Toroidal Fusion Devices Research Articles

FLARE: field line analysis and reconstruction for 3D boundary plasma modeling

Abstract The FLARE code is a magnetic mesh generator that is integrated within a suite of tools for the analysis of the magnetic geometry in toroidal fusion devices. A magnetic mesh is constructed from field line segments and permits fast reconstruction of field lines in 3D boundary plasma codes such as EMC3-EIRENE. Both intrinsically non-axisymmetric configurations (stellarators) and those with symmetry breaking perturbations of an axisymmetric equilibrium (tokamaks) are supported. The code itself is written in Modern Fortran with MPI support for parallel computing, and it incorporates object-oriented programming for the definition of the magnetic field and the material surface geometry. Extended derived types for a number of different magnetohydrodynamic equilibrium and plasma response models are implemented. The core element of FLARE is a field line tracer with adaptive step-size control, and this is integrated into tools for the construction of Poincaré maps and invariant manifolds of X-points. A collection of high-level procedures that generate output files for visualization is build on top of that. The analysis modules are build with Python frontends that facilitate customization of tasks and/or scripting of parameter scans.

Tangentially viewing phase contrast imaging for turbulence measurementsin toroidal fusion devices

Phase contrast imaging (PCI) is an established and powerful techniquefor measuring density fluctuations in plasmas and has been successfullyapplied to several fusion devices. Rooted in a concept first developed formicroscopy, PCI belongs to the category of internal-reference interferometersand has been shown to possess superior qualities among such techniques,particularly in terms of spatial linearity. In essence, it produces a true imageof fluctuations in the plane perpendicular to the propagation direction of theprobing laser beam, provided their characteristic spatial scale is smaller thanthe beam width. The measurement in itself is line-integrated and thus notspatially resolved longitudinally to the beam. However, the properties of theturbulence itself can be exploited to achieve longitudinal resolution,particularly when the beam propagates nearly tangentially to the magnetic field.This assertion has been recently rigorously tested through numericalmodeling, which has revealed significant additional complexity while confirmingthe general principle. Tangential PCI has been employed extensively in the TCVtokamak and has resulted in a rich body of work on broadband microturbulence inthe ion-temperature-gradient/trapped-electron-moderange and on geodesic acoustic modes. A similar diagnosticarrangement is also at an advanced planning stage for the new superconductingtokamak JT-60SA.

Kinetic vs magnetic chaos in toroidal plasmas: A systematic quantitative comparison

Magnetic field line chaos occurs under the presence of non-axisymmetric perturbations of an axisymmetric equilibrium and is manifested by the destruction of smooth flux surfaces formed by the field lines. These perturbations also render the particle motion, as described by the guiding center dynamics, non-integrable and, therefore, chaotic. However, the chaoticities of the magnetic field lines and the particle orbits significantly differ in both strength and radial location in a toroidal configuration, except for the case of very low-energy particles whose orbits closely follow the magnetic field lines. The chaoticity of more energetic particles, undergoing large drifts with respect to the magnetic field lines, crucially determines the confinement properties of a toroidal device but cannot be inferred from that of the underlying magnetic field. In this work, we implement the smaller alignment index method for detecting and quantifying chaos, allowing for a systematic comparison between magnetic and kinetic chaos. The efficient quantification of chaos enables the assignment of a value characterizing the chaoticity of each orbit in the space of the three constants of the motion, namely, energy, magnetic moment, and toroidal momentum. The respective diagrams provide a unique overview of the different effects of a specific set of perturbations on the entire range of trapped and passing particles, as well as the radial location of the chaotic regions, offering a valuable tool for the study of particle energy and momentum transport and confinement properties of a toroidal fusion device.

Study of Geodesic Acoustic and Alfvén Modes in Toroidal Fusion Devices (Brief Review)

Study of Geodesic Acoustic and Alfvén Modes in Toroidal Fusion Devices (Brief Review)

Kinetic simulations of collision-less plasmas in open magnetic geometries *

Laboratory plasmas in open magnetic geometries can be found in many different applications such as (a) scrape-of-layer (SOL) and divertor regions in toroidal confinement fusion devices, (b) linear divertor simulators, (c) plasma-based thrusters and (d) magnetic mirrors etc. A common feature of these plasma systems is the need to resolve, in addition to velocity space, at least one physical dimension (e.g. along flux lines) to capture the relevant physics. In general, this requires a kinetic treatment. Fully kinetic particle-in-cell (PIC) simulations can be applied but at the expense of large computational effort. A common way to resolve this is to use a hybrid approach: kinetic ions and fluid electrons. In the present work, the development of a hybrid PIC computational tool suitable for open magnetic geometries is described which includes (a) the effect of non-uniform magnetic fields, (b) finite fully-absorbing boundaries for the particles and (c) volumetric particle sources. Analytical expressions for the momentum transport in the paraxial limit are presented with their underlying assumptions and are used to validate the results from the PIC simulations. A general method is described to construct discrete particle distribution functions in a state of mirror-equilibrium. This method is used to obtain the initial state for the PIC simulation. Collisionless simulations in a mirror geometry are performed. The results show that the effect of magnetic compression is correctly described and momentum is conserved. The self-consistent electric field is calculated and is shown to modify the ion velocity distribution function in a manner consistent with analytic theory. Based on this analysis, the ion distribution function is understood in terms of a loss-cone distribution and an isotropic Maxwell-Boltzmann distribution driven by a volumetric plasma source. Finally, the inclusion of a Monte Carlo based Fokker-Planck collision operator is discussed in the context of future work.

Experimental Estimation of Dust Generation Under ELM-Like Transient Heat Loads in Divertor Plasma Simulator-2

Although plasma-facing components composed of tungsten are less likely to generate dust when compared to other materials, dust generation is still possible during severe transient phenomena in fusion devices. The generation of tungsten dusts was experimentally investigated by exposing tungsten targets to a transient heat flux factor (FHF) simulated by a high-energy pulsed laser so that the rate of dust generation would be analyzed. The rate of dust generation is observed to be increased linearly with respect to FHF: G [mg/min] = C (FEX – F0), where FEX is the experimental value of FHF, F0 is the threshold FHF, and C [mg∙m2∙s1/2/min∙MJ] = 0.0031 ± 0.0002. FHF indicates that the characteristics of dusts such as size and FHF are similar to those observed in several toroidal fusion devices. The threshold of FHF for dust generation was also observed as 41 MJ/m2∙ s1/2, which is similar to that of the international thermonuclear experimental reactor ITER (50 MJ/m2∙ s1/2).

Electron Bernstein wave excitation by beating of two copropagating super-Gaussian laser beam in a collisional nanocluster plasma

An analytic formalism is developed to study electron Bernstein wave excitation by two copropagating high power super-Gaussian laser beams in a collisional nanocluster plasma. The medium is assumed to contain spherical plasma plume ball of nanocluster. As the electric field of two laser beams interact with nanoclustered plasma, it would cause the beat wave frequency ω=ω1−ω2. The laser beat wave exerts a nonlinear pondermotive force on electron cloud of clustered plasma that in turns lead to excite the electron Bernstein wave in the laser field polarizations direction. The effective finite y-component of the beat wave experiences group velocity and it might cause convective losses. The spatial shape of electron Bernstein wave normalized potential and power profile promises better excitation mechanism in nanoclustered plasma as compared to only plasma medium. It is observed that excitation is much enhanced when the laser beat frequency lies near the effective plasmons frequency of nanoclustered plasma. The excitation is detuned by varying the laser mode index, clustered radius, collisional frequency, parameter b. One may apply this theory of electron Bernstein wave excitation in toroidal fusion devices.

Particle resonances in toroidal fusion devices

Resonances of high energy particles in magnetic confinement devices due to electromagnetic instabilities can strongly modify the distribution, leading to a reduction in fusion power and even discharge termination and particle loss to the device walls through avalanche. The existence of a mode particle resonance depends on properties of the equilibrium, particle trajectories, and perturbation mode harmonic content. Resonance location is a function of particle energy and equilibrium field line helicity. Different methods for finding resonance location and energy dependence are developed. The properties of resonances are discussed using examples from magnetic fusion devices. We show that if mode resonances exist at low particle energy, they very likely also exist at high energy, thus modifying high energy beam particles and fusion products. It is possible for a resonance to appear due to mode induced orbit helicity modification when it is forbidden at low mode amplitude.

Quasi-geometric integration of guiding-center orbits in piecewise linear toroidal fields

A numerical integration method for guiding-center orbits of charged particles in toroidal fusion devices with three-dimensional field geometry is described. Here, high order interpolation of electromagnetic fields in space is replaced by a special linear interpolation, leading to locally linear Hamiltonian equations of motion with piecewise constant coefficients. This approach reduces computational effort and noise sensitivity, while the conservation of total energy, magnetic moment and phase space volume is retained. The underlying formulation treats motion in piecewise linear fields exactly and, thus, preserves the non-canonical symplectic form. The algorithm itself is only quasi-geometric due to a series expansion in the orbit parameter. For practical purposes, an expansion to the fourth order retains geometric properties down to computer accuracy in typical examples. When applied to collisionless guiding-center orbits in an axisymmetric tokamak and a realistic three-dimensional stellarator configuration, the method demonstrates stable long-term orbit dynamics conserving invariants. In Monte Carlo evaluation of transport coefficients, the computational efficiency of quasi-geometric integration is an order of magnitude higher than with a standard fourth order Runge–Kutta integrator.

Low-power-threshold parametric decay instabilities of powerful microwave beams in toroidal fusion devices

We discuss the experimental conditions responsible for a drastic decrease in the power threshold of parametric decay instabilities under auxiliary electron cyclotron resonance heating (ECRH) in toroidal magnetic fusion devices when the upper hybrid (UH) resonance for the pump wave is absent. We show that for a finite-width pump in the presence of a nonmonotonic (hollow) density profile occurring due to plasma equilibrium in the magnetic islands or anomalous particle fluxes from the ECR layer, 3D localization of one or both daughter waves is possible. This localization leads to the full suppression of daughter wave energy losses from the decay layer and a substantial increase in the nonlinear pumping efficiency. This decreases the power threshold of nonlinear excitation, which can be easily overcome in current ECRH experiments utilizing 1 MW microwave beams. Different scenarios of extraordinary and ordinary wave decays are investigated. The secondary decays of primary daughter waves and pump wave depletion are considered as the most effective mechanisms leading to the transition of primary instability to the saturation regime. The proposed theoretical model was shown to be able to describe the anomalous phenomena discovered in ECRH experiments in different toroidal fusion devices all over the world.

Application of n-Fold Rotational Symmetries to Eddy Currents Integral Model in the Time Domain

Group Theory is a powerful “tool” which has been extensively exploited to reduce the computational cost in the numerical analysis of several physical problems, including computational electromagnetics. This article proposes the extension of the application of group theory to an integral formulation of the eddy current problems in the presence of n-fold rotational symmetries. The proposed approach is applied to the eddy currents computation in toroidal fusion devices, where rotational symmetries play a key role.

Низкопороговые параметрические распадные неустойчивости мощных СВЧ-пучков в термоядерных тороидальных магнитных ловушках

Низкопороговые параметрические распадные неустойчивости мощных СВЧ-пучков в термоядерных тороидальных магнитных ловушках

Evaluation of relativistic transport coefficients and the generalized Spitzer function in devices with 3D geometry and finite collisionality

The relativistic generalization of the linearized drift kinetic equation solver NEO-2 is presented which is used for computation of neoclassical transport coefficients and the generalized Spitzer function in 3D toroidal fusion devices (tokamaks and stellarators). This upgrade allows computations of the Spitzer function playing the role of current drive efficiency in the whole experimentally relevant temperature range, from mild temperatures where finite plasma collisionality effects are important to high temperatures where relativistic effects should be taken into account. Within the Galerkin method used for problem discretization over energy, relativistic effects are included into a set of matrices constant on a flux surface. Those matrices determine coefficients of a coupled set of integro-differential equations with a reduced dimension which is of the same form as in the non-relativistic case. For energy discretization of the linearized relativistic Coulomb collision operator, it is presented in spherical momentum space variables in the symmetric integral form derived directly from Beliaev-Budker expressions. The cancellation problem pertinent to the fully analytical representation of Braams and Karney [Phys. Fluids B 1, 1355 (1989)] does not appear in this form. Examples of evaluation of relativistic transport coefficients and the Spitzer function are presented.

High detection efficiency scintillating fiber detector for time-resolved measurement of triton burnup 14 MeV neutron in deuterium plasma experiment.

The behavior of the 1 MeV triton has been studied in order to understand the alpha particle confinement property in the deuterium operation of toroidal fusion devices. To obtain time evolution of the deuterium-tritium (D-T) neutron emission rate where the secondary DT neutron emission rate is approximately 1012 n/s, we designed two high detection efficiency scintillating fiber (Sci-Fi) detectors: a 1 mm-diameter scintillation fiber-based detector Sci-Fi1 and a 2 mm-diameter scintillation fiber-based detector Sci-Fi2. The test in an accelerator-based neutron generator was performed. The result shows that the directionality of each detector is 15° and 25°, respectively. It is found that detection efficiency for DT neutrons is around 0.23 counts/n cm2 for the Sci-Fi1 detector and is around 1.0 counts/n cm2 for the Sci-Fi2 detector.

Nonlinear gyrokinetic simulation of fast ion-driven modes including continuum interaction

Energetic particle transport in toroidal magnetic confinement fusion devices can be enhanced by the particles' interaction with electromagnetic global modes. This process has been modelled numerically. The most extensive work has been with reduced models, which may use a simplified description of the bulk plasma, assuming a perturbative approximation for mode structure evolution, restrict simulation to the linear phase, or some combination. In this work, nonlinear non-perturbative simulations are performed using a fully gyrokinetic and reduced models of the bulk plasma. Previous linear investigation of a simple model tokamak case is extended to show that, at least under some conditions, dramatic qualitative differences in mode structure and saturated mode amplitude can exist due to non-perturbative response in the linear and nonlinear phases that depends upon the bulk plasma physics. This supports analytical work which has shown that the non-perturbative energetic particle response should depend upon the magnetic geometry and kinetic physics. It is also shown that energetic particle modes that dominate in the linear phase can be subdominant to a non-perturbative toroidal Alfvén eigenmode-based global structure in the nonlinear phase.

Fast-ion Dα spectrum diagnostic in the EAST.

In toroidal magnetic fusion devices, fast-ion D-alpha diagnostic (FIDA) is a powerful method to study the fast-ion feature. The fast-ion characteristics can be inferred from the Doppler shifted spectrum of Dα light according to charge exchange recombination process between fast ions and probe beam. Since conceptual design presented in the last HTPD conference, significant progress has been made to apply FIDA systems on the Experimental Advanced Superconducting Tokamak (EAST). Both co-current and counter-current neutral beam injectors are available, and each can deliver 2-4 MW beam power with 50-80 keV beam energy. Presently, two sets of high throughput spectrometer systems have been installed on EAST, allowing to capture passing and trapped fast-ion characteristics simultaneously, using Kaiser HoloSpec transmission grating spectrometer and Bunkoukeiki FLP-200 volume phase holographic spectrometer coupled with Princeton Instruments ProEM 1024B eXcelon and Andor DU-888 iXon3 1024 CCD camera, respectively. This paper will present the details of the hardware descriptions and experimental spectrum.

RETRACTED: Control of heat and mass transfer processes by plasma equilibrium reconstruction in toroidal magnetic confinement nuclear fusion devices

Abstract Heat and mass transfers can be controlled by plasma equilibrium reconstruction in toroidal confinement nuclear fusion systems such as tokamaks. The Magnetohydrodynamic equilibrium in axisymmetric plasma is described by the Grad-Shafranov equation in terms of the magnetic flux. In this paper, we have proposed a new numerical solution to the Grad-Shafranov equation of an axisymmetric, transformed in quasi-cylindrical coordinates solved with the Chebyshev collocation method, when the source term (current density function) on the right hand side is quadratics as it is described by Atanasiu et al. The Chebyshev collocation method is a method for computing highly accurate numerical solutions differential equations. We have described a circular cross section of tokamak and presented numerical result of magnetic surfaces on the IR-T1 tokamak and compared the results with an analytical solution and then calculated the Shafranov shift using a minimization procedure based on the Newton method.

Study of plasma equilibrium in toroidal fusion devices using mesh-free numerical calculation method

Plasma confinement using external magnetic field is one of the successful ways leading to the controlled nuclear fusion. Development and validation of the solution process for plasma equilibrium in the experimental toroidal fusion devices is the main subject of this work. Solution of the nonlinear 2D stationary problem as posed by the Grad-Shafranov equation gives quantitative information about plasma equilibrium inside the vacuum chamber of hot fusion devices. This study suggests solving plasma equilibrium equation which is essential in toroidal nuclear fusion devices, using a mesh-free method in a condition that the plasma boundary is unknown. The Grad-Shafranov equation has been solved numerically by the point interpolation collocation mesh-free method. Important features of this approach include truly mesh free, simple mathematical relationships between points and acceptable precision in comparison with the parametric results. The calculation process has been done by using the regular and irregular nodal distribution and support domains with different points. The relative error between numerical and analytical solution is discussed for several test examples such as small size Damavand tokamak, ITER-like equilibrium, NSTX-like equilibrium, and typical Spheromak.

Non-perturbative measurement of cross-field thermal diffusivity reduction at the O-point of 2/1 neoclassical tearing mode islands in the DIII-D tokamak

Neoclassical tearing modes (NTMs) often lead to the decrease of plasma performance and can lead to disruptions, which makes them a major impediment in the development of operating scenarios in present toroidal fusion devices. Recent gyrokinetic simulations predict a decrease of plasma turbulence and cross-field transport at the O-point of the islands, which in turn affects the NTM dynamics. In this paper, a heat transport model of magnetic islands employing spatially non-uniform cross-field thermal diffusivity (χ⊥) is presented. This model is used to derive χ⊥ at the O-point from electron temperature data measured across 2/1 NTM islands in DIII-D. It was found that χ⊥ at the O-point is 1 to 2 orders of magnitude smaller than the background plasma transport, in qualitative agreement with gyrokinetic predictions. As the anomalously large values of χ⊥ are often attributed to turbulence driven transport, the reduction of the O-point χ⊥ is consistent with turbulence reduction found in recent experiments. Finally, the implication of reduced χ⊥ at the O-point on NTM dynamics was investigated using the modified Rutherford equation that predicts a significant effect of reduced χ⊥ at the O-point on NTM saturation.

Modeling and control of plasma rotation for NSTX using neoclassical toroidal viscosity and neutral beam injection

A model-based feedback system is presented to control plasma rotation in a magnetically confined toroidal fusion device, to maintain plasma stability for long-pulse operation. This research uses experimental measurements from the National Spherical Torus Experiment (NSTX) and is aimed at controlling plasma rotation using two different types of actuation: momentum from injected neutral beams and neoclassical toroidal viscosity generated by three-dimensional applied magnetic fields. Based on the data-driven model obtained, a feedback controller is designed, and predictive simulations using the TRANSP plasma transport code show that the controller is able to attain desired plasma rotation profiles given practical constraints on the actuators and the available measurements of rotation.