A novel efficient solver for Ampere's equation in general toroidal topologies based on singular value decomposition techniques

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.This research has been sponsored in part by the Ministerio de Economía y Competitividad (MINECO) of Spain under Project No. ENE2015-68265-P. Use have also been made of Uranus, a supercomputer cluster located at Universidad Carlos III de Madrid (Spain) funded jointly by EU FEDER Project No. UNC313-4E-2361, by the Ministerio de Economía, Industria y Competitividad (MICINN) via the National Research Project No. ENE2009-12213-C03-03 and by the Ministerio de Economía y Competitividad (MINECO) via the National Research Project Nos. ENE2012-33219 and ENE2012-31753

Board of European Students of Technology

Ponencia presentada en la Jornada de Innovación Docente 2019: metodologías activas en el aula, celebrada el 17 de junio de 2019 en la Universidad Carlos III de Madrid

Bootstrap current control studies in the Wendelstein 7-X stellarator using the free-plasma-boundary version of the SIESTA MHD equilibrium code

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.Research was funded in part by the Spanish National Project No. ENE2015-68265. Research carried in part at the Max-PlanckInstitute for Plasma Physics in Greifswald (Germany), whose hospitality is gratefully acknowledged. SIESTA free-boundary runs have been carried out in Uranus, a supercomputer cluster located at Universidad Carlos III de Madrid and funded jointly by EU-FEDER funds and by the Spanish Government via the National Projects No. UNC313-4E-2361, No. ENE2009-12213- C03-03, No. ENE2012-33219, and No. ENE2012-31753

Extension of the SIESTA MHD equilibrium code to free-plasma-boundary problems

is a recently developed MHD equilibrium code designed to perform fast and accurate calculations of ideal MHD equilibria for three-dimensional magnetic configurations. Since SIESTA does not assume closed magnetic surfaces, the solution can exhibit magnetic islands and stochastic regions. In its original implementation SIESTA addressed only fixed-boundary problems. That is, the shape of the plasma edge, assumed to be a magnetic surface, was kept fixed as the solution iteratively converges to equilibrium. This condition somewhat restricts the possible applications of SIESTA. In this paper, we discuss an extension that will enable SIESTA to address free-plasma-boundary problems, opening up the possibility of investigating problems in which the plasma boundary is perturbed either externally or internally. As an illustration, SIESTA is applied to a configuration of the W7-X stellarator.This research was funded in part by the Ministerio de Economía, Industria y Competitividad of Spain, Grant No. ENE2015-68265. This research was carried out in part at the Max-Planck-Institute for Plasma Physics in Greifswald (Germany), whose hospitality is gratefully acknowledged. This research was supported in part by the U.S. Department of Energy, Office of Fusion Energy Sciences under Award DE-AC05-00OR22725. SIESTA runs have been carred out in Uranus, a supercomputer cluster located at Universidad Carlos III de Madrid and funded jointly by the European Regional Development Funds (EU-FEDER) Project No. UNC313-4E-2361, and by the Ministerio de Economía, Industria y Competitividad via the National Project Nos. ENE2009-12213-C03-03, ENE2012-33219, and ENE2012-31753

Quasi-symmetry and the nature of radial turbulent transport in quasi-poloidal stellarators

Quasi-symmetric configurations have a better neoclassical confinement compared to that of standard stellarators. The reduction of the neoclassical viscosity along the direction of quasi-symmetry should facilitate the self-generation of zonal flows and, consequently, the mitigation of turbulent fluctuations and the ensuing radial transport. Therefore, it is expected that quasi-symmetries should also result in better confinement properties regarding radial turbulent transport. In this paper we show that, at least for quasi-poloidal configurations, the influence of quasi-symmetry on radial transport exceeds the expected reduction of fluctuation levels and associated effective transport coefficients, and that the intimate nature of transport itself is affected. In particular, radial turbulent transport becomes increasingly subdiffusive as the degree of quasi-symmetry becomes larger. This behavior is somewhat reminiscent of what has been previously reported in tokamaks with strong radially sheared zonal flows. Published by AIP Publishing.Research funded in part by the Spanish National Project Nos. ENE2012-33219 and ENE2012-31753. Research supported in part by the DOE Office of Science Grant No. DE-FG02-04ER5741 at the University of Alaska. Research carried out in part at the Institüt für Plasmaphysik of the Max-Planck Institüt in Greifswald (Germany), whose hospitality is gratefully acknowledged. Fruitful interactions with members of the ABIGMAP research network, funded by the Spanish National Project No. MAT2015-69777-REDT, is also acknowledged. Gene simulations have been possible thanks in part to a continued grant (Nos. FI-2014-1-0021, FI-2014-2-0026, FI-2014-3-0012, and FI-2015-1-0011) to use resources from the MareNostrum supercomputer at BSC (Barcelona, Spain). Gene and TRACER runs have also been carried out in Uranus, a supercomputer cluster located at Universidad Carlos III de Madrid (Spain) funded jointly by EU FEDER funds and by the Spanish Government via the National Project Nos. UNC313-4E-2361, ENE2009-12213-C03-03, ENE2012-33219, and ENE2012-31753

Reconstrucción de la función de distribución electrónica mediante la emisión ciclotrónica electrónica en plasma de fusión

Tesis doctoral inédita leida en la Universidad Autónoma de Madrid, Facultad de Física Teórica. Fecha de lectura: 24-11-199

Effect of non axisymmetric perturbations on the ambipolar ᵣ and neoclassical particle flux inside the ITER pedestal region

The transport dynamics of impurities in the pedestal region of ITER plasmas is of crucial interest since this regulates the penetration of impurities from the edge into the core plasma, where an excessive accumulation of impurities can degrade their fusion performance. In the pedestal region of H-mode tokamak plasmas anomalous transport is highly reduced and impurity transport is found to be well described by neoclassical theory. Under these conditions, perturbations to the axisymmetric tokamak geometry can strongly affect both radial electric field and particle transport. In this work, we describe the results of numerical studies performed to quantify the effects on the pedestal ambipolar electric field and radial particle fluxes of the non-axisymmetric fields, associated with both the intrinsic toroidal field ripple and extrinsic fields applied for ELM control, for ITER Q = 10 plasma conditions with emphasis on high Z impurity transport. It is found that the effect of the ITER toroidal field ripple on high Z impurity transport is negligible. On the contrary, extrinsic three-dimensional fields applied for ELM control cause a strong modification of the pedestal ambipolar electric (to less negative values) and the appearance of multi-valued solutions for the pedestal electric field, analogue to core stellarator transport significantly increasing the outward character of neoclassical pedestal transport for both the main plasma ions (D and T in ITER) and high Z impurities, suggesting a strong modification of the background plasma profiles. Finally, it is found that, for the Z impurity, its quantitative evaluation has uncertainties (with important implications for the radial ow direction) associated with the high poloidal Mach number ~ 1, due to the high pedestal electric field...

Non-diffusive nature of collisionless alfa-particle transport: Dependence on toroidal symmetry in stellarator geometries

An adequate confinement of -particles is fundamental for the operation of future fusion powered reactors. An even more critical situation arises for stellarator devices, whose complex magnetic geometry can substantially increase -particle losses. A traditional approach to transport evaluation is based on a diffusive paradigm; however, a growing body of literature presents a considerable amount of examples and arguments toward the validity of non-diffusive transport models for fusion plasmas, particularly in cases of turbulent driven transport [R. Sánchez and D. E. Newman, Plasma Phys. Controlled Fusion 57, 123002 (2015)]. Likewise, a recent study of collisionless -particle transport in quasi-toroidally symmetric stellarators [A. Gogoleva et al., Nucl. Fusion 60, 056009 (2020)] puts the diffusive framework into question. In search of a better transport model, we numerically characterized and quantified the underlying nature of transport of the resulting -particle trajectories by employing a whole set of tools, imported from the fractional transport theory. The study was carried out for a set of five configurations to establish the relation between the level of the magnetic field toroidal symmetry and the fractional transport coefficients, i.e., the Hurst H, the spatial α, and the temporal β exponents, each being a merit of non-diffusive transport. The results indicate that the -particle ripple-enhanced transport is non-Gaussian and non-Markovian. Moreover, as the degree of quasi-toroidal symmetry increases, it becomes strongly subdiffusive, although the validity of the fractional model itself becomes doubtful in the limiting high and low symmetry casesThis work was supported, in part, by Spanish Project No. ENE2012–33219, Project No. SIMTURB-CM-UC3M from the Convenio Plurianual Comunidad de Madrid, Universidad Carlos III de Madrid, and the Erasmus Mundus Program: International Doctoral College in Fusion Science and Engineering FUSION-DC. Part of this research was carried out at the Max-Planck Institute for Plasma Physics in Greifswald (Germany), whose hospitality is gratefully acknowledged. MOCA calculations were done in Uranus, a supercomputer cluster located at Universidad Carlos III de Madrid and jointly funded by EU-FEDER and the Spanish Government via Project Nos. UNC313-4E-2361, ENE2009-12213-C03-03, ENE2012-33219, and ENE2015-68265