The RAPTOR code is used to model how the time required for controlled termination of Ohmic plasmas scales from present tokamaks like TCV and JET, to reactor-grade tokamaks like ITER and DEMO. We show that ramping the plasma current $I_p$ down to 20% of the flat-top value over a time $Δt_{ramp-down}=τ_{LR}=L_i/R$, with internal inductance $L_i$ and resistance $R$ evaluated at flat-top conditions, results in an approximately self-similar peaking of the current density for these four tokamaks, indicating the adequacy of $τ_{LR}$ as a relevant timescale for cross-machine comparison, yielding $τ_{LR} =$ 0.033s (TCV), 2.87s (JET), 63.2s (ITER) and 166.9s (DEMO). Note that $τ_{LR}$ is easy to evaluate, both in systems codes and on a real-time control system. For the simulated ramp-downs with $Δt_{ramp-down}=τ_{LR}$, the end-of-ramp-down normalized internal inductance $\ell_{i3}$ is limited below 2. An $I_p$ ramp-down faster than $τ_{LR}=L_i/R$ requires a reversal of the boundary loop voltage and leads to the formation of a broad plasma layer carrying current in the direction opposite to the total plasma current, concomitant with $\ell_{i3}>2$, a central region with low magnetic shear and strongly peaked pressure profiles. Significant reduction of plasma volume and elongation, as foreseen for ITER and DEMO, is shown to counteract the reversal of current density and the $\ell_{i3}$ increase, while easing vertical stability control, potentially enabling faster $I_p$ ramp-down scenarios. Experimental and theoretical studies should be performed to test the feasibility of such fast termination scenarios, notably with respect to vertical position control, shape control and (resistive) beta limits. A simple analytical model is proposed and applied to estimate $τ_{LR}$ based on 0D engineering parameters for different tokamaks and for different operating points.
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）
In this paper, the secular full-orbit simulations of runaway electrons with synchrotron radiation in tokamak fields are carried out using a relativistic volume-preserving algorithm. Detailed phase-space behaviors of runaway electrons are investigated in different dynamical timescales spanning 11 orders. When looking into the small timescale, i.e., the characteristic timescale imposed by Lorentz force, the severely deformed helical trajectory of energetic runaway electron is witnessed. A qualitative analysis of the neoclassical scattering, a kind of collisionless pitch-angle scattering phenomen…
The potential formation of multi-mega-ampere beams of relativistic "runaway" electrons (REs) during sudden terminations of tokamak plasmas poses a significant challenge to the tokamak's development as a fusion energy source. Here, we use state-of-the-art modeling of disruption magnetohydrodynamics coupled with a self-consistent evolution of RE generation and transport to show that a non-axisymmetric in-vessel coil will passively prevent RE beam formation during disruptions in the SPARC tokamak, a compact, high-field, high-current device capable of achieving a fusion gain Q > 2 in deuterium-tri…
Implementation and verification of the avalanche source in a 3D full-f particle-in-cell model of relativistic electrons for studies of tokamak disruptions
An Inverse Grad-Shafranov Neural Network Approach to Tokamak Magnetic Control
MIT Plasma Science and Fusion Center（麻省理工学院等离子体科学与聚变中心）；École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院）；Google DeepMind（谷歌DeepMind）；Fusionality SA；Commonwealth Fusion Systems（联邦聚变系统）
In this paper, we extend the multiscale approach developed in [Abel et. al., Rep. Prog. Phys., submitted] by exploiting the scale separation between ions and the electrons. The gyrokinetic equation is expanded in powers of the electron to ion mass ratio, which provides a rigorous method for deriving the reduced electron model. We prove that ion-scale electromagnetic turbulence cannot change the magnetic topology, and argue that to lowest order the magnetic field lies on fluctuating flux surfaces. These flux surfaces are used to construct magnetic coordinates, and in these coordinates a closed …
For the first time the pellet cycle of a multiple-isotope plasma is successfully reproduced with reduced turbulent transport modelling, within an integrated simulation framework. Future nuclear fusion reactors are likely to be fuelled by cryogenic pellet injection, due to higher penetration and faster response times. Accurate pellet cycle modelling is crucial to assess fuelling efficiency and burn control. In recent JET tokamak experiments, deuterium pellets with reactor-relevant deposition characteristics were injected into a pure hydrogen plasma. Measurements of the isotope ratio profile inf…
A Rapid Integrated Tokamak Modelling Approach for Coupled Profile and Equilibrium Evolution
Key Laboratory of Materials Modification by Beams of the Ministry of Education, School of Physics, Dalian University of Technology（大连理工大学物理学院材料束改性教育部重点实验室）；Beijing VeloAlpha Technology Co., Ltd.（北京维洛阿尔法科技有限公司）
This paper presents a complete theoretical framework for plasma turbulence and transport in tokamak plasmas. The fundamental scale separations present in plasma turbulence are codified as an asymptotic expansion in the ratio of the gyroradius to the equilibrium scale length. Proceeding order-by-order in this expansion, a framework for plasma turbulence is developed. It comprises an instantaneous equilibrium, the fluctuations driven by gradients in the equilibrium quantities, and the transport-timescale evolution of mean profiles of these quantities driven by the fluctuations. The equilibrium d…
Spacecraft heat shield study in the DIII-D tokamak
University of California San Diego（加州大学圣迭戈分校）；Auburn University（奥本大学）；General Atomics（通用原子能公司）；Princeton Plasma Physics Laboratory（普林斯顿等离子体物理实验室）；Baylor University（贝勒大学）；University of Stuttgart（斯图加特大学）；Oak Ridge National Laboratory（橡树岭国家实验室）；Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）
We describe the evolution of a plasma equilibrium having a toroidal topology in the presence of constant electric resistivity. After outlining the main analytical properties of the solution, we illustrate its physical implications by reproducing the essential features of a scenario for the upcoming Italian experiment Divertor Tokamak Test Facility, with a good degree of accuracy. Although we find the resistive diffusion timescale to be of the order of $10^4\,$s, we observe a macroscopic change in the plasma volume on a timescale of $10^2\,$s, comparable to the foreseen duration of the plasma d…
Mitigation of the multiple risks associated with disruptions and runaway electrons in tokamaks involves competing demands. Success requires that each risk be understood sufficiently that appropriate compromises can be made. Here the focus is on the interaction of short timescale magnetic-perturbations with the structure in ITER that is closest to the plasma, blanket modules covered by separated beryllium tiles. The effect of this tiled surface on the perturbations and on the forces on structures are subtle. Indeterminacy can be introduced by tile-to-tile shorting. A determinate subtlety is int…
A new global two-fluid electromagnetic turbulence code, CENTORI, has been developed for the purpose of studying magnetically-confined fusion plasmas on energy confinement timescales. This code is used to evolve the combined system of electron and ion fluid equations and Maxwell equations in toroidal configurations with axisymmetric equilibria. Uniquely, the equilibrium is co-evolved with the turbulence, and is thus modified by it. CENTORI is applicable to tokamaks of arbitrary aspect ratio and high plasma beta. A predictor-corrector, semi-implicit finite difference scheme is used to compute th…
Hybrid MHD-gyrokinetic code simulations are used to investigate the dynamics of frequency sweeping reversed shear Alfvén eigenmode (RSAE) strongly driven by energetic particles (EPs) during plasma current ramp-up in a conventional tokamak configuration. A series of weakly reversed shear equilibria representing time slices of long timescale MHD equilibrium evolution is considered, where the self-consistent RSAE-EP resonant interactions on the short timescale are analyzed in detail. Both linear and nonlinear RSAE dynamics are shown to be subject to the non-perturbative effect of EPs by maximizin…
The vertical motion of a tokamak plasma is analytically modelled during its non-linear phase by a free-moving current-carrying rod inductively coupled to a set of fixed conducting wires or a cylindrical conducting shell. The solutions capture the leading term in a Taylor expansion of the Green's function for the interaction between the plasma column and the surrounding vacuum vessel. The plasma shape and profiles are assumed not to vary during the vertical drifting phase such that the plasma column behaves as a rigid body. In the limit of perfectly conducting structures, the plasma is prevente…
Observations of ion-scale (k_y*rho_i <= 1) density turbulence of relative amplitude dn_e/n_e <= 0.2% are available on the Mega Amp Spherical Tokamak (MAST) using a 2D (8 radial x 4 poloidal channel) imaging Beam Emission Spectroscopy (BES) diagnostic. Spatial and temporal characteristics of this turbulence, i.e., amplitudes, correlation times, radial and perpendicular correlation lengths and apparent phase velocities of the density contours, are determined by means of correlation analysis. For a low-density, L-mode discharge with strong equilibrium flow shear exhibiting an internal transport b…
