy cascade offers an explanation of the RMP-induced ELM mitigation achieved in HL-2A. Detailed examination of the simulation results shows persistent resonant field screening even during the ELM mitigation phase. Finite plasma resistivity however does enable partial penetration of the resonant field thus modifying the edge magnetic topology and characteristics of the edge transport. Plasma radial profiles undergo pronounced changes around the pedestal region, when the magnetic energy of the most unstable toroidal mode reaches the maximum value. Systematic scans of the applied RMP coil current with the JOREK simulations find a threshold value of around $4.5\,\,{\text{kAt}}$ required for achieving the ELM mitigation on HL-2A.

The n = 1 ( n is the toroidal mode number) resistive wall mode (RWM) stability is numerically investigated for two DIII-D high- β _N discharges 176440 and 172461, utilizing the MARS-F (Liu et al 2000 Phys. Plasmas 7 3681) and MARS-K (Liu et al 2008 Phys. Plasmas 15 112503) codes. Systematic validation efforts are attempted, for the first time, for discharges with very slow or vanishing toroidal flow for a large fraction of the plasma volume. While gaining physics insights in accessing stable operation regime at β _N exceeding the Troyon no-wall limit in these slow-rotation experiments, the predictive capability of fluid and non-perturbative magnetohydrodynamic-kinetic hybrid models for the RWM is further confirmed. The MARS-F fluid model, with a strong but numerically tunable viscosity mimicking ion Landau damping of parallel sound waves, finds complete stabilization of the n = 1 RWM in the considered DIII-D plasmas under the experimental flow conditions. Similarly, either full stabilization (for discharge 176440) or marginal stability (for discharge 172461) of the mode is computed by the MARS-K hybrid model, which is first-principle based without free model parameters. In particular, all drift kinetic resonances, including those of thermal and energetic particles, are found to synergistically act to marginally stabilize the RWM in discharge 172461. These MARS-F/K modeling results explain the experimentally observed stable operational regime in DIII-D, as far as the RWM stability is concerned. Extensive numerical sensitivity studies, with respect to the plasma toroidal flow speed as well as the radial location of the resistive wall, are also carried out to further support the validation study.

Since the first plasma realized in 2020, a series of key systems on HL-3 (known as HL-2M before) tokamak have been equipped/upgraded, including in-vessel components (the first wall, lower divertor, and toroidal cryogenic/water-cooling/baking/glow discharge systems, etc.), auxiliary heating system of 11 MW, and 28 diagnostic systems (to measure the plasma density, electron temperature, radiation, magnetic field, etc.). Magnet field systems were commissioned firstly for divertor plasma discharges. During the 2nd experimental campaign of HL-3 tokamak, several great progresses have been achieved. Firstly, the successful operation with plasma current larger than 1 MA was achieved under a divertor configuration. Secondly, the advanced divertor concept with two distinct snowflake configurations was realized. It is found that the distribution of ion saturation current and heat flux on bottom plate becomes wide due to magnetic surface expansion, demonstrating the advantage of such configuration in the heat flux mitigation. In addition, using the combination of NBI, ECRH and LHCD, the standard sawtoothing high confinement mode of megampere plasma was firstly accessed on the HL-3. The successful commissioning of HL-3 is beneficial for the initial operation of ITER.

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 the toroidal distribution of these window-frame coils, toroidal sidebands always exist together with the fundamental harmonics designed for ELM control. In this work, the MARS-F code (Liu et al 2000 Phys. Plasmas 7 3681) is applied to investigate the detailed features of the RMP spectra considering both the dominant harmonic ( n = 2) and the associated sideband ( n = 6), and the impact of the combined fields 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. The 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. When the threshold criterion is satisfied, the combined n = 2 and n = 6 RMP fields enhance the fast ion loss rate by ${\sim}20\%$ , 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.

Reduction of both the plasma density and toroidal flow speed, due to application of the predominantly n = 1 ( n is the toroidal mode number) resonant magnetic perturbation (RMP) for controlling the edge localized mode in the HL-2A tokamak, is numerically investigated utilizing the quasi-linear initial-value code MARS-Q (Liu et al 2013 Phys. Plasmas 20 042503). Simulation results reveal that the neoclassical toroidal viscosity (NTV) due to three dimensional fields plays the key role in modifying the plasma momentum and particle transport in the HL-2A discharge. By comparing the modeling results with the measured density pump-out in the experiment, the electron NTV particle flux model, in combination with the free-boundary condition for the axisymmetric change of the density at the plasma edge, is found to yield the best agreement in terms of both the pump-out level and the overall time scale. Further sensitivity studies show that the simulated density pump-out level is reasonably robust against variations in the model assumptions, including the particle diffusion model and the non-ambipolar versus ambipolar NTV particle flux. The latter however affects the time scale for reaching the steady state solution. Finally, it is found that the plasma edge-peeling response, the NTV torque, as well as the plasma momentum and particle transport, all are sensitive to the toroidal phase difference between the upper and lower rows of the RMP coil currents in HL-2A, with the 30 ^∘ coil phasing producing the minimal side effects on the plasma.

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 2000 Phys. Plasmas 7 3681) 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 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.