En route to realistic modeling of the kinetic-MHD interaction between macroscopic modes and fast particles induced by neutral beam injection in tokamaks
F. Orain, G. Brochard, T. Nicolas, H. Lütjens, X. Garbet, R. Dumont, P. Maget
A new model of fast ion source induced by Neutral Beam Injection (NBI) in tokamaks has been implemented in the hybrid kinetic-magnetohydrodynamic code XTOR-K. This source, combined with the collisions also recently implemented, allows for the modeling of realistic slowing-down populations and their interplay with macroscopic modes. This paper describes the Neutral Beam injection and ionization model designed to reproduce experimental configurations and its validation for a typical discharge of the ASDEX Upgrade tokamak. The application to the interaction of NBI-induced fast particles with a kink mode in ASDEX Upgrade demonstrates a resonance between passing particles and the n=1 mode. This resonance partially stabilizes the kink mode and induces a radial transport of fast particles. Preliminary results in ITER-like circular geometry show that NBI induces a toroidal torque but has little impact on the kink mode dynamics.
Analytic solutions of the magnetohydrodynamic equilibrium equations for a cylindrically symmetric magnetically confined plasma with reversed magnetic shear, s < 0, and sheared flow are constructed by prescribing the safety factor-, poloidal velocity- and axial velocity- profiles consistently with experimental ones.
The purpose of this paper is to further investigate the major disruptions occurring in low-q(a) discharges in Iran Tokamak 1, and to compare the theoretical and experimental results for the rate of island growth. The study of precursor phase of disruption can be predicted and avoided using suitable control systems. In this paper are described the stability analysis and the observed growth rates indicate that the rotating modes are tearing modes.
The tearing mode instability and the associated magnetic islands can lead to a degradation of tokamak plasma performance and eventually to a disruption. A crucial issue for the extension of advanced tokamak scenarios to long pulse operation is to avoid these MHD instabilities. Prevention of disruptions and limitations of adverse effect on energy confinement depend on the avoidance of formation of magnetic islands, and it depends also on the successful control of the growth modes excited by intrinsic plasma effects such as the neo-classical drive of unfavourable bootstrap current gradient at so…
The effect of magnetic perturbations (MPs) on the helical self-organization of shaped tokamak plasmas is discussed in the framework of the nonlinear 3D MHD model. Numerical simulations performed in toroidal geometry with the \textsc{pixie3d} code [L. Chacón, Phys. Plasmas {\bf 15}, 056103 (2008)] show that $n=1$ MPs significantly affect the spontaneous quasi-periodic sawtoothing activity of such plasmas. In particular, the mitigation of sawtooth oscillations is induced by $m/n=1/1$ and $2/1$ MPs. These numerical findings provide a confirmation of previous circular tokamak simulations, and are …
In preparation for extending the JOREK nonlinear MHD code to stellarators, a hierarchy of stellarator-capable reduced and full MHD models has been derived and tested. The derivation was presented at the EFTC 2019 conference. Continuing this line of work, we have implemented the reduced MHD model (arXiv:1907.12486) as well as an alternative model which was newly derived using a different set of projection operators for obtaining the scalar momentum equations from the full MHD vector momentum equation. With the new operators, the reduced model matches the standard JOREK reduced models for tokama…
The effect of momentum injection on the temperature gradient in tokamak plasmas is studied. A plausible scenario for transitions to reduced transport regimes is proposed. The transition happens when there is sufficient momentum input so that the velocity shear can suppress or reduce the turbulence. However, it is possible to drive too much velocity shear and rekindle the turbulent transport. The optimal level of momentum injection is determined. The reduction in transport is maximized in the regions of low or zero magnetic shear.
Sawtooth crash in tokamak as a sequence of Multi-region Relaxed MHD equilibria
Nanyang Technological University（南洋理工大学）；Shanghai Jiao Tong University（上海交通大学）；Massachusetts Institute of Technology（麻省理工学院）；the Australian National University（澳大利亚国立大学）；École Polytechnique Fédérale de Lausanne（洛桑联邦理工学院）；Australian Nuclear Science and Technology Organisation（澳大利亚核科学与技术组织）
Verification and 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 suppresed. The simulated radial mode structures agree quantitatively with the electron cyclotron emission measurement after adjusting, within the experimental uncer…
The injection of lower hybrid waves for current drive into a tokamak affects the profile of intrinsic rotation. In this article, the momentum deposition by the lower hybrid wave on the electrons is studied. Due to the increase in the poloidal momentum of the wave as it propagates into the tokamak, the parallel momentum of the wave increases considerably. The change of the perpendicular momentum of the wave is such that the toroidal angular momentum of the wave is conserved. If the perpendicular momentum transfer via electron Landau damping is ignored, the transfer of the toroidal angular momen…
The Hall term has often been neglected in MHD codes as it is difficult to compute. Nevertheless setting it aside for numerical reasons led to ignoring it altogether. This is especially problematic when dealing with tokamak physics as the Hall term cannot be neglected as this paper shows.
In high-current tokamak devices such as ITER, a runaway avalanche can cause a large amplification of a seed electron population. We show that disruption mitigation by impurity injection may significantly increase the runaway avalanche growth rate in such devices. This effect originates from the increased number of target electrons available for the avalanche process in weakly ionized plasmas, which is only partially compensated by the increased friction force on fast electrons. We derive an expression for the avalanche growth rate in partially ionized plasmas and investigate the effects of imp…
An effective disruption mitigation system in a tokamak reactor should limit the exposure of the wall to localized heat losses and to the impact of high current runaway electron beams, and avoid excessive forces on the structure. We evaluate with respect to these aspects a two-stage deuterium-neon shattered pellet injection in an ITER-like plasma, using simulations with the DREAM framework [M. Hoppe et al (2021) Comp. Phys. Commun. 268, 108098]. To minimize the obtained runaway currents an optimal range of injected deuterium quantities is found. This range is sensitive to the opacity of the pla…
Toroidal rotation is well known to play significant roles in the edge transport and L-H transition dynamics of tokamaks. Our recent calculation finds that a sufficiently strong localized toroidal rotation can directly bring out the formation of edge pressure pedestal with reversed magnetic shear that is reminiscent of an H-mode plasma, purely through the effects of toroidal rotation on the tokamak MHD equilibrium itself. In particular, the enhanced edge toroidal rotation enables a substantial peaking of the parallel current profile near edge in higher $β$ regimes, which leads to the flattening…
A simulated annealing (SA) relaxation method is used for calculation of high-beta reduced magnetohydrodynamics (MHD) equilibria in toroidal geometry. The SA method, based on artificial dynamics derived from the MHD Hamiltonian structure, is used to calculate equilibria of large-aspect-ratio and circular-cross-section tokamaks as well as toroidally averaged stellarators. Tokamak equilibria including incompressible poloidal rotations are obtained and the Shafranov shift is seen to increase nearly quadratically in the rotation speed. A mapping procedure between non-rotating and poloidally rotatin…
A highly elongated plasma is desirable in order to increase plasma pressure and energy confinement to maximize fusion power output. However, there is a limit to the maximum achievable elongation which is set by vertical instabilities driven by the $n=0$ MHD mode. This limit can be increased by optimizing several parameters characterizing the plasma and the wall. The purpose of our study is to explore how and to what extent this can be done. Specifically, we extend many earlier calculations of the $n=0$ mode and numerically determine scaling relations for the maximum elongation as a function of…
The results of a comprehensive investigation into the effects of various MHD modes on the NBI-generated fast-ion population in MAST plasmas are reported. Fast-ion redistribution due to low-frequency (20-50 kHz) chirping energetic particle modes known as fishbones, as well as the long-lived internal kink mode, is observed with the Fast-Ion Deuterium Alpha (FIDA) spectrometer and radially-scanning collimated neutron camera. In addition, strongly-driven chirping toroidicity-induced Alfven eigenmodes are observed to cause fast-ion redistribution, as are sawteeth and large edge-localised modes. In …
Fundamental Lagrangian, frozen-in and topological invariants can be useful to explain systematic connections between plasma parameters. At high plasma temperature the dissipation is small and the robust invariances are manifested. We invoke a frozen-in invariant which is an extension of the Ertel's theorem and connects the vorticity of the large scale motions with the profile of the safety factor and of particle density. Assuming ergodicity of the small scale turbulence we consider the approximative preservation of the invariant for changes of the vorticity in an annular region of finite radia…
Evolution of electron temperature, electron density and its fluctuation with high spatial and temporal resolutions are presented for the cold pulse propagation induced by super-sonic molecular beam injection (SMBI) in ohmic plasmas in the EAST tokamak. The non-local heat transport occurs for discharges with plasma current $I_p$=450 kA ($q_{95}\sim5.55$), and electron density $n_{e0}$ below a critical value of $(1.35\pm0.25)\times10^{19}~\mathrm{m^{-3}}$. In contrary to the response of core electron temperature and electron density (roughly 10 ms after SMBI), the electron density fluctuation in…
Variability of MHD Instabilities in Benign Termination of High-Current Runaway Electron Beams in the JET and DIII-D Tokamaks
Columbia University（哥伦比亚大学）；CEA-IRFM（法国原子能和替代能源委员会研究部）；Institute of Plasma Physics of the CAS（捷克科学院等离子体物理研究所）；UKAEA（英国原子能管理局）；ITER Organization（国际热核聚变实验堆组织）；General Atomics（通用原子能公司）
Injection of relatively high density spheromaks with significant helicity-content into a tokamak has been proposed as a means for fueling and current drive. The CHI (Co-axial Helicity Injection) device was devised to inject current to the STOR-M tokamak. Various circuit modifications were made to the CHI controls, enabling testing of various injection configurations. The charge/discharge circuits for CT formation/acceleration and stuffing field were modified, and the power supplies and power converters were replaced. Various modifications were implemented to solve the original slow bank trigge…
In recent years, the nonlinear 3D magnetohydrodynamic codes JOREK, M3D-C$^1$ and NIMROD developed the capability of modelling realistic 3D vertical displacement events (VDEs) including resistive walls. In this paper, a comprehensive 3D VDE benchmark is presented between these state of the art codes. The simulated case is based on an experimental NSTX plasma but with a simplified rectangular wall. In spite of pronounced differences between physics models and numerical methods, the comparison shows very good agreement in the relevant quantities used to characterize disruptions such as the 3D wal…
We demonstrate a fast adjoint-based method to optimize tokamak and stellarator equilibria against a pressure-driven instability known as the infinite-$n$ ideal ballooning mode. We present three finite-$β$ (the ratio of thermal to magnetic pressure) equilibria: one tokamak equilibrium and two stellarator equilibria that are unstable against the ballooning mode. Using the self-adjoint property of ideal MHD, we construct a technique to rapidly calculate the change in the growth rate, a measure of ideal ballooning instability. Using the~\texttt{SIMSOPT} framework, we then implement our fast adjoin…
Impurity-driven turbulence opens a pathway to ELM-free operation and enhanced pedestal stability in tokamaks
Princeton Plasma Physics Laboratory（普林斯顿等离子体物理实验室）；Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）；General Atomics（通用原子公司）；UCLA（加州大学洛杉矶分校）；University of Wisconsin-Madison（威斯康星大学麦迪逊分校）
During disruptions in fusion-grade tokamaks like ITER, large electric fields are induced following the thermal quench (TQ) period which can generate a substantial amount of Runaway Electrons (REs) that can carry up to 10 MA current with energies as high as several tens of MeV [1-3] in current quench phase (CQ). These runaway electrons can cause significant damage to the plasma-facing-components due to their localized energy deposition. To mitigate these effects, impurity injections of high-Z atoms have been proposed [1-3]. In this paper, we use a self-consistent 0D tokamak disruption model as …
It is proved that irrespective of compressibility tokamak steady states with purely poloidal mass flow can not exist in the framework of either magnetohydrodynamics (MHD) or Hall MHD models. Non-existence persists within single fluid plasma models with pressure anisotropy and incompressible flows.
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, PPCF 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 is to understand the extent to which the modelling approaches agree, and identify the important physical effects which can modify the dynamics. For the simulated external kink, which is dom…
The dynamics of large scale plasma instabilities can strongly be influenced by the mutual interaction with currents flowing in conducting vessel structures. Especially eddy currents caused by time-varying magnetic perturbations and halo currents flowing directly from the plasma into the walls are important. The relevance of a resistive wall model is directly evident for Resistive Wall Modes (RWMs) or Vertical Displacement Events (VDEs). However, also the linear and non-linear properties of most other large-scale instabilities may be influenced significantly by the interaction with currents in …
Massive gas injection (MGI) experiments have been carried out in many tokamaks to study disruption dynamics and mitigation schemes. Two events often observed in those experiments are the excitation of the $m=2, n=1$ magnetohydrodynamic (MHD) mode, and the formation of cold bubble structure in the temperature distribution before the thermal quench (TQ). Here $m$ is the poloidal mode number, $n$ the toroidal mode number. The physics mechanisms underlying those phenomena, however, have not been entirely clear. In this work, our recent NIMROD simulations of the MGI process in a tokamak have reprod…
Study of Low-Frequency Core-Edge Coupling in a Tokamak: II. Spatial Channeling & Focusing In Antenna-Driven MHD
National Institutes for Quantum Science and Technology (QST), Rokkasho Institute for Fusion Energy（量子科学和技术研究院（QST），六所聚变能研究所）；QST, Naka Institute for Fusion Science and Technology（量子科学和技术研究院（QST），那波聚变科学与技术研究所）；Department of Nuclear and Quantum Engineering, Korea Advanced Institute of Science and Technology (KAIST)（韩国科学技术院（KAIST）核与量子工程系）；Center for Nonlinear Plasma Science and C.R. ENEA Frascati（非线性等离子体科学与ENEA弗拉斯卡蒂研究中心）；Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Roma（意大利国家核物理研究所（INFN），罗马分部）
For ITER-relevant runaway electron studies, such as suppression, mitigation, termination and/or control of runaway beam, obtaining the runaway electrons after the disruption is important. In this paper we report on the first achieved discharges with post-disruptive runaway electron beam, entitled "runaway plateau", in the COMPASS tokamak. The runaway plateau is produced by massive gas injection of argon. Almost all of the disruptions with runaway electron plateaus occurred during the plasma current ramp-up phase. Comparison between the Ar injection discharges with and without plateau has been …
Feedback stabilization of magnetohydrodynamic (MHD) modes is studied in a cylindrical model for a tokamak with resistivity, viscosity and toroidal rotation. The control is based on a linear combination of the normal and tangential components of the magnetic field just inside the resistive wall. The feedback includes complex gain, for both the normal and for the tangential components, and the imaginary part of the feedback for the former is equivalent to plasma rotation. The work includes (1) analysis with a reduced resistive MHD model for a tokamak with finite βand with stepfunction current de…
The effects that energetic trapped ions have on linear resistive magnetohydrodynamic (MHD) instabilities are studied in a reduced model that captures the essential physics driving or damping the modes through variations in the magnetic shear. The drift-kinetic orbital interaction of a slowing down distribution of trapped energetic ions with a resistive MHD instability is integrated to a scalar contribution to the perturbed pressure, and entered into an asymptotic matching formalism for the resistive MHD dispersion relation. Toroidal magnetic field line curvature is included to model trapping i…
For the simulation of disruptions in tokamak fusion plasmas, a fluid model describing the evolution of relativistic runaway electrons and their interaction with the background plasma is presented. The overall aim of the model is to self-consistently describe the nonlinear coupled evolution of runaway electrons (REs) and plasma instabilities during disruptions. In this model, the runaway electrons are considered as a separate fluid species in which the initial seed is generated through the Dreicer source, which eventually grows by the avalanche mechanism (further relevant source mechanisms can …
Based on the analysis of data from the numerous dedicated experiments on plasma disruptions in the TEXTOR tokamak the mechanisms of the formation of runaway electron beams and their losses are proposed. The plasma disruption is caused by strong stochastic magnetic field formed due to nonlinearly excited low-mode number magnetohydrodynamic (MHD) modes. It is hypothesized that the runaway electron beam is formed in the central plasma region confined by an intact magnetic surface due to the acceleration of electrons by the inductive toroidal electric field. In the case of plasmas with the safety …
A new physical mechanism of formation of runaway electron (RE) beams during plasma disruptions in tokamaks is proposed. The plasma disruption is caused by a strong stochastic magnetic field formed due to nonlinearly excited low-mode number magnetohydrodynamic (MHD) modes. It is conjectured that the runaway electron beam is formed in the central plasma region confined inside the intact magnetic surface located between $q=1$ and the closest low--order rational magnetic surfaces [$q=5/4$ or $q=4/3$, \dots]. It results in that runaway electron beam current has a helical nature with a predominant $…
Saskatchewan Torus-Modified (STOR-M) is a small tokamak, well known for various fusion related basic experimental studies such as edge turbulent heating, different instabilities, AC (alternating current) tokamak operation, Ohmic H-mode triggering by the electrode biasing, fueling and momentum injection by Compact Torus (CT) injection, and effects of Resonance Magnetic Perturbations (RMP), among others. Some of those experiments require real time visualization of magnetic surface reconstructions either through EFIT or quick analyses and visualization of experimental data during experiments. Rec…
University of Science and Technology of China（中国科学技术大学）
A model for tokamak discharge through deep learning has been done on a superconducting long-pulse tokamak (EAST). This model can use the control signals (i.e. Neutral Beam Injection (NBI), Ion Cyclotron Resonance Heating (ICRH), etc) to model normal discharge without the need for doing real experiments. By using the data-driven methodology, we exploit the temporal sequence of control signals for a large set of EAST discharges to develop a deep learning model for modeling discharge diagnostic signals, such as electron density $n_{e}$, store energy $W_{mhd}$ and loop voltage $V_{loop}$. Comparin…
The effect of a narrow sub-Alfvenic shear flow layer near the minimum q_min of the tokamak safety factor profile in a configuration with reversed central shear is analyzed. Sufficiently strong velocity shear gives rise to a broad spectrum of fast growing Kelvin-Helmholtz (KH)-like ideal magnetohydrodynamic (MHD) modes with dominant mode numbers m,n ~ 10. Nonlinear simulations with finite resistivity show magnetic reconnection near ripples caused by KH-like vortices, the formation of turbulent structures, and a flattening of the flow profile. The KH modes are compared to double tearing modes (D…
The radiation response and the MHD destabilization during the thermal quench after a mixed species Shattered Pellet Injection (SPI) with impurity species neon and argon are investigated via 3D non-linear MHD simulation using the JOREK code. Both the $n=0$ global current profile contraction and the local helical cooling at each rational surface caused by the pellet fragments are found to be responsible for MHD destabilization after the injection. Significant current driven mode growth is observed as the fragments cross low order rational surfaces, resulting in rapidly inward propagating stochas…
