Haowei Zhang

During tokamak disruptions, the Ohmic current may be replaced by a non-inductive runaway electron (RE) current, affecting resistive stability. Previous analytical and numerical studies suggest that, in the linear phase, the presence of REs acts destabilizing for tearing modes (TMs) compared to a scenario with Ohmic current. In the non-linear regime, this translates to larger saturation amplitudes; in particular, for small Δ ′ , the saturated TM island width is approximately 1.5 times larger than that in the corresponding Ohmic scenario. These results, however, are based on the assumption of zero drift orbit deviation from the magnetic flux surfaces, which corresponds to the low RE energy limit. This work investigates the importance of this kinetic effect, i.e. linear and non-linear TM dynamics are studied in RE beams with different RE energies, providing a clear picture of the finite-orbit-width (FOW) effects. We use a hybrid fluid-kinetic model in the 3D non-linear magnetohydrodynamic (MHD) code JOREK, treating REs kinetically with a full-f Monte-Carlo approach in self-consistent interaction with the MHD mode dynamics. The study shows that the presence of REs modifies the characteristics of the instability in several ways. Firstly, we find that the major-radial displacement of drift orbits from flux surfaces induces an m = 1 perturbation to the equilibrium current introducing additional mode coupling of m,n instabilities with m ± 1 , n modes, where m and n refer to the poloidal and toroidal mode numbers, respectively. Secondly, we find that increasing RE energy has a stabilizing effect on the MHD modes since REs cannot support narrow current sheets on rational flux surfaces due to the drift orbit displacements, reducing both the linear growth rate and the non-linear saturation level. This counteracts the destabilizing effect that REs have on TMs in the low energy limit. For the scenario investigated, the stabilizing effects dominate over the additional mode coupling such that the development of stochastic magnetic regions is reduced with increasing RE energies, leading to lower radial particle transport. Overall, our findings indicate that FOW effects can substantially alter MHD stability and non-linear dynamics of RE beams.

Flux pumping was achieved in recent hybrid scenario experiments in the ASDEX Upgrade (AUG) tokamak, which is characterized by a sawtooth-free helical quiescent state and the anomalous radial redistribution of toroidal current density and poloidal magnetic flux. In this article, the self-regulation mechanism of the AUG core plasma during flux pumping is investigated at realistic parameters using the JOREK code based on the two-temperature, nonlinear, full magnetohydrodynamic (MHD) model. A key milestone in AUG flux pumping modelling is achieved by quantitatively reproducing the clamped current density and safety factor profiles in the plasma core, demonstrating the effectiveness of the dynamo effect in sustaining the flux pumping state. The dynamo term, which is of particular interest, is primarily generated by the pressure-gradient-driven m/n = 1/1 quasi-interchange-like MHD instability. The work systematically extrapolates the parameter regimes of flux pumping from the above AUG base case by scanning dissipation coefficients and plasma beta. The simulation results reveal bifurcated plasma behaviours at different Hartmann numbers, including distinct states such as flux pumping (helical core with a flat current density), sawteeth (periodic kink-cycling), single crash (without subsequent cycle), and quasi-stationary magnetic island (peaked current density). Transitions from marginal flux-pumping state to sawteeth in long-term simulations are observed and analyzed. The relationships between system dissipation, plasma beta, and different plasma states are carefully analyzed. For practical purposes, the potential operational window for flux pumping, as determined by plasma density and temperature, is estimated. The modelling efforts advance the understanding of flux pumping and facilitate the development of a fast surrogate model for efficient evaluation of flux pumping.

Transient phenomena and their control are of high relevance in magnetic confinement fusion plasmas to guarantee a stable and safe plasma operation. Interpretative simulations can maximize the insights gained from experiments on present machines and predictive simulations can help in the preparation of design, mitigation techniques and operational scenarios for future devices. In this article, we provide an overview of recent advances and novel scientific results obtained with the 3D non-linear hybrid fluid-kinetic code JOREK, covering physics of plasma transients from the core to the scrape-off layer (SOL) both for tokamak and stellarator devices. Substantial progress was made in the physics understanding, model validation with experiments and experiment interpretation, thus, giving confidence for predictions to devices like DTT, ITER and DEMO. The topics addressed comprise a wide range: the edge physics of new operation scenarios and edge localized mode suppression; major disruptions with a focus on runaway electrons and vertical displacement events as well as disruption mitigation by shattered pellet injection; the physics mechanisms and operational limits of the flux pumping regime for sawtooth control; MHD limits of stellarators and work towards incorporating advanced edge/SOL/exhaust dynamics; continuing improvements of the code for more efficient hybrid simulations on conventional and accelerated high performance computing architectures.

Accurate modeling of core instabilities in tokamak plasmas is essential to understand the underlying physical mechanisms and their impact on plasma confinement. The ideal stability of the internal kink mode and the m=1 collisionless tearing mode are analyzed numerically both with gyrokinetic and magnetohydrodynamic (MHD) codes. The simulation results show that the stability of the internal kink mode strongly depends on the choice of several setup parameters like the inclusion of parallel magnetic field fluctuations, the tokamak aspect ratio, the drift kinetic or gyrokinetic treatment of the ions, and the electron mass. Furthermore, we demonstrate the stabilization of the instabilities by diamagnetic effects. Our results indicate that gyrokinetic and MHD models can be reconciled in the description of the internal kink mode by careful consideration of the simulation setup and model assumptions, but instabilities like the collisionless tearing mode require a more advanced treatment beyond MHD.

Flux pumping was achieved in recent hybrid scenario experiments in the ASDEX Upgrade (AUG) tokamak, which is characterized by a sawtooth-free helical quiescent state and the anomalous radial redistribution of toroidal current density and poloidal magnetic flux. In this article, the self-regulation mechanism of the AUG core plasma during flux pumping is investigated at realistic parameters using the JOREK code based on the two-temperature, nonlinear, full magnetohydrodynamic (MHD) model. A key milestone in AUG flux pumping modelling is achieved by quantitatively reproducing the clamped current density and safety factor profiles in the plasma core, demonstrating the effectiveness of the dynamo effect in sustaining the flux pumping state. The dynamo term, that is of particular interest, is primarily generated by the pressure-gradient driven m/n = 1/1 quasi-interchange-like MHD instability. The work systematically extrapolates the parameter regimes of flux pumping from the above AUG base case by scanning dissipation coefficients and plasma beta. The simulation results reveal bifurcated plasma behaviours at different Hartmann numbers, including distinct states such as flux pumping (helical core with a flat current density), sawteeth (periodic kink-cycling), single crash (without subsequent cycle), and quasi-stationary magnetic island (peaked current density). Transitions from marginal flux pumping state to sawteeth are observed in long-term simulations. The relationships between system dissipation, plasma beta, and different plasma states are carefully analyzed. For practical purposes, the potential operational window for flux pumping, as determined by plasma density and temperature, is estimated. The modelling efforts advance the understanding of flux pumping and facilitate the development of a fast surrogate model for efficient evaluation of flux pumping.

Sawtooth oscillations, driven by internal kink modes (IKMs), are fundamental phenomena in tokamak plasmas. They can be classified into different types, including normal sawteeth, small sawteeth, and in some cases, evolving into the steady-island state, each having a different impact on energy confinement in fusion reactors. This study investigates the interaction between sawtooth oscillations and energetic particles (EPs) using the initial-value MHD-kinetic hybrid code CLT-K, which can perform long-term self-consistent nonlinear simulations. We analyze the redistribution of EPs caused by sawtooth crashes and the effect of EPs on sawtooth behavior and type transitions. The results show that co-passing EPs tend to re-excite sawtooth oscillations, extending their period, while counter-passing EPs promote the system evolution toward small sawteeth, potentially leading to the steady-island state. Additionally, we provide a physical picture of how EPs influence sawtooth type through the mechanism of magnetic flux pumping. We demonstrate that the radial residual flow in the core plays a crucial role in determining the reconnection rate and sawtooth type. Quantitatively, the residual flow generates a convective dynamo electromotive force (EMF) that prevents the accumulation of central current density and poloidal magnetic flux, thereby favoring the formation of small sawteeth or a steady state. Moreover, we observe new phenomena about couplings of various instabilities, such as the excitation of global multi-mode toroidal Alfvén eigenmodes (TAEs) due to EP redistribution following a sawtooth crash and the excitation of the resonant tearing mode (r-TM) after the core enters a sawtooth-free steady state when injecting counter-passing EPs. The study also explores the impact of EP energy and the safety factor profile on the development of stochastic magnetic fields and EP transport. These findings emphasize the necessity of multi-mode simulations in capturing the complexity of EP-sawtooth interactions and provide insights for optimizing sawtooth control in future reactors such as ITER.

The electron inertia and the off‐diagonal electron pressure terms are well‐known for the frozen‐in condition breakdown in collisionless magnetic reconnection, which are naturally kinetic and difficult to employ in magnetohydrodynamic (MHD) simulations. Considering the limitations of MHD and Hall MHD in neglecting the important electron dynamics such as the inertia and the nongyrotropic pressure, the kinetic characteristics of electrons and ions in the diffusion region are studied and an effective resistivity model involving dynamics of charged particles is proposed (Ma et al. 2018, https://doi.org/10.1038/s41598‐018‐28851‐7 Sci. Rep. 8 10521), where the guide field is omitted to simplify the model by primarily considering the out‐of‐plane velocity of charged particles and the in‐plane reconnecting field. The amplitude of the effective resistivity is mainly determined by electrons in most realistic situations with large ion‐electron mass ratios. In this work, the effective resistivity model for collisionless magnetic reconnection is successfully applied in the 2.5D MHD and Hall MHD simulations, which remarkably improves the simulation results compared with traditional MHD models. For the MHD case, the effective resistivity significantly increases the reconnection rate to a reasonable value of . For the Hall MHD case with effective resistivity, the peak reconnection rate is , and the major structures of the reconnecting field and the current sheet agree well with the particle‐in‐cell (PIC) simulations. Meanwhile, a more general effective resistivity model incorporating guide field corrections for MHD simulations is under development.

The electron inertia and the off-diagonal electron pressure terms are well-known for the frozen-in condition breakdown in collisionless magnetic reconnection, which are naturally kinetic and difficult to employ in magnetohydrodynamic (MHD) simulations. Considering the limitations of MHD and Hall MHD in neglecting the important electron dynamics such as the inertia and the nongyrotropic pressure, the kinetic characteristics of electrons and ions in the diffusion region are studied and an effective resistivity model involving dynamics of charged particles is proposed (Ma et al. 2018 Sci. Rep. 8 10521), where the guide field is omitted to simplify the model by primarily considering the out-of-plane velocity of charged particles and the in-plane reconnecting field. The amplitude of the effective resistivity is mainly determined by electrons in most realistic situations with large ion-electron mass ratios. In this work, the effective resistivity model for collisionless magnetic reconnection is successfully applied in the 2.5D MHD and Hall MHD simulations, which remarkably improves the simulation results compared with traditional MHD models. For the MHD case, the effective resistivity significantly increases the reconnection rate to a reasonable value of ∼0.1B0vA. For the Hall MHD case with effective resistivity, the peak reconnection rate is ∼0.25B0vA, and the major structures of the reconnecting field and the current sheet agree well with the particle-in-cell (PIC) simulations. Meanwhile, a more general effective resistivity model incorporating guide field corrections for MHD simulations is under development.