Ideally, binary-collision algorithms conserve kinetic momentum and energy. In practice, the finite size of collision cells and the finite difference in the particle locations affect the conservation properties. In the present work, we investigate numerically how the accuracy of these algorithms is affected when the size of collision cells is large compared with gradient scale length of the background plasma, a parameter essential in full-f fusion plasma simulations. Additionally, we discuss implications for the conserved quantities in drift-kinetic formulations when fluctuating magnetic and electric fields are present: we suggest how the accuracy of the algorithms could potentially be improved with minor modifications.
A fast Alfvén wave with finite amplitude is shown to grow by a stimulated emission process that we propose for exploitation in toroidal magnetically confined fusion plasmas. Stimulated emission occurs while the wave propagates inward through the outer mid-plane plasma, where a population inversion of the energy distribution of fusion-born ions is observed to arise naturally. Fully nonlinear first principles simulations, which self-consistently evolve particles and fields under the Maxwell-Lorentz system, demonstrate this novel "alpha-particle channelling" scenario for the first time.
The idea of new diagnostics method for the small-scale irregular structures of magnetically confined plasma is suggested in the present paper. The method can be based on measurements of intensity attenuation of the normal sounding waves. Anomalous attenuation arises due to multiple scattering effects investigated earlier for ionospheric radio propagation. It has been shown that multiple scattering regime can realize in a tokamak plasma. Calculations of normal sounding wave anomalous attenuation in a tokamak plasma have been carried out. This quantity is large enough to be registered experiment…
Strong electrostatic turbulence in magnetically confined plasmas is characterized by trapping or eddying of particle trajectories produced by the $E\times B$ stochastic drift. Trapping is shown to produce strong effects on test particles and on test modes. It determines non-standard statistics of trajectories: non-Gaussian distribution, memory effects and coherence. Trapped trajectories form quasi-coherent structure. Trajectory trapping has strong nonlinear effects on the test modes on turbulent plasmas. We determine the growth rate of drift modes as function of the statistical characteristics…
Ion cyclotron emission (ICE) offers unique promise as a diagnostic of the fusion born alpha-particle population in magnetically confined plasmas. Pioneering observations from JET and TFTR found that ICE intensity $P_{ICE}$ scales approximately linearly with the measured neutron flux from fusion reactions, and with the inferred concentration, $n_α/n_i$, of fusion-born alpha-particles confined within the plasma. We present fully nonlinear self-consistent kinetic simulations that reproduce this scaling for the first time. This resolves a longstanding question in the physics of fusion alpha-partic…
The transport of energetic electrons is sensitive to magnetic perturbations. By using 3D numerical simulation of test particle drift orbits we show that the transport of untrapped electrons through an open region with magnetic perturbations cannot be described by a diffusive process. Based on our test particle simulations, we propose a model that leads to an exponential loss of particles.
Impact of geodesic curvature on zonal flow generation in magnetically confined plasmas
National Institute for Fusion Science（国立核聚变科学研究所）；The Graduate University for Advanced Studies（高级研究大学院大学）；PRESTO, Japan Science and Technology Agency（日本科学技术振兴机构 PRESTO 项目）；Faculty of Arts and Sciences, Komazawa University（驹泽大学文理学部）
It is shown that the thermodynamic maximum entropy principle predicts negative specific heat for a stationary magnetically self-confined current-carrying plasma torus. Implications for the magnetic self-confinement of fusion plasma are considered.
The efficient production of electricity from nuclear fusion in magnetically confined plasmas relies on a good confinement of the thermal energy. For more than thirty years, the observation that such confinement depends on the mass of the plasma isotope and its interaction with apparently unrelated plasma conditions has remained largely unexplained and it has become one of the main unsolved issues. By means of numerical studies based on the gyrokinetic theory, we quantitatively show how the plasma microturbulence depends on the isotope mass through nonlinear multiscale microturbulence effects i…
Compared to present experiments, tokamak and stellarator reactors will be subject to higher heat loads, sputtering, erosion and subsequent coating, tritium retention, higher neutron fluxes, and a number of radiation effects. Additionally, neutral beam penetration in tokamak reactors will only be limited to the plasma edge. As a result, several optical, beam-based and magnetic diagnostics of today's plasmas might not be applicable to tomorrow's reactors, but the present discussion suggests that reactors could largely rely on microwave diagnostics, including techniques based on mode conversions …
The concept of available energy of a collisionless plasma is discussed in the context of magnetic confinement. The available energy quantifies how much of the plasma energy can be converted into fluctuations (including nonlinear ones) and is thus a measure of plasma stability, which can be used to derive linear and nonlinear stability criteria without solving an eigenvalue problem. In a magnetically confined plasma, the available energy is determined by the density and temperature profiles as well as the magnetic geometry. It also depends on what constraints limit the possible forms of plasma …
We construct a model for the turbulence near the X-point of a Tokamak device and, under suitable assumptions, we arrive to a closed equation for the electric field potential fluctuations. The analytical and numerical analysis is focused on a reduced two-dimensional formulation of the dynamics, which allows a direct mapping to the incompressible Navier-Stokes equation. The main merit of this study is to outline how the turbulence near the X-point, in correspondence to typical operation conditions of medium and large size Tokamaks, is dominated by the enstrophy cascade from large to smaller spat…
We derive exact solutions of a linear form of the Grad-Shafranov (GS) equation, including incompressible equilibrium flow, using ansatz-based similarity reduction methods. The linearity of the equilibrium equation allows linear combinations of solutions in order to obtain axisymmetric MHD equilibria with closed and nested magnetic surfaces which are favorable for the effective confinement of laboratory plasmas. In addition, employing the same reduction methods we obtain analytical solutions for several non-linear forms of the GS equation. In this context analytic force-free solutions in both l…
The electromagnetic theory of the strongly driven ion-temperature-gradient (ITG) instability in magnetically confined toroidal plasmas is developed. Stabilizing and destabilizing effects are identified, and a critical $β_{e}$ (the ratio of the electron to magnetic pressure) for stabilization of the toroidal branch of the mode is calculated for magnetic equilibria independent of the coordinate along the magnetic field. Its scaling is $β_{e}\sim L_{Te}/R,$ where $L_{Te}$ is the characteristic electron temperature gradient length, and $R$ the major radius of the torus. We conjecture that a fast p…
Theory for a gridded inertial electrostatic confinement (IEC) fusion system is presented that shows a net energy gain is possible if the grid is magnetically shielded from ion impact. A simplified grid geometry is studied, consisting of two negatively-biased coaxial current-carrying rings, oriented such that their opposing magnetic fields produce a spindle cusp. Our analysis indicates that better than break-even performance is possible even in a deuterium-deuterium system at bench-top scales. The proposed device has the unusual property that it can avoid both the cusp losses of traditional mag…
We propose a new mechanism for the generation of zonal flows in magnetically confined plasmas, complementing previous theories based on a modulational instability. We derive a new conservation law that operates in the regime of weakly nonlinear dynamics, and show that it serves to focus the inverse cascade of turbulent drift wave energy into zonal flows. This mechanism continues to operate in the absence of the separation of dynamical scales typically assumed in instability calculations.
It is shown, using results of measurements of ion saturation current in the plasma edges of different magnetic fusion confinement devices (tokamaks and stellarators), that the plasma dynamics in the edges is dominated by distributed chaos with spontaneously broken translational symmetry at low magnetic field, and with spontaneously broken reflexional symmetry (by helical solitons) at high magnetic field.
Conceptual design of Thomson scattering system with high wavelength resolution in magnetically confined plasmas for electron phase-space measurements
National Institute for Fusion Science（国立研究开发法人核融合科学研究所）；Division of Quantum Science and Engineering, Graduate School of Engineering, Hokkaido University（北海道大学工学研究科量子科学与工程专攻）；The Graduate University for Advanced Studies (SOKENDAI)（综合研究大学院大学）；Graduate School of Science, Nagoya University（名古屋大学理学研究科）
Significant progress has been made towards laser-driven fusion ignition via different schemes, including direct and indirect central ignition, fast ignition, shock ignition, and impact ignition schemes. However, to reach ignition conditions, there are still various technical and physical challenges to be solved for all these schemes. Here, our multi-dimensional integrated simulation shows that the fast-ignition conditions could be achieved when two 2.8 petawatt heating laser pulses counter-propagate along a 3.5 kilotesla external magnetic field. Within a period of 5 picoseconds, the laser puls…
We consider the tilting instability of a magnetically confined spheromak using 3D MHD and relativistic PIC calculations with an application to astrophysical plasmas, specifically those occurring in magnetar magnetospheres. The instability is driven by the counter alignment of the spheromak's intrinsic magnetic dipole with the external magnetic field. Initially the spheromak rotates - tilts - trying to lower its magnetic potential energy. As a result a current sheet forms between the internal magnetic field of a spheromak and the confining field. Magnetic reconnection sets in; this leads to the…
A first-principles method to calculate the critical temperature gradient for the onset of the ion-temperature-gradient mode (ITG) in linear gyrokinetics is presented. We find that conventional notions of the connection length previously invoked in tokamak research should be revised and replaced by a generalized correlation length to explain this onset in stellarators. Simple numerical experiments and gyrokinetic theory show that localized "spikes" in shear, a hallmark of stellarator geometry, are generally insufficient to constrain the parallel correlation length of the mode. ITG modes that lo…
We investigate the intermittency of magnetic turbulence as measured in Reversed Field Pinch plasmas. We show that the Probability Distribution Functions of magnetic field differences are not scale invariant, that is the wings of these functions are more important at the smallest scales, a classical signature of intermittency. We show that scaling laws appear also in a region very close to the external wall of the confinement device, and we present evidences that the observed intermittency increases moving towards the wall.
A Unified theory of transport barriers (TBs) in magnetically confined systems
Institute for Fusion Studies, The University of Texas at Austin（德克萨斯大学奥斯汀分校聚变研究所）；Department of Mathematics, The University of Tokyo（东京大学数学系）；ExoFusion
Recently, it has been proposed that the turbulent fluctuations measured in a linear plasma device could be described as a superposition of uncorrelated Lorentzian pulses with a narrow distribution of durations, which would provide an explanation for the reported quasi-exponential power spectra. Here, we study the applicability of this proposal to edge fluctuations in toroidal magnetic confinement fusion plasmas. For the purpose of this analysis, we introduce a novel wavelet-based pulse detection technique that offers important advantages over existing techniques. It allows extracting the prope…
In the presented field line map approach the simulation domain of a tokamak is covered with a cylindrical grid, which is Cartesian within poloidal planes. Standard finite-difference methods can be used for the discretisation of perpendicular (w.r.t.~magnetic field lines) operators. The characteristic flute mode property $\left(k_{\parallel}\ll k_{\perp}\right)$ of structures is exploited computationally by a grid sparsification in the toroidal direction. A field line following discretisation of parallel operators is then required, which is achieved via a finite difference along magnetic field …
We derive the differential equation governing the asymptotic quasi-stationary states of the two dimensional plasma immersed in a strong confining magnetic field and of the planetary atmosphere. These two systems are related by the property that there is an intrinsic constant length: the Larmor radius and respectively the Rossby radius and a condensate of the vorticity field in the unperturbed state related to the cyclotronic gyration and respectively to the Coriolis frequency. Although the closest physical model is the Charney-Hasegawa-Mima (CHM) equation, our model is more general and is rela…
We present Aurora, an open-source package for particle transport, neutrals and radiation modeling in magnetic confinement fusion plasmas. Aurora's modern multi-language interface enables simulations of 1.5D impurity transport within high-performance computing frameworks, particularly for the inference of particle transport coefficients. A user-friendly Python library allows simple interaction with atomic rates from the Atomic Data and Atomic Structure database as well as other sources. This enables a range of radiation predictions, both for power balance and spectroscopic analysis. We discuss …
Based on a stochastic model for intermittent fluctuations in the boundary region of magnetically confined plasmas, an expression for the level crossing rate is derived from the joint distribution of the process and its derivative. From this the average time spent by the process above a certain threshold level is obtained. This provides novel predictions of plasma-wall interactions due to transient transport events associated with radial motion of blob-like structures in the scrape-off layer.
The turbulence in magnetically confined fusion plasmas has important and non-trivial effects on the quality of the energy confinement. These effects are hard to make a quantitative assessment of analytically. The problem investigated in this article is the transport of energy and particles, in particular impurities, in a Tokamak plasma. Impurities from the walls of the plasma vessel cause energy losses if they reach the plasma core. It is therefore important to understand the transport mechanisms to prevent impurity accumulation and minimize losses. This is an area of research where turbulence…
The transition dynamics from the low (L) to the high (H) confinement mode in magnetically confined plasmas is investigated using a first-principles four-field fluid model. Numerical results are in close agreement with measurements from the Experimental Advanced Superconducting Tokamak - EAST. Particularly, the slow transition with an intermediate dithering phase is well reproduced by the numerical solutions. Additionally, the model reproduces the experimentally determined L-H transition power threshold scaling that the ion power threshold increases with increasing particle density. The results…
This work explores the potential of an information-theoretical causality detection method for unraveling the relation between fluctuating variables in complex nonlinear systems. The method is tested on some simple though nonlinear models, and guidelines for the choice of analysis parameters are established. Then, measurements from magnetically confined fusion plasmas are analyzed. The selected data bear relevance to the all-important spontaneous confinement transitions often observed in fusion plasmas, fundamental for the design of an economically attractive fusion reactor. It is shown how the…
A novel magnetic confined fusion scheme for the fusion reactor is proposed in this paper. A simple numerical estimation shows that ignition of D-T plasma can be achieved in tokamak with only OH heating by major and minor radius adiabatic compression. The density and temperature of compressed plasma can reach 1-3*10^22/m^3 and 15-25keV, respectively. Alternating current with adiabatic compression pulse of ACACT with R0 = 1.8m can deliver 400MW fusion power.
We present first principles simulations of the direct collisionless coupling of the free energy of fusion-born ions into electron current in a magnetically confined fusion plasma. These simulations demonstrate, for the first time, a key building block of some "alpha channelling" scenarios for tokamak experiments. A fully self-consistent electromagnetic 1D3V particle-in-cell code is used to evolve a parallel drifting ring-beam distribution of 3MeV protons in a 10keV thermal deuterium-electron plasma with realistic mass ratio. Collective instability gives rise to electromagnetic field activity i…
We report on experiments in which magnetically driven radiatively cooled plasma jets were produced by a 1 MA, 250 ns current pulse on the MAGPIE pulsed power facility. The jets were driven by the pressure of a toroidal magnetic field in a ''magnetic tower'' jet configuration. This scenario is characterized by the formation of a magnetically collimated plasma jet on the axis of a magnetic ''bubble'', confined by the ambient medium. The use of a radial metallic foil instead of the radial wire arrays employed in our previous work allows for the generation of episodic magnetic tower outflows which…
Our analysis of the model [J. Phys.: Conf. Ser. 941 (2017) 012008] elaborated for interpreting the initial stage of the fast nonlocal transport events, which exhibit immediate response, in the heat diffusion time scale, of the spatial profile of electron temperature to its local perturbation, shows that the nonlocal transport by electromagnetic (EM) waves needs too high reflectivity of vacuum vessel walls to describe the experimental data. Here we try another model, which assumes high internal reflections and is compatible with the "wild cable" transport of TEM waves along magnetically-bound s…
Magnetic confinement fusion researches are an approach to demonstrate the feasibility of nuclear fusion power for energy production. In these experiments, mega-watt range power Radio-Frequency waves, from tens of MHz to hundreds of GHz, are injected into magnetically confined plasmas in order to increase its temperature and to extend its duration. These RF systems are subjected to the magnetic field environment of the experiments, ranging from few tenth of Tesla to Tesla, and various orientations depending of their locations. As these RF systems made of copper, silver or ceramics are located i…
JOREK is a massively parallel fully implicit non-linear extended MHD code for realistic tokamak X-point plasmas. It has become a widely used versatile code for studying large-scale plasma instabilities and their control developed in an international community. This article gives a comprehensive overview of the physics models implemented, numerical methods applied for solving the equations and physics studies performed with the code. A dedicated section highlights some of the verification work done for the code. A hierarchy of different physics models is available including a free boundary and …
Nuclear fusion offers the potential for being a near limitless energy source by fusing together deuterium and tritium nuclei to form helium inside a plasma burning at 100 million kelvin. However, scientific and engineering challenges remain. This paper describes how such a plasma can be confined on Earth and discusses the similarities and differences with fusion in stars. It focusses on the magnetic confinement technique and, in particular, the method used in a tokamak. The confinement achieved in the equilibrium state is reviewed and it is shown how the confinement can be too good, leading to…
Intermittent fluctuations in the boundary of magnetically confined plasmas are investigated by numerical turbulence simulations of a reduced fluid model describing the evolution of the plasma density and electric drift vorticity in the two-dimensional plane perpendicular to the magnetic field. Two different cases are considered, one describing resistive drift waves in the edge region and another including only the interchange instability due to unfavorable magnetic field curvature in the scrape-off layer. Analysis of long data time series obtained by single-point recordings are compared to pre…
Spontaneous transport barrier generation at the edge of a magnetically confined plasma is investigated. To this end, a model of electrostatic turbulence in three-dimensional geometry is extended to account for the impact of friction between trapped and passing particles on the radial electric field. Non-linear flux-driven simulations are carried out, and it is shown that considering the radial and temporal variations of the neoclassical friction coefficients allows for a transport barrier to be generated above a threshold of the input power.
Past and ongoing research activities at the Heidelberg heavy-ion storage-ring TSR are reviewed which aim at providing accurate absolute rate coefficients and cross sections of atomic collision processes for applications in astrophysics and magnetically confined fusion. In particular, dielectronic recombination and electron impact ionization of iron ions are discussed as well as dielectronic recombination of tungsten ions.
Atomic Beam Probe (ABP) is an extension of the routinely used Beam Emission Spectroscopy (BES) diagnostic for plasma edge current fluctuation measurement at magnetically confined plasmas. Beam atoms ionized by the plasma are directed to a curved trajectory by the magnetic field and may be detected close to the wall of the device. The arrival location and current distribution of the ions carry information about the plasma current distribution, the density profile and the electric potential in the plasma edge. This paper describes a micro-Faraday cup matrix detector for the measurement of the fe…
Fast particle-driven waves in the ion cyclotron frequency range (ion cyclotron emission or ICE) have provided a valuable diagnostic of confined and escaping fast ions in many tokamaks. This is a passive, non-invasive diagnostic that would be compatible with the high radiation environment of deuterium-tritium plasmas in ITER, and could provide important information on fusion α-particles and beam ions in that device. In JET, ICE from confined fusion products scaled linearly with fusion reaction rate over six orders of magnitude and provided evidence that α-particle confinement was close to class…
Neutron penumbral imaging technique has been successfully used as the diagnosis method in Inertial Confined Fusion. To help the design of the imaging systems in the future in CHINA. We construct the Monte carlo imaging system by Geant4. Use the point spread function from the simulation and decode algorithm (Lucy-Rechardson algorithm) we got the recovery image.
Turbulent plasmas notably self-organize to higher energy states upon application of additional free energy sources or modification of edge operating conditions. Mechanisms whereby such bifurcations occur have been actively debated for decades. Enhanced confinement occurs at the plasma edge, where a shortfall of predicted turbulence intensity has been puzzling scientists for decades. We show, from the primitive kinetic equations that both problems are connected and that interplay of confined plasma turbulence with its material boundaries is essential to curing the shortfall of predicted turbule…
The phenomena of nonlocal transport in magnetically confined plasma are theoretically analyzed. A hybrid model is proposed, which brings together the notion of inverse energy cascade, typical of drift-wave- and two-dimensional fluid turbulence, and the ideas of avalanching behavior, associable with self-organized critical (SOC) behavior. Using statistical arguments, it is shown that an amplification mechanism is needed to introduce nonlocality into dynamics. We obtain a consistent derivation of nonlocal Fokker-Planck equation with space-fractional derivatives from a stochastic Markovian proces…
Fusion energy will be the ultimate clean energy source for mankind. One of the most visible concerns of the future fusion device is the threat of deleterious runaway electrons (REs) produced during unexpected disruptions of the fusion plasma. Both efficient long-term algorithms and super-large scale computing power are necessary to reveal the complex dynamics of REs in a realistic fusion reactor. In the present study, we deploy the world's fastest supercomputer, Sunway TaihuLight, and the newly developed relativistic volume-preserving algorithm to carry out long-term particle simulations of 10…
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…
Thermonuclear reactors hold a great promise for the future of Humankind. Within Tokamak and Stellarator reactors, plasma is confined by twisted magnetic fields. Reactors which produce fusion energy have existed since Princeton Large Torus Tokamak in 1978, nevertheless in all reactors built up to now, energy loss from plasma vastly exceeded fusion energy production. In order for a thermonuclear power plant to run, generated fusion energy must significantly exceed energy loss by the plasma. There are four processes by which plasma looses energy -- neutron radiation, Bremsstrahlung radiation, syn…
A new approach to high pressure magnetically-confined plasmas is necessary to design efficient fusion devices. This paper presents an equilibrium combining two solutions of the Grad-Shafranov equation, which describes the magnetohydrodynamic equilibrium in toroidal geometry. The outer equilibrium is paramagnetic and confines the inner equilibrium, whose strong diamagnetism permits to balance large pressure gradients. The existence of both equilibria in the same volume yields a dual equilibrium structure. Their combination also improves free-boundary mode stability.
