Major results from the first plasma campaign of the Wendelstein 7-X stellarator

After completing the main construction phase of Wendelstein 7-X (W7-X) and successfully commissioning the device, first plasma operation started at the end of 2015. Integral commissioning of plasma start-up and operation using electron cyclotron resonance heating (ECRH) and an extensive set of plasma diagnostics have been completed, allowing initial physics studies during the first operational campaign. Both in helium and hydrogen, plasma breakdown was easily achieved. Gaining experience with plasma vessel conditioning, discharge lengths could be extended gradually. Eventually, discharges lasted up to 6 s, reaching an injected energy of 4 MJ, which is twice the limit originally agreed for the limiter configuration employed during the first operational campaign. At power levels of 4 MW central electron densities reached 3 x 1019 m-3, central electron temperatures reached values of 7 keV and ion temperatures reached just above 2 keV. Important physics studies during this first operational phase include a first assessment of power balance and energy confinement, ECRH power deposition experiments, 2nd harmonic O-mode ECRH using multi-pass absorption, and current drive experiments using electron cyclotron current drive. As in many plasma discharges the electron temperature exceeds the ion temperature significantly, these plasmas are governed by core electron root confinement showing a strong positive electric field in the plasma centre.This work has been carried out within the framework of the EUROfusion Consortium and has received funding from the EURATOM research and training programme 2014-2018 under grant agreement No 633053. The views and opinions expressed herein do not necessarily reflect those of the European Commission

Characterization of α-particle transport in reactor relevant burning plasmas

Mención Internacional en el título de doctorErasmus-Mundus FUSIONNuclear fusion has the potential to provide humanity with a safe, clean, abundant, efficient and reliable energy source for the generations to come, but up to date finding a viable fusion reactor concept remains an ongoing area of research. One of the main difficulties to attain economically viable magnetically controlled thermonuclear fusion reactors is the confinement of α-particles. These α-particles are responsible of sustaining the extreme temperatures required for nuclear reactions, and their loss poses a serious threat to the reactor operational control and to its plasma-facing components. In toroidally shaped fusion devices with a non-uniform magnetic field, α-particles with small parallel velocity become trapped between areas of the high field bouncing between reection points, whose position is highly susceptible to field corrugations. With the exception of symmetric magnetic fields, like those of ideal tokamaks, these socalled trapped α-particles experience non-zero radial average drifts, which might lead to their collisionless losses. There are two principal collisionless mechanisms connecting trapped particle losses with the inhomogeneities of the confining magnetic field. The first is ripple trapping, in which particles fall into local ripples and experience strong radial drifts usually being convective (ballistic). The second mechanism is ripple induced stochastic processes with milder drifts caused by the radial motion of particle reection points, which result either in the banana tip stochastic diffusion or particle transitions, in which the particles change the orbit type near the reection points. While the mitigation of these losses is widely considered in the literature on fusion reactor designs, far too little attention was paid to the statistical characterization of the processes underlying collisionless transport of trapped α-particles, whose nature is generally considered diffusive. This thesis is intended to provide such statistical description and clarify the nature of collisionless trapped α-particle transport for reactor scale configurations in cases of broken symmetry of the underlying magnetic field. To this end, detailed analyses were performed on large ensembles of α-particle trajectories, calculated with the guiding center orbit following Monte Carlo code MOCA for several magnetic configurations: a purely toroidal model with ITER parameters and four quasi-toroidal stellarators loosely based on NCSX project with different levels of magnetic field symmetry. The simulations suggest that while the perfect toroidal magnetic field symmetry of the ITER configuration grants perfect confinement, an increasing departure from quasi-toroidal symmetry leads to faster and larger α-particle losses, most of which belong to particles born with a small parallel velocity in areas of a weak magnetic field on the outer midplane of the configurations. Based on the resulting numerical trajectories, novel techniques were developed capable to calculate the fraction of trapped α-particles and identify the orbit types. Estimates show that about a third of the particles are trapped for ITER, and a fifth for the stellarators, independently on the level of symmetry. These trapped particles mainly follow banana orbits and, to a lesser extent, potato, transition and ripple trapped orbits. Statistical analysis was done for the basic parameters of banana orbits, and it was found that the most probable banana width becomes wider, and that the most probable bouncing time becomes longer as configuration departs from toroidal symmetry. The results of the trapped particle fractions and the most probable bouncing times are in agreement with those obtained by an independent numerical procedure based on the depth of the confining magnetic field and the assumption that α-particles move along the filed lines. To that end, a new figure of merit measuring the level of toroidal symmetry was introduced. The convection velocity and the diffusion transport coefficients were estimated by two methods: using the most probable banana widths and bouncing times, and fitting the time dependence of the moments of the radial probability density functions of banana centers, which were calculated with a new algorithm based on the positions of the reection points. Their statistical analysis suggests that the collisionless transport of trapped α-particles cannot be properly described as being diffusive when the magnetic configuration departs from symmetry. The assumption that ripple-enhanced radial transport of trapped α-particles is diffusive has been extensively used to model experimental data. But it is limited to describe only Gaussian and Markovian transport processes and thus neglects correlations, memory, and spatial effects, that have recently been proved relevant for fusion plasma, especially in cases of turbulent driven transport. In this thesis, the techniques used in characterizing the non-diffusive dynamics of turbulent transport were adapted to study collisionless α-particle neoclassical transport. To build an effective transport model, α-particle trajectories were analyzed with a whole set of tools imported from fractional transport theory. Using the Eulerian propagator and Lagrangian rescale range [R=S] analysis techniques, the Hurst H, the spatial α and the temporal β exponents appearing in fractional transport theory were estimated to describe non-diffusive transport. The results for the ideal toroidally symmetric ITER ripple-less magnetic configuration analyzed by the Lagrangian [R=S] method show an almost zero Hurst exponent pointing out, as expected, to the absence of radial transport. While all perfectly confined trapped α-particles were analyzed for ITER, for the four stellarators, only the particles contributing the most to the losses were considered, i.e. α-particles that get lost in the region with the steepest slope in the loss fraction. The estimated spatial and temporal transport exponents found indicate that the underlying nature of transport is nondiffusive with non-Gaussian and non-Markovian statistics. As the level of toroidal symmetry decreases, the presence of spatial correlations, particularly strong anti-correlations, becomes more pronounced. For all stellarators, there are signs of self-similarity and significant memory effects. The agreement in the Hurst exponents, estimated by both the Lagrangian and Eulerian techniques, shows that as the level of quasitoroidal symmetry increases transport becomes strongly subdiffusive. Although, the validity of the fractional model itself becomes doubtful in the limiting high and low symmetry cases. The work presented in the thesis can be naturally extended to study the validity of the fractional transport model onto other types of confining magnetic fields and various α-particle-related effects, such as collisions, α-particle birth profiles, etc.La fusión nuclear tiene el potencial de abastecer a la humanidad con una energía segura, limpia, abundante, eficiente y fiable para las generaciones venideras, pero hasta la fecha, encontrar un concepto viable de reactor de fusión es un área de investigación en curso. Una de las mayores dificultades a la hora de conseguir reactores termonucleares económicamente viables es el confinamiento de las partículas α. Estas partículas son las encargadas de mantener las temperaturas extremas que se requieren para las reacciones nucleares y su pérdida supone una seria amenaza para la operación y control del reactor y el de sus componentes en contacto con el plasma. En dispositivos de fusión con forma toroidal y con un campo magnético no uniforme, las partículas α con una velocidad paralela pequeña, quedan atrapadas entre las zonas del campo alto, rebotando entre puntos, cuya posición es muy sensible a las ondulaciones del campo. Exceptuando los campos magnéticos simétricos, como los de los tokamaks ideales, dichas partículas α atrapadas experimentan derivas radiales promedio distintas de cero, que pueden conducir a pérdidas no colisionales. Hay dos mecanismos principales no colisionales que conectan las pérdidas de partículas atrapadas con las heterogeneidades del campo magnético confinante. El primero es el debido al ripple trapping, en el que las partículas caen en ripples locales y experimentan fuertes desviaciones radiales que generalmente son convectivas (balísticas). El segundo mecanismo consiste en procesos estocásticos inducidos por los ripples donde las leves desviaciones causadas por el movimiento radial de los puntos de rebote de las partículas dan como resultado una difusión estocástica al cambiar la trayectoria las partículas cerca de los puntos de reeflxón. Mientras que la mitigación de estas pérdidas ha sido ampliamente estudiada en la literatura relativa a los diseños de reactores de fusión, no se ha prestado mucha atención a la caracterización estadística de los procesos de transporte de las partículas α atrapadas no colisionales, cuya naturaleza en general se ha considerado difusiva. El objetivo de esta tesis es aportar dicha descripción estadística y aclarar la naturaleza del transporte de las partículas α atrapadas no colisionales en configuraciones de tipo reactor cuando hay una ruptura de simetría α en su campo magnético. Con este propósito, realizaremos análisis detallados en muestras amplias de trayectorias de partículas α calculadas con el código Monte Carlo MOCA de seguimiento de órbitas del centro guía, para varias configuraciones magnéticas: un modelo puramente toroidal con parámetros de ITER y cuatro stellarators cuasi-toroidales, inspirados en el proyecto NCSX, con diferentes niveles de simetría magnética. Las simulaciones sugieren que, si bien la perfecta simetría toroidal del campo magnético de la configuración ITER garantiza un confinamiento perfecto, una desviación creciente de la simetría cuasitoroidal conduce a mayores y más rápidas pérdidas de partículas α, la mayoría de las cuales pertenecen a partículas nacidas con un ángulo de ataque pequeño en regiones de campo magnético bajo en la zona externa del plano ecuatorial de las configuraciones. Sobre la base de las trayectorias numéricas resultantes, se desarrollaron nuevas técnicas capaces de calcular la fracción de partículas α atrapadas e identificar los tipos de órbitas. Las estimaciones muestran que alrededor de un tercio de las partículas están atrapadas para ITER, y un quinto para los stellarator, independientemente del nivel de simetría. Estas partículas atrapadas siguen principalmente órbitas de tipo banana y, en menor medida, órbitas potatoes, en tránsito y ripple trapped. En el análisis estadístico de los parámetros básicos de las órbitas banana se encontró que el ancho más probable de las bananas se hace mayor, y que el tiempo de rebote más probable se hace más largo cuando la configuración magnética carece de simetría toroidal. Los resultados de las fracciones de partículas atrapadas y los tiempos de rebote más probables están de acuerdo con los obtenidos por un procedimiento numérico independiente basado en la profundidad del campo magnético confinante y la suposición de que las partículas α se mueven a lo largo de las líneas del campo. Con este propósito, se introdujo una nueva figura de mérito que mide el nivel de simetría toroidal. Las velocidades convectivas y los coeficientes de difusión se estimaron con dos métodos: utilizando los valores más probables de los anchos de las banana y los tiempos de rebote y ajustando la dependencia temporal de la función de distribución radial de probabilidad de los centros de las órbitas de las bananas, que se calcularon con un nuevo algoritmo basado en las posiciones de los puntos de reflexión. Su análisis estadístico sugiere que el transporte de las partículas α atrapadas no colisionales no puede ser descrito como difusivo cuando la configuración magnética pierde la simetría. La suposición de que el transporte radial de partículas α atrapadas inducido por ripple es difusivo se ha utilizado ampliamente para modelar datos experimentales. No obstante, su aplicación se limita a describir solo los procesos de transporte Gaussianos y Markovianos y por lo tanto no tiene en cuenta las correlaciones, la memoria y los efectos espaciales, que recientemente han demostrado ser relevantes en plasmas de fusión, especialmente en casos de transporte turbulento. En esta tesis, las técnicas utilizadas para caracterizar la dinámica no difusiva del transporte turbulento se adaptaron para estudiar el transporte neoclásico de partículas α no colisionales. Para construir un modelo de transporte efectivo, se han analizado las trayectorias de las partículas α con un conjunto de herramientas importadas de la teoría de transporte fraccionario. Usando las técnicas de propagadores Eulerianos y el análisis [R=S] Lagrangiano, se estimaron el exponente de Hurst H y los exponentes espacial α y temporal β que aparecen en la teoría del transporte fraccionario para describir el transporte no difusivo. Los resultados para la configuración magnética sin ripple de ITER con simetría toroidal ideal analizada por el método [R=S] Lagrangiano muestran un exponente de Hurst casi igual a cero que señala, como se esperaba, la ausencia de transporte radial. Mientras que para ITER se analizaron las trayectorias de todas las partículas α atrapadas perfectamente confinadas, para los cuatro stellarators, solo se consideraron las partículas que más contribuyeron a las pérdidas, es decir, partículas α que se pierden en la región con la pendiente más pronunciada en la fracción de pérdidas. Los exponentes espaciales y temporales estimados que se encontraron indican que la naturaleza subyacente del transporte es no difusiva y con estadísticas no Gaussianas y no Markovianas. A medida que disminuye el nivel de simetría toroidal, la presencia de correlaciones espaciales, particularmente fuertes anti-correlaciones, se vuelve más pronunciada. Para todos los stellarators, hay signos de autosimilaridad y efectos significativos en la memoria. El acuerdo entre los exponentes de Hurst, estimados por las técnicas Lagrangiana y Euleriana, muestra que a medida que el nivel de simetría aumenta, el transporte se vuelve fuertemente subdifusivo. Aunque, la validez del modelo fraccionario en sí mismo se vuelve dudosa en los casos limites de alta y baja simetría. El trabajo presentado en esta tesis puede extenderse naturalmente para estudiar la validez del modelo de transporte fraccionario en otros tipos de campos magnéticos confinantes y estudiar varios efectos relacionados con las partículas α, como colisiones, perfiles de nacimiento de las partículas α, etc.Programa de Doctorado en Plasmas y Fusión Nuclear por la Universidad Carlos III de MadridPresidente: José Ramón Martín Solís.- Secretario: José Ángel Mier Maza.- Vocal: Roger Jasper

Demonstration of reduced neoclassical energy transport in Wendelstein 7-X

Documento escrito por un elevado número de autores/as, solo se referencia el/la que aparece en primer lugar y los/as autores/as pertenecientes a la UC3M.Beidler, C. D., et al. (2021). Publisher Correction: Demonstration of reduced neoclassical energy transport in Wendelstein 7-X. Nature, 598(7882), E5.Research on magnetic confinement of high-temperature plasmas has the ultimate goal of harnessing nuclear fusion for the production of electricity. Although the tokamak1 is the leading toroidal magnetic-confinement concept, it is not without shortcomings and the fusion community has therefore also pursued alternative concepts such as the stellarator. Unlike axisymmetric tokamaks, stellarators possess a three-dimensional (3D) magnetic field geometry. The availability of this additional dimension opens up an extensive configuration space for computational optimization of both the field geometry itself and the current-carrying coils that produce it. Such an optimization was undertaken in designing Wendelstein 7-X (W7-X), a large helical-axis advanced stellarator (HELIAS), which began operation in 2015 at Greifswald, Germany. A major drawback of 3D magnetic field geometry, however, is that it introduces a strong temperature dependence into the stellarator's non-turbulent 'neoclassical' energy transport. Indeed, such energy losses will become prohibitive in high-temperature reactor plasmas unless a strong reduction of the geometrical factor associated with this transport can be achieved; such a reduction was therefore a principal goal of the design of W7-X. In spite of the modest heating power currently available, W7-X has already been able to achieve high-temperature plasma conditions during its 2017 and 2018 experimental campaigns, producing record values of the fusion triple product for such stellarator plasmas. The triple product of plasma density, ion temperature and energy confinement time is used in fusion research as a figure of merit, as it must attain a certain threshold value before net-energy-producing operation of a reactor becomes possible. Here we demonstrate that such record values provide evidence for reduced neoclassical energy transport in W7-X, as the plasma profiles that produced these results could not have been obtained in stellarators lacking a comparably high level of neoclassical optimization.This work has been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training programme 2014-2018 and 2019-2020 under grant agreement no. 633053. The views and opinions expressed herein do not necessarily reflect those of the European Commission

Overview of first Wendelstein 7-X high-performance operation

The optimized superconducting stellarator device Wendelstein 7-X (with major radius , minor radius , and plasma volume) restarted operation after the assembly of a graphite heat shield and 10 inertially cooled island divertor modules. This paper reports on the results from the first high-performance plasma operation. Glow discharge conditioning and ECRH conditioning discharges in helium turned out to be important for density and edge radiation control. Plasma densities of with central electron temperatures were routinely achieved with hydrogen gas fueling, frequently terminated by a radiative collapse. In a first stage, plasma densities up to were reached with hydrogen pellet injection and helium gas fueling. Here, the ions are indirectly heated, and at a central density of a temperature of with was transiently accomplished, which corresponds to with a peak diamagnetic energy of and volume-averaged normalized plasma pressure . The routine access to high plasma densities was opened with boronization of the first wall. After boronization, the oxygen impurity content was reduced by a factor of 10, the carbon impurity content by a factor of 5. The reduced (edge) plasma radiation level gives routinely access to higher densities without radiation collapse, e.g. well above line integrated density and central temperatures at moderate ECRH power. Both X2 and O2 mode ECRH schemes were successfully applied. Core turbulence was measured with a phase contrast imaging diagnostic and suppression of turbulence during pellet injection was observed

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

Confirmation of the topology of the Wendelstein 7-X magnetic field to better than 1:100,000

Fusion energy research has in the past 40 years focused primarily on the tokamak concept, but recent advances in plasma theory and computational power have led to renewed interest in stellarators. The largest and most sophisticated stellarator in the world, Wendelstein 7-X (W7-X), has just started operation, with the aim to show that the earlier weaknesses of this concept have been addressed successfully, and that the intrinsic advantages of the concept persist, also at plasma parameters approaching those of a future fusion power plant. Here we show the first physics results, obtained before plasma operation: that the carefully tailored topology of nested magnetic surfaces needed for good confinement is realized, and that the measured deviations are smaller than one part in 100,000. This is a significant step forward in stellarator research, since it shows that the complicated and delicate magnetic topology can be created and verified with the required accuracy

Major results from the first plasma campaign of the Wendelstein 7-X stellarator

\u3cp\u3eAfter completing the main construction phase of Wendelstein 7-X (W7-X) and successfully commissioning the device, first plasma operation started at the end of 2015. Integral commissioning of plasma start-up and operation using electron cyclotron resonance heating (ECRH) and an extensive set of plasma diagnostics have been completed, allowing initial physics studies during the first operational campaign. Both in helium and hydrogen, plasma breakdown was easily achieved. Gaining experience with plasma vessel conditioning, discharge lengths could be extended gradually. Eventually, discharges lasted up to 6 s, reaching an injected energy of 4 MJ, which is twice the limit originally agreed for the limiter configuration employed during the first operational campaign. At power levels of 4 MW central electron densities reached 3 10\u3csup\u3e19\u3c/sup\u3e m\u3csup\u3e-3\u3c/sup\u3e, central electron temperatures reached values of 7 keV and ion temperatures reached just above 2 keV. Important physics studies during this first operational phase include a first assessment of power balance and energy confinement, ECRH power deposition experiments, 2nd harmonic O-mode ECRH using multi-pass absorption, and current drive experiments using electron cyclotron current drive. As in many plasma discharges the electron temperature exceeds the ion temperature significantly, these plasmas are governed by core electron root confinement showing a strong positive electric field in the plasma centre.\u3c/p\u3

Major results from the first plasma campaign of the Wendelstein 7-X stellarator

After completing the main construction phase of Wendelstein 7-X (W7-X) and successfully commissioning the device, first plasma operation started at the end of 2015. Integral commissioning of plasma start-up and operation using electron cyclotron resonance heating (ECRH) and an extensive set of plasma diagnostics have been completed, allowing initial physics studies during the first operational campaign. Both in helium and hydrogen, plasma breakdown was easily achieved. Gaining experience with plasma vessel conditioning, discharge lengths could be extended gradually. Eventually, discharges lasted up to 6 s, reaching an injected energy of 4 MJ, which is twice the limit originally agreed for the limiter configuration employed during the first operational campaign. At power levels of 4 MW central electron densities reached 3 1019 m-3, central electron temperatures reached values of 7 keV and ion temperatures reached just above 2 keV. Important physics studies during this first operational phase include a first assessment of power balance and energy confinement, ECRH power deposition experiments, 2nd harmonic O-mode ECRH using multi-pass absorption, and current drive experiments using electron cyclotron current drive. As in many plasma discharges the electron temperature exceeds the ion temperature significantly, these plasmas are governed by core electron root confinement showing a strong positive electric field in the plasma centre.Peer reviewe