A hybrid spectral/finite-element code is developed to numerically solve the resistive finite-pressure magneto-hydrodynamic equilibria without the necessity of postulating nested magnetic flux surfaces in the nonaxisymmetric toroidal systems. The adopted approach integrates a hyperbolic parallel damping equation for pressure updating, along with a dynamic resistive relaxation for magnetic field. To address the non-axisymmetry in toroidal geometry, a pseudo flux mapping is employed to relate the axisymmetric computational domain to the physical domain. On the computational mesh, an isoparametric C1-continuous triangular element is utilized to discretize the poloidal plane, which is complemented with a Fourier decomposition in the toroidal direction. The versatility of the code is demonstrated through its application to several different non-axisymmetric toroidal systems, including the inherently three-dimensional equilibria in stellarators, the helical-core equilibrium states in tokamak plasmas, and the quasi-single-helicity states in a reversed-field pinch.

A critical challenge for operating fusion burning plasma in high-confinement mode lies in mitigating damage caused by edge-localized modes (ELMs). While impurity seeding has been experimentally validated as a reliable and effective ELM mitigation technique, its underlying physics remains insufficiently understood and requires further clarification. Through nonlinear magnetohydrodynamic simulations, this work reproduces key features of a natural ELM crash and reveals its trigger mechanism. Impurity seeding significantly affects nonlinear ELM dynamics by inducing local and global modifications to the pedestal pressure profile, driving high-n ballooning mode instabilities that govern an ELM crash. Two critical control parameters-impurity density level and poloidal seeding location-are systematically investigated, which play key roles in the timing of ELM crash onset and the resulting energy loss magnitude.

High plasma density operation is crucial for a tokamak to achieve energy breakeven and burning plasma. However, there is often an empirical upper limit of electron density in tokamak operation, namely, the Greenwald density limit nG, above which tokamaks generally disrupt. Achieving high-density operation above the density limit has been a long-standing challenge in magnetic confinement fusion research. Here, we report experimental results on the Experimental Advanced Superconducting Tokamak (EAST) achieving line-averaged electron density in the range of (1.3 to 1.65) nG, significantly above the typical EAST operational range of (0.8 to 1.0) nG. This is performed with electron cyclotron resonance heating (ECRH)-assisted ohmic start-up and sufficiently high initial neutral density. These experiments are shown to operate in the density-free regime first predicted by a recent plasma-wall self-organization theory. These results suggest a promising scheme for substantially increasing the density limit in tokamaks, a critical advancement toward achieving burning plasma.

Effects of reversed magnetic shear on the plasma rotation stabilization of resistive wall modes (RWMs) in tokamaks are investigated using the AEGIS code. magnetohydrodynamic equilibria in toroidal configuration from circular cross-sections to realistic China Fusion Engineering Test Reactor (CFETR)-like scenarios with various magnetic shear profiles are considered. Two critical aspects of the n = 1 RWM are examined: the influence of toroidal rotation on the RWM-unstable beta N range and the toroidal rotation frequency thresholds required for complete stabilization. It is found that strongly reversed magnetic shear consistently broadens the RWM-unstable beta N range in both circular and CFETR equilibria when toroidal rotation is included. Furthermore, reversed magnetic shear significantly reduces the rotational stabilization, resulting in narrower wall-stabilization window width and notably higher toroidal rotation frequency thresholds required for complete RWM suppression compared to the cases with positive shear only. These results clearly demonstrate that the reversed magnetic shear in the advanced tokamak configuration imposes more stringent requirements for the effective toroidal rotation stabilization of the n = 1 RWM.

The nonlinear evolution of the tilt instability in a field reversed configuration (FRC) during the dynamic magnetic compression process has been investigated using magnetohydrodynamic simulations with the NIMROD code (Sovinec et al 2004 J. Comput. Phys. 195 355). The tilt mode induces significant deformations in the linear growth phase and results in complete confinement loss of the FRC in the nonlinear phase, with no evidence of dynamic nonlinear stabilization. The growth rate of the tilt mode increases with the compression field ramping rate and approaches an asymptotic value. Toroidal flow can reduce both the growth rate and the nonlinear saturation amplitude of the tilt mode. The stabilizing effect of the toroidal rotation is enhanced with higher compression field ramping rates due to the spontaneous toroidal field generation and increased flow shear during compression. Although the tilt mode remains unstable with a toroidal rotation Mach number close to 0.5, the onset of tilt distortion can be delayed, allowing a magnetic compression ratio up to 5.3 before the compressional heating terminates.

The formation of a quasi-single helicity (QSH) state from a paramagnetic pinch in the Keda Torus eXperiment-reverse field pinch (KTX-RFP) regime has been observed in recent NIMROD simulations. The quasi-single helicity state has a dominant helical component of the magnetic field that is known to improve the RFP confinement. For the initial paramagnetic pinch, linear calculations indicate that the tearing mode growth rate decreases with the plasma beta . The initial QSH state arises from the dominant linear instability of the initial force-free paramagnetic pinch. The plasma's self-organization toward the second QSH state after the relaxation of the initial QSH state is found to depend on beta . Specifically, when beta < 4 % , the plasma relaxes to an MH state; when 4 % <= beta <= 8 % , the plasma first transitions from a double axis (DAx) to a single helical axis (SHAx) state, and eventually returns to the DAx state. Whereas in our simulation setup, the implicitly introduced source of the induced electric field likely differs significantly from those in actual QSH experiments, the demonstrated existence of such an optimal beta regime in our simulations that is beneficial to the formation and maintenance of the QSH state, suggests an experimental scheme for the QSH formation based on beta tuning and control. (c) 2025 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license.

The physics of neoclassical tearing modes (NTMs) is of great concern to tokamak plasma stability and performance, especially in the burning plasma regime. Whereas in many situations the seed events can be clearly identified, such as sawteeth and edge localized modes, the potential seeding mechanism of NTMs due to the resistive tearing instability driven by the impurity radiation cooling still needs more study. Recent NIMROD simulations have demonstrated that local impurity radiation cooling can drive the seed island growth and trigger the subsequent onset of NTM instability. The seed island is mainly driven by the local helical perturbation of the diamagnetic current induced by the perturbed pressure gradient as a result of the impurity radiative cooling on the rational surface. A heuristic closure for the neoclassical viscosity is adopted, and the seed island is further driven by the perturbed bootstrap current induced from the neoclassical electron viscous stress in the extended Ohm's law. The growth rate of the NTM in simulations is found proportional to the electron neoclassical viscosity, and a theoretical neoclassical driving term is adopted to account for the nonlinear neoclassical island growth in the simulations.

The density limit is one of the major obstacles to achieving the desired fusion performance in tokamaks. However, the underlying physics mechanism for its recently observed power dependence in experiments has not been well understood or predicted in theory. In this work, we derive the power-dependent scaling of the density limit from the plasma-wall self-organization (PWSO) theory [DF. Escande 2022 NF] for the first time. These newly derived scalings successfully match the experimentally observed power dependence of density limits in multiple tokamak devices, such as ASDEX-U and W7-AS, confirming the validity of the PWSO theory. Critically influencing factors are identified as plasma-wall sputtering and particle confinement time. In addition, the effects of nonsputtered impurities and fusion products are evaluated, and the refined PWSO-density limit model is extended to the burning plasma regime to predict the conditions necessary for entering the burning plasma. © 2025 IOP Publishing Ltd. All rights, including for text and data mining, AI training, and similar technologies, are reserved.

The scaling laws for the magnetic compression of a toroidally rotating field reversed configuration (FRC) have been investigated in this work. The magnetohydrodynamics (MHD) simulations of the magnetic compression on rotating FRCs employing the NIMROD code (Sovinec et al 2004 J. Comput. Phys. 195 355), are compared with the Spencer's one-dimensional (1D) theory (Spencer et al 1983 Phys. Fluids 26 1564) for a wide range of initial flow speeds and profiles. The toroidal flow can influence the scalings directly through the alteration of the compressional work as also evidenced in the 1D adiabatic model, and indirectly by reshaping the initial equilibrium. However, in comparison to the static initial FRC equilibrium cases, the pressure and the radius scalings remain invariant for the magnetic compression ratio Bw2/Bw1 up to 6 in presence of the initial equilibrium flow, suggesting a broader applicable regime of the Spencer scaling law for FRC magnetic compression. The invariant scaling has been proven a natural consequence of the conservation of angular momentum of both fluid and magnetic field during the dynamic compression process.

Plasma differential rotation is found to be capable of preventing disruptive neoclassical tearing modes (NTMs) seeded by nonlinear three-wave coupling. As tearing modes degrade confinement and can lead to disruptions, stabilization strategies are crucial to the successful operation of future devices. In ITER-relevant scenarios on DIII-D, rotationally coupled m/n = 1/1 and 3/2 modes have been observed to drive 2/1 islands through three-wave coupling. The frequency of the driven 2/1 mode is set by matching conditions and the frequencies of the driving modes. When the driven mode frequency matches the local plasma rotation frequency, e.g. at low differential rotation, the driven 2/1 island can grow into a disruptive NTM. Using neutral beam torque as an actuator to scan the differential rotation, these experiments demonstrate that a sufficiently large frequency mismatch prevents destabilization of disruptive 2/1 NTMs by three-wave coupling. This work indicates that differential rotation can be used as an actuator to prevent NTMs seeded by three-wave coupling.