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.

Neural network based fast prediction of βN limits in HL-2M

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.

Investigation Into Magnetic Reconnection Formation on Propellant Ignition in Electrical Explosion

In magnetic reconnection, magnetic lines break and reconnect to change their topology to a lower-energy state. This process can liberate stored magnetic field energy and accelerate particles during unsteady explosive events. Here, we report the observations of the magnetic reconnection and kink instability of plasma jet in single wire electrical explosion and their effect on propellant ignition. The results showed that the initial velocity of plasma was ∼2,000 m/s, and when the magnetic reconnection occurred, the velocity increased by ∼400–∼2,400 m/s. The evaluated Alfvén velocity was ∼500 m/s, the Alfvén time was ∼20 µs, and the Lundquist number S = 1.7 × 107. Based on these experimental results and model, the three-dimensional magnetic field topology and its evolution process was evaluated and presented. Furthermore, the magnetic reconnection occurred when its curvature reached a certain value due to the fact that the motion of the current sheet changes the topology of the magnetic field, and then, the plasma jet was accelerated and exhausted. The plasma jet angle was ∼50° in experiment 1, and it was consistent with the calculated results. The resulting magnetic reconnection plays an important role in propellant ignition, which enhances the ignition ability of wire electrical explosion. Furthermore, the results represent a key step towards resolving one of the most important problems of plasma physics and can be used to improve the understanding of wire array explosion and propellant ignition.

Reconnection and particle acceleration in three-dimensional current sheet evolution in moderately magnetized astrophysical pair plasma

Magnetic reconnection, a plasma process converting magnetic energy to particle kinetic energy, is often invoked to explain magnetic energy releases powering high-energy flares in astrophysical sources including pulsar wind nebulae and black hole jets. Reconnection is usually seen as the (essentially two-dimensional) nonlinear evolution of the tearing instability disrupting a thin current sheet. To test how this process operates in three dimensions, we conduct a comprehensive particle-in-cell simulation study comparing two- and three-dimensional evolution of long, thin current sheets in moderately magnetized, collisionless, relativistically hot electron–positron plasma, and find dramatic differences. We first systematically characterize this process in two dimensions, where classic, hierarchical plasmoid-chain reconnection determines energy release, and explore a wide range of initial configurations, guide magnetic field strengths and system sizes. We then show that three-dimensional (3-D) simulations of similar configurations exhibit a diversity of behaviours, including some where energy release is determined by the nonlinear relativistic drift-kink instability. Thus, 3-D current sheet evolution is not always fundamentally classical reconnection with perturbing 3-D effects but, rather, a complex interplay of multiple linear and nonlinear instabilities whose relative importance depends sensitively on the ambient plasma, minor configuration details and even stochastic events. It often yields slower but longer-lasting and ultimately greater magnetic energy release than in two dimensions. Intriguingly, non-thermal particle acceleration is astonishingly robust, depending on the upstream magnetization and guide field, but otherwise yielding similar particle energy spectra in two and three dimensions. Although the variety of underlying current sheet behaviours is interesting, the similarities in overall energy release and particle spectra may be more remarkable.

Kinetic Plasma Turbulence Generated in a 3D Current Sheet With Magnetic Islands

In this article we aim to investigate the kinetic turbulence in a reconnecting current sheet (RCS) with X- and O-nullpoints and to explore its link to the features of accelerated particles. We carry out simulations of magnetic reconnection in a thin current sheet with 3D magnetic field topology affected by tearing instability until the formation of two large magnetic islands using particle-in-cell (PIC) approach. The model utilizes a strong guiding field that leads to the separation of the particles of opposite charges, the generation of a strong polarization electric field across the RCS, and suppression of kink instability in the “out-of-plane” direction. The accelerated particles of the same charge entering an RCS from the opposite edges are shown accelerated to different energies forming the “bump-in-tail” velocity distributions that, in turn, can generate plasma turbulence in different locations. The turbulence-generated waves produced by either electron or proton beams can be identified from the energy spectra of electromagnetic field fluctuations in the phase and frequency domains. From the phase space analysis we gather that the kinetic turbulence may be generated by accelerated particle beams, which are later found to evolve into a phase-space hole indicating the beam breakage. This happens at some distance from the particle entrance into an RCS, e.g. about 7di (ion inertial depth) for the electron beam and 12di for the proton beam. In a wavenumber space the spectral index of the power spectrum of the turbulent magnetic field near the ion inertial length is found to be −2.7 that is consistent with other estimations. The collective turbulence power spectra are consistent with the high-frequency fluctuations of perpendicular electric field, or upper hybrid waves, to occur in a vicinity of X-nullpoints, where the Langmuir (LW) can be generated by accelerated electrons with high growth rates, while further from X-nullponts or on the edges of magnetic islands, where electrons become ejected and start moving across the magnetic field lines, Bernstein waves can be generated. The frequency spectra of high- and low-frequency waves are explored in the kinetic turbulence in the parallel and perpendicular directions to the local magnetic field, showing noticeable lower hybrid turbulence occurring between the electron’s gyro- and plasma frequencies seen also in the wavelet spectra. Fluctuation of the perpendicular electric field component of turbulence can be consistent with the oblique whistler waves generated on the ambient density fluctuations by intense electron beams. This study brings attention to a key role of particle acceleration in generation kinetic turbulence inside current sheets.

Plasma turbulence generated during particle acceleration in magnetic islands

<div> <div> <div> <p>We investigate plasma turbulence generated during particle acceleration in magnetic islands within 3D Harris-type reconnecting current sheets (RCSs),using the particle-in-cell approach.  RCSs with a strong guiding magnetic field  ar shown to lead to separation of electrons and ions into the opposite sides from the current sheet mid-plane that significantly reduces kink instability along the guiding field direction. Particles with the same charge also have asymmetric trajectories forming two distinct populations of beams: ‘transit’ particles, which pass through RCS from one edge to another, become strongly energised and form nearly unidirectional beams; and ‘bounced’ particles, which are reflected from the diffusion region and move back to the same side they entered the current sheet, gaining much less energy and forming more dispersive spatial distributions. Thes transit and bounced particles form the ‘bump-on-tail’ velocity distributions that naturally generate plasma turbulence. Using the wavelet analysis of electric and magnetic field fluctuations in the frequency domain, we identified some characteristic waves produced by particle beams. In particular, we found thre are Langmuir waves near X-nullpoints produced by two electron beam instabilities, while the presence of anisotropic temperature variations inside magnetic islands lead to whistler waves. The lower-hybrid waves are generated inside the magnetic islands, owing to the two-stream instabilities of the ions. While the high-frequency fluctuations, upper hybrid waves, or electron Bernstein waves, pile up near X-nullpoints. The results can be beneficial for understanding in-situ observations with modern space missions of energetic particles in the heliosphere.</p> </div> </div> </div>