Instabilities In Tokamaks Research Articles

Prediction of fishbone linear instability in tokamaks with machine learning methods

Abstract A machine learning based surrogate model for fishbone linear instability in tokamaks is constructed. Hybrid simulations with the kinetic-magnetohydrodynamic (MHD) code M3D-K is used to generate the database of fishbone linear instability, through scanning the four key parameters which are thought to determine the fishbone physics. The four key parameters include (1) central total beta of both thermal plasma and fast ions, (2) the fast ion pressure fraction, (3) central value of safety factor q and (4) the radius of q = 1 surface. Four machine learning methods including linear regression, support vector machines (SVM) with linear kernel, SVM with nonlinear kernel and multi-layer perceptron are used to predict the fishbone instability, growth rate and real frequency, mode structure respectively. Among the four methods, SVM with nonlinear kernel performs very well to predict the linear instability with accuracy ≈ 95 % , growth rate and real frequency with R 2 ≈ 98 % , mode structure with R 2 ≈ 98 % .

Verification of electromagnetic simulation capabilities in global gyrokinetic particle-in-cell code GTS

Recently, the numerical scheme presented by Mishchenko et al. [Phys. Plasmas 21, 052113 (2014); 21, 092110 (2014)] enabled explicit gyrokinetic simulations of low-frequency electromagnetic instabilities in tokamaks at experimentally relevant values of plasma β. This scheme resolved the long-standing cancellation problem that previously hindered gyrokinetic particle-in-cell code simulations of magnetohydrodynamic phenomena with inherently small parallel electric fields. Moreover, the scheme did not employ approximations that eliminate critical tearing-type instabilities. Here, we report on the implementation of this numerical scheme in the global gyrokinetic particle-in-cell code GTS. This implementation allows for a more complete and accurate picture of interaction between small scale turbulence and MHD modes in tokamaks. Additionally, we present a comprehensive set of verification simulations of numerous electromagnetic instabilities relevant to present-day tokamaks. These simulations encompass the kinetic ballooning mode, the internal kink mode, the tearing mode, the micro-tearing mode, and the toroidal Alfven eigenmode destabilized by energetic ions, which are all instrumental in understanding tokamak physics. We will also showcase the preliminary nonlinear simulations of kinetic ballooning instabilities and (2,1) island formation due to tearing mode instability. These simulations validate the accuracy of the scheme implementation and pave the way for studying how these instabilities affect plasma confinement and performance.

Global gyrokinetic study of density gradient driven instability in tokamaks: the ubiquitous mode

The ubiquitous mode is investigated in the linear regime for the first time using a global gyrokinetic model. These modes are driven by the density gradient in trapped electron population but with mode frequency in the ion diamagnetic drift direction, in contrast to the conventional trapped electron mode. The dispersion relation is calculated along with the global mode structure. The ubiquitous mode is quite global although appears at a shorter wavelength ( 12ky2ρi2>1 ). We show that the main driving mechanism is the density gradient and the temperature gradient has only a modest effect; the mode can persist at higher temperature gradient scenarios making it another possible channel of anomalous transport. The magnetic shear reduces the growth of the mode; while the electron to ion temperature ratio has a nonmonotonic effect on the mode growth rate—growth rate increases initially for the ubiquitous branch of the mode and decreases afterwards as the conventional trapped electron mode starts dominating. The role of safety factor and toroidicity is also analyzed. Finally, a mixing length-based estimation of transport is presented.

Gyrokinetic Particle-in-Cell simulation of the effect of compressional magnetic perturbations on the microscopic instabilities in Tokamak

The compressional magnetic component δB|| has been implemented in the gyrokinetic Particle-in-Cell (PIC) code GEM for the fully electromagnetic simulation of microscopic instabilities in high-β tokamak plasmas. The simulation model is formulated for the split-weight scheme that is based on the canonical momentum formulation of the gyrokinetic equation. A pseudo-spectral method is used to solve the coupled gyrokinetic field equations while preserving all finite-Larmor-radius (FLR) effects. The algorithm is verified by the method of manufactured solutions. Simulations of the ion-temperature-gradient-driven (ITG) mode, the kinetic balloon mode (KBM) and the trapped electron mode (TEM) are presented.

Shifting and Splitting of Resonance Lines due to Dynamical Friction in Plasmas.

A quasilinear plasma transport theory that incorporates Fokker-Planck dynamical friction (drag) and pitch angle scattering is self-consistently derived from first principles for an isolated, marginally unstable mode resonating with an energetic minority species. It is found that drag fundamentally changes the structure of the wave-particle resonance, breaking its symmetry and leading to the shifting and splitting of resonance lines. In contrast, scattering broadens the resonance in a symmetric fashion. Comparison with fully nonlinear simulations shows that the proposed quasilinear system preserves the exact instability saturation amplitude and the corresponding particle redistribution of the fully nonlinear theory. Even in situations in which drag leads to a relatively small resonance shift, it still underpins major changes in the redistribution of resonant particles. This novel influence of drag is equally important in plasmas and gravitational systems. In fusion plasmas, the effects are especially pronounced for fast-ion-driven instabilities in tokamaks with low aspect ratio or negative triangularity, as evidenced by past observations. The same theory directly maps to the resonant dynamics of the rotating galactic bar and massive bodies in its orbit, providing new techniques for analyzing galactic dynamics.

Ideal conductive wall and magnetohydrodynamic instability in Tokamak

In order to explore the conductive wall effect of plasma magnetohydrodynamic (MHD) instability and the wall designing idea, the various forms of ideal conductive walls based on divertor equilibrium configurations in the HL-2A Tokamak and their role in suppressing kink modes are studied. The MHD instabilities and the ideal MHD operational <i>β</i> limits under free boundary or ideal wall conditions are compared. In the stability calculation, <i>n</i> = 1 kink mode is considered, which has a decisive influence on the MHD instability of Tokamak plasma. The research focuses on verifying the effectiveness of various shapes of conductive walls in suppressing internal and external kink modes, and observing the operational <i>β</i> limit changes, and discussing and analyzing related physics. It is found that an ideal conducting wall placed at a suitable distance from the plasma can effectively suppress the external kink modes. Under the condition that the average distance between the wall and the plasma surface is the same and small enough, the circular cross-section wall is not necessarily the best option. Setting an optimized polygonal conductive wall can more effectively suppress the MHD instability. It makes the ideal MHD operational <i>β</i> limit of the device, <i>β</i><sub><i>N</i></sub>, increase to 2.73, which is about 6.5% higher than that for the device with a wall assumed to be set at infinity (<inline-formula><tex-math id="Z-20230129122243-1">\begin{document}$ \sim $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20222043_Z-20230129122243-1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20222043_Z-20230129122243-1.png"/></alternatives></inline-formula>2.56). This implies that it is necessary to optimize and make a polygonal conductive wall as close as possible to the average distance from the plasma surface according to the poloidal-section shape of the elongated and shaped plasma, so as to achieve the suppression of external kink mode and increase the operational <i>β</i> limits. The physical mechanism of the stabilizing effect of the ideal wall on external kink modes is analyzed. With the development of the kink mode, when the plasma column is twisted closely to the wall, the plasma column will squeeze the magnetic field in the vacuum area, making the magnetic field line compressed and bent. At this time, the magnetic pressure and the component force of the magnetic tension in the opposite direction of the radial direction push the plasma back, thus stabilizing the kink mode. Finally, a conclusion is given.

Modeling of saturated external MHD instabilities in tokamaks: A comparison of 3D free boundary equilibria and nonlinear stability calculations

3D free boundary equilibrium computations have recently been used to model external kinks and edge harmonic oscillations (EHOs), comparing with linear MHD stability codes, and nonlinear analytic theory [Kleiner et al., Phys. Plasma Controlled Fusion 61, 084005 (2019)]. In this study, results of the VMEC equilibrium code are compared further with nonlinear reduced MHD simulations, using the JOREK code. The purpose of this investigation was to understand the extent to which the modeling approaches agree, and identify the important physical effects, which can modify the dynamics. For the simulated external kink, which is dominated by a single toroidal harmonic, good agreement is found when a large Lundquist number is used in the JOREK simulation, such that resistive effects are sub-dominant. Modeling EHOs where multiple toroidal harmonics are linearly unstable, the saturated perturbation observed can differ in the dominant toroidal harmonic. On the ideal timescale, a n = 2 EHO is observed in JOREK, while the saturated perturbation predicted by VMEC is a n = 1 mode. Extending simulations into timescales where resistive effects can play a role, similar n = 1 perturbations can be found. The coupling of different linearly unstable toroidal harmonics in the JOREK simulation broadens the magnetic energy spectrum and ergodises the plasma edge region, resulting in a more localized pressure perturbation. These effects are not observed in VMEC, because closed magnetic flux surfaces are enforced. Despite the sensitivity of JOREK results on the assumed resistivity, saturated states can be found using both approaches that are in reasonable agreement, even for this more advanced case.

Verification and validation of linear gyrokinetic and kinetic-MHD simulations for internal kink instability in DIII-D tokamak

Verification and linear validation of the internal kink instability in tokamak have been performed for both gyrokinetic (GTC) and kinetic-MHD codes (GAM-solver, M3D-C1-K, NOVA, XTOR-K). Using realistic magnetic geometry and plasma profiles from the same equilibrium reconstruction of the DIII-D shot #141216, these codes exhibit excellent agreement for the growth rate and mode structure of the internal kink mode when all kinetic effects are suppressed. The simulated radial mode structures, obtained from linear simulations, are in reasonable agreement with the normalised electron cyclotron emission measurement after adjusting, within the experimental uncertainty, the safety factor q = 1 flux-surface location in the equilibrium reconstruction. Compressible magnetic perturbations strongly destabilize the kink, while poloidal variations of the equilibrium current density reduce the growth rate of the kink. Furthermore, kinetic effects of thermal ions are found to decrease the kink growth rate in kinetic-MHD simulations, but increase the kink growth rate in gyrokinetic simulations, due to the additional drive of the ion temperature gradient and parallel electric field. Kinetic thermal electrons are found to have negligible effects on the internal kink instability.

Two-dimensional gyrokinetic integral eigenmode equation for drift instabilities in tokamak

Based on the Vlasov equation, a set of two-dimensional gyrokinetic integral eigenmode equations for drift instabilities in tokamak plasmas is derived. All kinetic effects of ions, including transience parallel to the magnetic field, drifts induced by the curvature and gradient of the magnetic field, and drifts induced by the equilibrium electric potential, and the effects of finite Larmor radius are taken into account. Not only the radial structure but also the poloidal structure of the modes as well as coupling of neighboring poloidal modes induced by toroidicity of the magnetic field can be obtained from these equations. This is an alternative to ballooning mode representation treatment, which can give mode structures along magnetic field lines only. The equations provide a theoretical base for relevant numerical simulation investigations.

Influence of Off-Axis Neutral Beam Injection on Resistive Wall Mode Stability

Investigated are the effects of energetic particles (EPs), arising from off-axis neutral beam injection, on the resistive wall mode (RWM) instability in tokamaks. The analytic results for a cylindrical plasma show that EPs contribute the strongest kinetic damping to the RWM, as the deposition radius approaches the peak location of the mode eigenfunction. Toroidal computations are also carried out utilizing the MARS-K code, which includes EPs with anisotropic equilibrium distribution in the particle pitch angle space. These self-consistent numerical results confirm the analytic finding, that the RWM growth rate decreases as the peak of the EPs’ radial density profile approaches the maximum of the mode displacement. This study thus demonstrates the possibility of the RWM stabilization by the off-axis neutral beam injection in tokamak experiments.

Magnetic reconnection and thermal equilibration

When a magnetic field is forced to evolve on a time scale τev, as by footpoint motions driving the solar corona or non-axisymmetric instabilities in tokamaks, the magnetic field lines undergo large-scale changes in topology on a time scale approximately an order of magnitude longer than τev. But the physics that allows such changes operates on a time scale eight or more orders of magnitude slower. An analogous phenomenon occurs in air. Temperature equilibration occurs on a time scale approximately an order of magnitude longer than it takes air to cross a room, τev, although the physical mechanism that allows temperature equilibration is approximately four orders of magnitude slower than τev. The use of Lagrangian coordinates allows the fundamental equations to be solved and both phenomena explained. The theories of thermal equilibration and magnetic reconnection are developed in parallel to help readers obtain an understanding of the importance and implications of analyses using Lagrangian coordinates.

Extended full-MHD simulation of non-linear instabilities in tokamak plasmas

Non-linear magnetohydrodynamic (MHD) simulations play an essential role in active research and understanding of tokamak plasmas for the realization of a fusion power plant. The development of MHD codes such as JOREK is a key aspect of this research effort. In this paper, we present an operational version of the full-MHD model implemented in JOREK, a significant advancement from the reduced-MHD model used for previous studies, where assumptions were made on the perpendicular dynamics and the toroidal magnetic field. The final model is presented in detail, and benchmarks are performed using both linear and non-linear simulations, including comparisons between the new full-MHD model of JOREK and the previously extensively studied reduced-MHD model, as well as results from the linear full-MHD code CASTOR3D. For the cases presented, this new JOREK full-MHD model is numerically and physically reliable, even without the use of numerical stabilization methods. Non-linear modeling results of typical tokamak instabilities are presented, including disruption and edge-localized-mode physics, most relevant to current open issues concerning future tokamaks such as ITER and DEMO.

Gyrokinetic investigation of the damping channels of Alfvén modes in ASDEX Upgrade

The linear destabilization and nonlinear saturation of energetic-particle driven Alfvénic instabilities in tokamaks strongly depend on the damping channels. In this work, the collisionless damping mechanisms of Alfvénic modes are investigated within a gyrokinetic framework by means of global simulations with the particle-in-cell code ORB5 and compared with the eigenvalue code LIGKA and reduced models. In particular, the continuum damping and the Landau damping (of ions and electrons) are considered. The electron Landau damping is found to be dominant compared to the ion Landau damping for experimentally relevant cases. As an application, the linear and nonlinear dynamics of toroidicity induced Alfvén eigenmodes and energetic-particle driven modes in ASDEX Upgrade is investigated theoretically and compared with experimental measurements.

3D extended magnetohydrodynamic simulations lead to new sawtooth phenomena theory

Computational advancements lead to a new theory on the sawtooth phenomena, paving the way for a predictive model of tokamak instabilities.

Acceleration of three-dimensional Tokamak magnetohydrodynamical code with graphics processing unit and OpenACC heterogeneous parallel programming

ABSTRACTIn this paper, the OpenACC heterogeneous parallel programming model is successfully applied to modification and acceleration of the three-dimensional Tokamak magnetohydrodynamical code (CLT). Through combination of OpenACC and MPI technologies, CLT is further parallelised by using multiple-GPUs. Significant speedup ratios are achieved on NVIDIA TITAN Xp and TITAN V GPUs, respectively, with very few modifications of CLT. Furthermore, the validity of the double precision calculations on the above-mentioned two graphics cards has also been strictly verified with m/n = 2/1 resistive tearing mode instability in Tokamak.

First principles gyrokinetic analysis of electromagnetic plasma instabilities

A two-fold analysis of electromagnetic core tokamak instabilities in the framework of the gyrokinetic theory is presented. First principle theoretical foundations of the gyrokinetic theory are used to explain and justify the numerical results obtained with the global electromagnetic particle-in-cell code Orb5 whose model is derived from the Lagrangian formalism. The energy conservation law corresponding to the Orb5 model is derived from the Noether theorem and implemented in the code as a diagnostics for energy balance and conservation verification. An additional Noether theorem based diagnostics is implemented in order to analyse destabilising mechanisms for the electrostatic and the electromagnetic ion temperature gradient instabilities in the core region of the tokamak. The transition towards the Kinetic Ballooning Modes at high electromagnetic β is also investigated.

Analysis of runaway electron expulsion during tokamak instabilities detected by a single-channel Cherenkov probe in FTU

The expulsion of runaway electrons (REs) during different types of tokamak instabilities is analysed by means of a Cherenkov probe inserted into the scrape-off layer of the FTU tokamak. One such type of instability, the well-known tearing mode, is involved in disruptive plasma termination events, during which the risk of RE avalanche multiplication is highest. The second type, known as anomalous Doppler instability, influences RE dynamics by enhancing pitch angle scattering. Three scenarios are analysed here, characterised by different RE generation rates and mechanisms. The main conclusions are drawn from correlations between the Cherenkov probe and other diagnostics. In particular, the Cherenkov probe permits the detection of fast electron expulsion with a high level of detail, presenting peaks with 100% signal contrast during tearing mode growth and rotation, and sub-peak structures reflecting the interplay between the magnetic island formed by the tearing mode, RE diffusion during island rotation and the geometry of obstacles in the vessel. Correlations between the Cherenkov signal, hard x-ray emission and electron cyclotron emission reveal the impulsive development of the anomalous Doppler instability with instability rise time in the microsecond scale resolved by the high time-resolution of the Cherenkov probe.

Kinetic micro-instabilities in the presence of impurities in toroidal magnetized plasmas

The theoretical and numerical studies on kinetic micro-instabilities, including ion temperature gradient (ITG) driven modes, trapped electron modes (TEMs) in the presence of impurity ions as well as impurity modes (IMs), induced by impurity density gradient alone, in toroidal magnetized plasmas, such as tokamak and reversed-field pinch (RFP) are reviewed briefly. The basic theory for IMs, the electrostatic instabilities in tokamak and RFP plasmas are discussed. The observations of hybrid and coexistence of the instabilities are categorized systematically. The effects of impurity ions on electromagnetic instabilities such as ITG modes, the kinetic ballooning modes (KBMs) and kinetic shear Alfvén modes induced by impurity ions in tokamak plasmas of finite β (=plasma pressure/magnetic pressure) are analyzed. The interesting topics for future investigation are suggested.

Fully Kinetic Simulation of Ion-Temperature-Gradient Instabilities in Tokamaks

The feasibility of using full ion kinetics, instead of gyrokinetics, in simulating low-frequency Ion-Temperature-Gradient (ITG) instabilities in tokamaks has recently been demonstrated. The present work extends the full ion kinetics to the nonlinear regime and investigates the nonlinear saturation of a single-n ITG instability due to the E × B trapping mechanism (n is the toroidal mode number). The saturation amplitude predicted by the E × B trapping theory is found to agree with the saturation level observed in the simulation. In extending to the nonlinear regime, we developed a toroidal Boris full orbit integrator, which proved to be accurate in capturing both the short-time scale cyclotron motion and long time scale drift motion, with good kinetic energy conservation and toroidal angular momentum conservation in tokamak equilibrium magnetic fields. This work also extends the previous work from analytic circular magnetic equilibria to general numerical magnetic equilibria, enabling simulation of realistic equilibria reconstructed from tokamak experiments.

Insights into type‐I edge localized modes and edge localized mode control from JOREK non‐linear magneto‐hydrodynamic simulations

Edge localized modes (ELMs) are repetitive instabilities driven by the large pressure gradients and current densities in the edge of H‐mode plasmas. Type‐I ELMs lead to a fast collapse of the H‐mode pedestal within several hundred microseconds to a few milliseconds. Localized transient heat fluxes to divertor targets are expected to exceed tolerable limits for ITER, requiring advanced insights into ELM physics and applicable mitigation methods. This paper describes how non‐linear magneto‐hydrodynamic (MHD) simulations can contribute to this effort. The JOREK code is introduced, which allows the study of large‐scale plasma instabilities in tokamak X‐point plasmas covering the main plasma, the scrape‐off layer, and the divertor region with its finite element grid. We review key physics relevant for type‐I ELMs and show to what extent JOREK simulations agree with experiments and help reveal the underlying mechanisms. Simulations and experimental findings are compared in many respects for type‐I ELMs in ASDEX Upgrade. The role of plasma flows and non‐linear mode coupling for the spatial and temporal structure of ELMs is emphasized, and the loss mechanisms are discussed. An overview of recent ELM‐related research using JOREK is given, including ELM crashes, ELM‐free regimes, ELM pacing by pellets and magnetic kicks, and mitigation or suppression by resonant magnetic perturbation coils (RMPs). Simulations of ELMs and ELM control methods agree in many respects with experimental observations from various tokamak experiments. On this basis, predictive simulations become more and more feasible. A brief outlook is given, showing the main priorities for further research in the field of ELM physics and further developments necessary.