The Hamiltonian representation of magnetic field lines enables one to study their confinement properties in tokamaks through the use of symplectic maps such as the symmetric tokamap and its bounded version, the latter being introduced here. In this time-independent purely magnetic framework, we observed the drastic improvement in the confinement of magnetic field lines produced by the local vanishing of the shear profile. This amounts to a non-twist condition that notably acts in the same way the safety profile being (non-strictly) monotonic or having a reversed shear. We single out the effect of the amount of flatness of the safety profile in the vicinity of its zero shear point. All other things being equal, the beneficial effect of the vanishing of the shear profile is shown to be increased if the radial extent of the low-shear region is increased. To be specific, the low-shear region induces the formation of a belt of robust KAM tori acting as an internal transport barrier whose width is all the larger as the extent of the low-shear region is broad.
In this paper we have studied the influence of reversed shear on the improvement of the confinement's quality in the plasma of tokamak and especially in reducing the anomalous transport. For that, we have used a special model for the drift wave fields. Comparison between particles trajectories for normal and reversed shear is carried out in 2 D and 3 D presentation. Also, the diffusion coefficient of particles for the two cases, normal and negative shear, is evaluated.
In this work we demostrate using a two-temperature volume average 0D model that robust stabilization, with regard the hellium ash confinement time, of the burn conditions of a tokamak reactor with the ITER FEAT design parameters can be achieved using Radial Basis Neural Networks (RBNN). Alpha particle thermalization time delay is taken into account in this model. The control actions implemented by means of a RBNN, include the modulation of the DT refueling rate, a neutral He-4 injection beam and auxiliary heating powers to ions and to electrons; all of them constrained to lie within allowable …
Mass flows and radial electric field driven by edge poloidal density asymmetries can be used as a highly effective control mechanism for the edge and thus global confinement in tokamaks. The underlying physics can be demonstrated entirely within a simple magnetohydrodynamic equilibrium model, without resorting to sophisticated and usually collisionality-dependent neoclassical physics arguments. As an example, strong dependence of the low to high (LH) transition power threshold on the magnetic topology, an experimental observation still poorly understood, can be easily explained within this fra…
Here diffusion and Ware pinch are analyzed as opposed effects for plasma confinement, when instabilities are not considered. In this work it is studied the equilibrium inductive electric field where both effects annul each other in the sense that the average normal velocity is zero, that is, marginal velocity confinement is reached. The critical electric field defined in that way is studied for different values of elliptic elongation, Shafranov shift and triangularity. A short complementary analysis is also performed of the variation of the poloidal magnetic field along a magnetic line. Magnet…
Improved Particle Confinement with Resonant Magnetic Perturbations in DIII-D Tokamak H-Mode Plasmas
Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）；Princeton Plasma Physics Laboratory（普林斯顿等离子体物理实验室）；General Atomics（通用原子能公司）；University of California, Los Angeles（加州大学洛杉矶分校）；Massachusetts Institute of Technology（麻省理工学院）
Nitrogen seeded detachment has been achieved in the Tokamak a Configuration Variable (TCV) in advanced divertor configurations (ADCs), namely X-divertor and X-point target, with and without baffles in H-mode plasmas with high core confinement. Both ADCs show a remarkable reduction in the inter-ELM particle and heat fluxes to the target compared to the standard divertor configuration. 95-98% of the peak heat flux to the target is mitigated as a synergetic effect of ADCs, baffling, and nitrogen seeded detachment. The effect of divertor geometry and baffles on core-divertor compatibility is inves…
Confinement phenomenology characteristic of magnetically confined plasmas emerges naturally from a simple sandpile algorithm when the parameter controlling redistribution scalelength is varied. Close analogues are found for enhanced confinement, edge pedestals, and edge localised modes (ELMs), and for the qualitative correlations between them. These results suggest that tokamak observations of avalanching transport are deeply linked to the existence of enhanced confinement and ELMs.
Non-dimensional confinement scaling in similar negative triangularity plasmas on the DIII-D and TCV tokamaks
University of California San Diego（加州大学圣地亚哥分校）；General Atomics（通用原子能公司）；Ecole Polytechnique Federale de Lausanne（洛桑联邦理工学院）；Consorzio RFX（RFX联合体）；University of Texas at Austin（德克萨斯大学奥斯汀分校）；Princeton Plasma Physics Laboratory（普林斯顿等离子体物理实验室）；Columbia University（哥伦比亚大学）；College of William and Mary（威廉玛丽学院）；Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）
A "carpet" of torsional Alfven waves, resonantly excited in an annulus inside a toroidal conducting vessel, could maintain magnetized plasma inside of the annulus against the inherent outward expansion. Such toroidal magnetic confinement for fusion could present some advantages over conventional tokamaks. The idea could also be used to stabilize interchange and ballooning modes in tokamaks and other interchange-limited fusion devices.
A change of the particle density (by gas puff, pellets or impurity seeding) during the plasma discharge in tokamak produces a radial current and implicitly a torque and rotation that can modify the state of confinement. After ionization the newly born ions will evolve toward the periodic neoclassical orbits (trapped or circulating) but the first part of their excursion, which precedes the periodicity, is an effective radial current. It is short, spatially finite and unique for each new ion, but multiplied by the rate of ionization and it can produce a substantial total radial current. The asso…
Long-pulse operation of a self-sustained fusion reactor using toroidal magnetic containment requires control over the content of alpha particles produced by D-T fusion reactions. On the one hand, MeV-class alpha particles must stay confined to heat the plasma. On the other hand, decelerated helium ash must be expelled before diluting the fusion fuel. Our kinetic-magnetohydrodynamic hybrid simulations of a large tokamak plasma confirm the existence of a parameter window where such energy-selective confinement can be accomplished by exploiting internal relaxation events known as `sawtooth crashe…
It is shown that rapid substantial changes in heating rate can induce transitions to improved energy confinement regimes in zero-dimensional models for tokamak plasma phenomenology. We examine for the first time the effect of step changes in heating rate in the models of E-J.Kim and P.H.Diamond, Phys.Rev.Lett. 90, 185006 (2003) and M.A.Malkov and P.H.Diamond, Phys.Plasmas 16, 012504 (2009) which nonlinearly couple the evolving temperature gradient, micro-turbulence and a mesoscale flow; and in the extension of H.Zhu, S.C.Chapman and R.O.Dendy, Phys.Plasmas 20, 042302 (2013), which couples to a…
Operation of a tokamak with q edge around 2 is discussed in this paper. It is shown that an L mode operation at a relatively high toroidal magnetic field can produce confinement conditions similar to ITER-FEAT.
Thermal ions in spherical tokamaks have two adiabatic invariants: the magnetic moment and the longitudinal invariant. For hot ions, variations in magnetic-field strength over a gyro period can become sufficiently large to cause breakdown of the adiabatic invariance. The magnetic moment is more sensitive to perturbations than the longitudinal invariant and there exists an intermediate regime, super-adiabaticity, where the longitudinal invariant remains adiabatic, but the magnetic moment does not. The motion of super-adiabatic ions remains integrable and confinement is thus preserved. However, a…
During a tokamak discharge, the plasma can vary between different confinement regimes: Low (L), High (H) and, in some cases, a temporary (intermediate state), called Dithering (D). In addition, while the plasma is in H mode, Edge Localized Modes (ELMs) can occur. The automatic detection of changes between these states, and of ELMs, is important for tokamak operation. Motivated by this, and by recent developments in Deep Learning (DL), we developed and compared two methods for automatic detection of the occurrence of L-D-H transitions and ELMs, applied on data from the TCV tokamak. These method…
The application of non-axisymmetric resonant magnetic perturbations (RMPs) to low current plasmas in the Mega Amp Spherical Tokamak (MAST) was found to be correlated with substantial drops in neutron production, suggesting a significant degradation of fast ion confinement. The effects of such perturbations on fast ions in MAST have been modelled using a revised version of a non-steady-state orbit-following Monte-Carlo code (NSS OFMC), in which the parametrization of fusion reaction rates has been updated and neutron rates have been recalculated. Losses of fast ions via charge-exchange (CX) wit…
The results of flux-driven, two-fluid simulations in single-null configurations are used to investigate the processes determining the turbulent transport in the tokamak edge. Three turbulent transport regimes are identified: (i) a developed transport regime with turbulence driven by an interchange instability, which shares a number of features with the standard L-mode of tokamak operation, (ii) a suppressed transport regime, characterized by a higher value of the energy confinement time, low-amplitude relative fluctuations driven by a Kelvin-Helmholtz instability, a strong E x B sheared flow, …
On the basis of an analysis of the ITER L-mode energy confinement database, two new scaling expressions for tokamak L-mode energy confinement are proposed, namely a power law scaling and an offset-linear scaling. The analysis indicates that the present multiplicity of scaling expressions for the energy confinement time TE in tokamaks (Goldston, Kaye, Odajima-Shimomura, Rebut-Lallia, etc.) is due both to the lack of variation of a key parameter combination in the database, fs = 0.32 R a^.75 k^ 5 ~ A a^.25 k^.5, and to variations in the dependence of rE on the physical parameters among the diffe…
Nitrogen-induced ELM suppression and confinement improvement in the EAST tokamak with a full metal wall
School of the Gifted Young, University of Science and Technology of China（中国科学技术大学少年班）；Institute of Plasma Physics, Chinese Academy of Sciences（中国科学院等离子体物理研究所）；School of Nuclear Science and Technology, University of Science and Technology of China（中国科学技术大学核科学与技术学院）；Southwestern Institute of Physics（西南物理研究所）
The goal of this paper is to understand from a mathematical point of view the magnetic confinement of plasmas for fusion. Following Frénod and Sonnendrücker \cite{FS2}, we first use two-scale convergence tools to derive a gyrokinetic system for a plasma submitted to a large magnetic field with a slowly spatially varying intensity. We formally derive from this system a simplified bi-temperature fluid system. We then investigate the behaviour of the plasma in such a regime and we prove nonlinear stability or instability depending on which side of the tokamak we are looking at. In our analysis, w…
Non-rotating (`locked') magnetic islands often lead to complete losses of confinement in tokamak plasmas, called major disruptions. Here locked islands were suppressed for the first time, by a combination of applied three-dimensional magnetic fields and injected millimetre waves. The applied fields were used to control the phase of locking and so align the island O-point with the region where the injected waves generated non-inductive currents. This resulted in stabilization of the locked island, disruption avoidance, recovery of high confinement and high pressure, in accordance with the expec…
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…
A new linked mirror device for magnetic confinement experiment is proposed. The new linked mirror device consists of two straight magnetic mirrors connected by two half-torus. The structure of the configuration as a whole is three dimensional because the two linear mirror sections are not parallel. The angle between the two mirror sections generates rotational transform which results in good magnetic confinement of toroidally processing passing particles. In this way the usual loss cone of the traditional linear mirror machines is eliminated. The single particle confinement is similar to that …
Spontaneous spin-up are widely observed in tokamak plasmas, which is crucially important for plasma confinement. A kinetic theory is proposed to show that a toroidal rotation of core plasma is induced by the topological transition of orbits driven by turbulent diffusion in a collisionless tokamak plasma. The theoretical prediction agrees well with the well-known Rice-scaling of intrinsic core plasma flow. This new theory predicts an intrinsic core parallel flow of $\sim 100km/s$ for the International Thermonuclear Experimental Reactor.
An expression for the extrapolated fusion gain G = Pfusion /5 Pheat (Pfusion being the total fusion power and Pheat the total heating power) of ITER in terms of the confinement improvement factor (H) and the normalised beta (betaN) is derived in this paper. It is shown that an increase in normalised beta can be expected to have a negative or neutral influence on G depending on the chosen confinement scaling law. Figures of merit like H betaN / q95^2 should be used with care, since large values of this quantity do not guarantee high values of G, and might not be attainable with the heating powe…
We analyze an axisymmetric equilibrium of a plasma endowed with toroidal and poloidal velocity fields, with the aim to characterize the influence of the global motion on the morphology of the magnetic confinement. We construct our configuration assuming that the poloidal velocity field is aligned with the poloidal magnetic field lines and, furthermore, we require that the plasma mass density depend on the magnetic flux function (or equivalently, that the plasma fluid be incompressible). We then derive a sort of Grad-Shafranov equation for such an equilibrium and implement it to tokamak relevan…
A pulsed oscillating power amplifier has been developed to apply high frequency biasing voltage to an electrode at the edge of the STOR-M tokamak plasma. The power amplifier can deliver a peak-to-peak oscillating voltage up to 120V and current 30A within the frequency range of 1kHz-50kHz. The electrode is located in the equatorial plane at radius $ρ= 0.88$. The frequency of the applied voltage has been varied between discharges. It is observed that the plasma density and soft x-ray intensity from the plasma core region usually increase at lower frequency regime 1kHz-5kHz as well as relatively …
Gyrokinetic simulation of the effect of transient fueling on plasma turbulence in ADITYA-U tokamak
Indian Institute of Science Bangalore（印度科学研究所班加罗尔分院）；Institute for Plasma Research, Bhat（巴特等离子体研究所）；Homi Bhabha National Institute（霍米·巴巴国立研究所）；Centre for Development of Advanced Computing（高级计算发展中心）；Department of Physics and Astronomy, University of California Irvine（加州大学尔湾分校物理与天文学系）
Local nonlinear gyrokinetic simulations of tokamak plasmas demonstrate that turbulent eddies can extend along magnetic field lines for hundreds of poloidal turns when the magnetic shear is very small. By accurately modeling different field line topologies (e.g. low-order, almost rational, or irrational safety factor), we show that the parallel self-interaction of such "ultra long" eddies can dramatically reduce heat transport. This reveals novel strategies to improve confinement, constitutes experimentally testable predictions, and illuminates past observations of internal transport barriers.
This paper deals with the new spectral and microturbulence experimental data and their analysis, which show, that the radial electric field Er generated at the LH heating (LHH) in the FT-2 is high enough to form the transport barriers. The ETB is formed when LHH is switched off. The radial fluctuation-induced EB drift flux densities near LCFS in SOL are measured at two different poloidal angles. For this purpose two Langmuir probes located at low and high field sides of the torus are used. Registration of the poloidal and radial components of the electric field and density fluctuations…
Tokamak stability to, potentially explosive, `ballooning' displacements of elliptical magnetic flux tubes is examined in large aspect ratio equilibrium. Above a critical pressure gradient the energy stored in the plasma may be lowered by finite (but not infinitesimal) displacements of such tubes (metastability). Above a higher pressure gradient, the linear stability boundary, such tubes are linearly and nonlinearly unstable. The flux tube displacement can be of the order of the pressure gradient scale length. Plasma transport from displaced flux tubes may result in rapid loss of confinement.
The collisional dynamics of test impurity ions in spherical tokamak plasmas with strongly-sheared radial electric fields is investigated by means of a test particle full orbit simulation code. The strength of the shear is such that the standard drift ordering can no longer be assumed and a full orbit approach is required. The effect of radial electric field shear on neoclassical particle transport is quantified for a range of test particle mass and charge numbers and electric field parameters. It is shown that the effect of a sheared electric field is to enhance the confinement of impurity spe…
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…
It is pointed that there is a current jump between the edge plasma inside the last closed magnetic surface and the scrape-off layer and the current jump can lead the external kink modes to convert to the tearing modes, due to the current interchange effects [L. J. Zheng and M. Furukawa, Phys. Plasmas 17, 052508 (2010)]. The magnetic reconnection in the presence of tearing modes subsequently causes the tokamak edge plasma to be peeled off to link to the diverters. In particular, the peeling or peeling-ballooning modes can become the "peeling-off" modes in this sense. This phenomenon indicates t…
Decay times of plasma flows and plasma profiles have been measured after a sudden biasing switch-off in experiments on the CASTOR tokamak. A biased electrode has been used to polarize the edge plasma. The edge plasma potential and flows have been characterized by means of Langmuir and Mach probes, the radiation was measured using an array of bolometers. Potential profiles and poloidal flows can be well fitted by an exponential decay time in the range of 10 - 30 microseconds when the electrode biasing is turn off in the CASTOR tokamak. The radiation shows a slower time scale (about 1 ms), which…
Power-law-anchored residual learning for H-mode energy confinement time in tokamaks: interpolation and parameter-defined extrapolation
School of Physics, East China University of Science and Technology（华东理工大学物理学院）；Beijing ENN Fusion Energy Science and Technology Co., Ltd.（北京新奥聚能科技有限公司）；Beijing Key Laboratory of High Magnetic Field Spherical Torus Fusion Energy（北京市高磁场球形环聚变能重点实验室）；Hebei Key Laboratory of Compact Fusion（河北省紧凑型聚变重点实验室）
The analytic theory presented in Paper I is converted into a form convenient for numerical analysis. A fast and accurate code has been written using this numerical formulation. The results are presented by first defining a reference set of physical parameters based on experimental data from high performance discharges. Numerically obtained scaling relations of maximum achievable elongation versus inverse aspect ratio are obtained for various values of poloidal beta, wall radius and feedback capability parameter in ranges near the reference values. It is also shown that each value of maximum el…
This overview presents a tutorial introduction to the theory of magnetic plasma confinement in toroidal confinement systems with particular emphasis on axisymmetric equilibrium geometries, and tokamaks. The discussion covers three important aspects of plasma physics: Equilibrium, Stability, and Transport. The section on equilibrium will go through an introduction to ideal magnetohydrodynamics, curvilinear system of coordinates, flux coordinates, extensions to axisymmetric equilibrium, Grad-Shafranov Equation (GSE), Green's function formalism, as well as analytical and numerical solutions to GS…
In tokamaks, internal transport barriers, produced by modifications of the plasma current profile, reduce particle transport and improve plasma confinement. The triggering of the internal transport barriers and their dependence on the plasma profiles is a key nonlinear dynamics problem still under investigation. We consider the onset of shearless invariant curves inside the plasma which create internal transport barriers. A non-integrable drift-kinetic model is used to describe particle transport driven by drift waves and to investigate these shearless barriers onset in tokamaks. We show that …
In a typical fusion experiment, the plasma can have several possible confinement modes. At the TCV tokamak, aside from the Low (L) and High (H) confinement modes, an additional mode, dithering (D), is frequently observed. Developing methods that automatically detect these modes is considered to be important for future tokamak operation. Previous work with deep learning methods, particularly convolutional recurrent neural networks (Conv-RNNs), indicates that they are a suitable approach. Nevertheless, those models are sensitive to noise in the temporal alignment of labels, and that model in par…
We discuss a stochastic model for the behavior of electrons in a magnetically confined plasma having axial symmetry. The aim of the work is to provide an explanation for the density limit observed in the Frascati Tokamak Upgrade machine. The dynamical framework deals with an electron embedded in a stationary and uniform magnetic field and affected by an orthogonal random electric field. The behavior of the average plasma profile is determined by the appropriate Fokker-Planck equation associated to the considered model and the disruptive effects of the stochastic electric field is shown. The co…
Boundary plasma physics plays an important role in tokamak confinement, but is difficult to simulate in a gyrokinetic code due to the scale-inseparable nonlocal multi-physics in magnetic separatrix and open magnetic field geometry. Neutral particles are also an important part of the boundary plasma physics. In the present paper, noble electrostatic gyrokinetic techniques to simulate the flux-driven, low-beta electrostatic boundary plasma is reported. Gyrokinetic ions and drift-kinetic electrons are utilized without scale-separation between the neoclassical and turbulence dynamics. It is found …
Nonlinear gyrokinetic simulations have been conducted to investigate turbulent transport in tokamak plasmas with rotational shear. At sufficiently large flow shears, linear instabilities are suppressed, but transiently growing modes drive subcritical turbulence whose amplitude increases with flow shear. This leads to a local minimum in the heat flux, indicating an optimal E x B shear value for plasma confinement. Local maxima in the momentum fluxes are also observed, allowing for the possibility of bifurcations in the E x B shear. The sensitive dependence of heat flux on temperature gradient i…
