Abstract
The aim of this study is to analyze the effect of the neutral beam injector (NBI) operation regime on the saturation phase of the Alfven Eigenmodes (AEs) in DIII-D plasma. The analysis is ...done using the linear and nonlinear versions of the gyro-fluid code FAR3d. A set of parametric analyses are performed modifying the nonlinear simulation EP
β
(NBI injection power), EP energy (NBI voltage) and the radial location of the EP density profile gradient (NBI radial deposition). The analysis indicates a transition from the soft (local plasma relaxation) to the hard MHD (global plasma relaxation) limit if the simulation EP
β
⩾
0.02
, leading to bursting MHD activity caused by radial AEs overlapping. MHD bursts cause an enhancement of the EP transport showing ballistic-like features as avalanche-like events. Simulations in the soft MHD limit show an increment of the EP density gradient as the EP
β
increases. On the other hand, there is a gradient upper limit in the hard MHD limit, consistent with the critical-gradient behavior. AEs induce shear flows and zonal current leading to the deformation of the flux surfaces and the safety factor profile, respectively, particularly strong for the simulation in the hard MHD limit. Simulations in the hard MHD regime show a decrease of the AE frequency in the saturation phase; this is caused by the destabilization of a transitional mode between a
9
/
3
−
10
/
3
TAE and a
9
/
3
RSAE that may explain the AE frequency down-sweeping observed in some DIII-D discharges. Reducing the EP energy in the nonlinear simulations leads to a weakening of the plasma perturbation. On the other hand, increasing the EP energy causes the opposite effect. Nonlinear simulations of off-axis NBI profiles indicate a lower plasma perturbation as the EP density gradient is located further away from the magnetic axis.
Parareal is a recent algorithm able to parallelize the time dimension in spite of its sequential nature. It has been applied to several linear and nonlinear problems and, very recently, to a ...simulation of fully-developed, two-dimensional drift wave turbulence. The mere fact that parareal works in such a turbulent regime is in itself somewhat unexpected, due to the characteristic sensitivity of turbulence to any change in initial conditions. This fundamental property of any turbulent system should render the iterative correction procedure characteristic of the parareal method inoperative, but this seems not to be the case. In addition, the choices that must be made to implement parareal (division of the temporal domain, election of the coarse solver and so on) are currently made using trial-and-error approaches. Here, we identify the mechanisms responsible for the convergence of parareal of these simulations of drift wave turbulence. We also investigate which conditions these mechanisms impose on any successful parareal implementation. The results reported here should be useful to guide future implementations of parareal within the much wider context of fully-developed fluid and plasma turbulent simulations.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPUK
•A new fast method is proposed to solve Ampere's equation in toroidal domains.•The method uses a mixed spectral – difference discretization.•A fast solver is found using the block structure of the ...involved matrices and SVD decomposition techniques.•The solution magnetic field has a zero divergence up to machine precision.•A successful comparison with an integral method is carried out for the case of W7-X stellarator.
A new method is proposed to solve Ampere's equation in an arbitrary toroidal domain in which all currents are known, given proper boundary conditions for the magnetic vector potential. The novelty of the approach lies in the application of singular value decomposition (SVD) techniques to tackle the difficulties caused by the kernel associated by the curl operator. This kernel originates physically due to the magnetic field gauge. To increase the efficiency of the solver, the problem is represented by means of a dual finite difference-spectral scheme in arbitrary generalized toroidal coordinates, which permits to take advantage of the block structure exhibited by the matrices that describe the discretized problem. The result is a fast and efficient solver, up to three times faster than the double-curl method in some cases, that provides an accurate solution of the differential form of Ampere law while guaranteeing a zero divergence of the resulting magnetic field down to machine precision.
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Parareal is an iterative algorithm that, in effect, achieves temporal decomposition for a time-dependent system of differential or partial differential equations. A solution is obtained in a shorter ...wall-clock time, but at the expense of increased compute cycles. The algorithm combines a fine solver that solves the system to acceptable accuracy with an approximate coarse solver. The critical task for the successful implementation of parareal on any system is the development of a coarse solver that leads to convergence in a small number of iterations compared to the number of time slices in the full time interval, and is, at the same time, much faster than the fine solver. Very fast coarse solvers may not lead to sufficiently rapid convergence, and slow coarse solvers may not lead to significant gains even if the number of iterations to convergence is satisfactory. We find that the difficulty of meeting these conflicting demands can be substantially eased by using a data-driven, event-based implementation of parareal. As a result, tasks for one iteration do not wait for the previous iteration to complete, but are started when the needed data are available. For given convergence properties, the event-based approach relaxes the speed requirements on the coarse solver by a factor of ∼K, where K is the number of iterations required for a converged solution. This may, for many problems, lead to an efficient parareal implementation that would otherwise not be possible or would require substantial coarse solver development. In addition, the framework used for this implementation executes a task when the data dependencies are satisfied and computational resources are available. This leads to improved computational efficiency over previous approaches that pipeline or schedule groups of tasks to a particular processor or group of processors.
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Large electrical transmission networks are susceptible to undergo very large blackouts due to cascading failures, with a very large associated economical cost. In this work we propose segmenting ...large power grids using controllable lines, such as high-voltage direct-current lines, to reduce the risk of blackouts. The method consists in modifying the power flowing through the lines interconnecting different zones during cascading failures in order to minimize the load shed. As a result, the segmented grids have a substantially lower risk of blackouts than the original network, with reductions up to 60% in some cases. The control method is shown to be specially efficient in reducing blackouts affecting more than one zone.
•Controlling the power flowing through interconnections in power grids during a cascading failure can reduce the size and risk of blackouts.•The control consists in choosing the impedance of the lines interconnecting different zones in such a way that minimizes the load shed in each dispatch.•Contrary to other control methods, the one proposed in this work reduces the size of blackouts without increasing their frequency.•In terms of risk reduction, segmenting large power grids in zones of similar size works better.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPUK, ZAGLJ, ZRSKP
The recently developed free-plasma-boundary version of the SIESTA MHD equilibrium code (Hirshman et al 2011 Phys. Plasmas 18 062504; Peraza-Rodriguez et al 2017 Phys. Plasmas 24 082516) is used for ...the first time to study scenarios with considerable bootstrap currents for the Wendelstein 7-X (W7-X) stellarator. Bootstrap currents in the range of tens of kAs can lead to the formation of unwanted magnetic island chains or stochastic regions within the plasma and alter the boundary rotational transform due to the small shear in W7-X. The latter issue is of relevance since the island divertor operation of W7-X relies on a proper positioning of magnetic island chains at the plasma edge to control the particle and energy exhaust towards the divertor plates. Two scenarios are examined with the new free-plasma-boundary capabilities of SIESTA: a freely evolving bootstrap current one that illustrates the difficulties arising from the dislocation of the boundary islands, and a second one in which off-axis electron cyclotron current drive (ECCD) is applied to compensate the effects of the bootstrap current and keep the island divertor configuration intact. SIESTA finds that off-axis ECCD is indeed able to keep the location and phase of the edge magnetic island chain unchanged, but it may also lead to an undesired stochastization of parts of the confined plasma if the EC deposition radial profile becomes too narrow.
Parareal is a recent time parallelization algorithm based on a predictor–corrector mechanism. Recently, it has been applied for the first time to a fully-developed plasma turbulent simulation, and a ...qualitative understanding of how parareal converges exists for this case. In this paper, we construct an analytical framework of the process of convergence that should be applicable to parareal simulations of general turbulent systems. This framework allows one to gain a quantitative understanding of the dependence of the convergence on the physics of the problem and the choices that must be made to implement parareal. The analytical knowledge provided by this new framework can be used to optimize the implementation of parareal. We illustrate the inner workings of the framework and demonstrate its predictive capabilities by applying it to the modeling of the parareal convergence of drift-wave plasma turbulent simulations.
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Abstract The most relevant features of FLIPEC (Free fLow Iterative Plasma Equilibrium Code) are presented. This new code iteratively calculates free-boundary, axisymmetric ideal MHD equilibria with ...arbitrary poloidal and toroidal plasma flows. FLIPEC is a mature code that has emerged from a complete overhaul of a previous version (F-Torija Daza 2022 et al Nucl. Fusion 62 126044). It uses a (inverse) curvilinear coordinate representation for the Grad–Shafranov–Bernoulli equation system, which allows FLIPEC to extend its free-boundary capabilities to arbitrary plasma shapes and removes many limitations with regards to the distance between plasma and external coils. Run-time stabilization of vertical modes has also been implemented by means of artificial feedback coils. Finally, active targeting schemes have also been included. These capabilities are illustrated on two very different cases: the ITER tokamak baseline configuration and a NSTX spherical tokamak equilibrium.
An algorithm to place ghost particles across the domain boundary in the context of Smoothed Particle Hydrodynamics (SPH) is derived from basic principles, and constructed for several simple, ...three-dimensional, geometries. The performance of the algorithm is compared against the more commonly used “mirrored with respect to the local tangent plane” approach and shown to converge to it whenever the distance of the particles to the reflecting boundary is much smaller than a local measure of the surface’s curvature. The algorithm is demonstrated, tested and compared against the usual approach via simulations of a compressible flow around a cylinder, and the numerical cost of implementing it is addressed. We conclude that use of ghost particles to enforce boundary conditions is not only viable in the presence of smoothly curved boundaries, but more robust than the usual method for low-resolution scenarios.
•An algorithm to place ghost particles across curved boundaries is developed.•The algorithm is explicitly implemented in simple 3D geometries (cylinder, sphere, torus).•The results converge to the usual mirror-technique when the curvature is negligible.•The solutions were successfully tested in static and dynamical scenarios and their performance was characterised showing a clear improvement with respect to the usual method.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPUK, ZAGLJ, ZRSKP
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