In Plasmen gibt es einen ganzen Zoo unterschiedlicher Wellentypen. Eine Einteilung in verschiedene Klassen ist nur bedingt möglich. So breiten sich im Plasma elektromagnetische Wellen aus. die das Plasma als dielektrisches Medium verändert, und wie in einem Gas gibt es Schallwellen, die von Störungen im Plasmadruck getrieben werden. Wenn dadurch gleichzeitig die Ladungsdichte gestört wird, dann muss der Einfluss der elektrischen Felder berücksichtigt werden, und es entstehen elektrostatische Wellen. Hinzu kommen die aus Kapitel 4 bekannten magnetohydrodynamischen Wellen, bei denen der Polarisationsstrom die Rolle des Verschiebungsstromes übernimmt. Die Existenzbereiche der Wellentypen hängen wiederum ab von der Propagationsrichtung relativ zum Magnetfeld und der Berücksichtigung einer endlichen Ionen- oder der Elektronentemperatur.

Ziel dieses Kapitels ist die Klassifizierung der verschiedenen Trajektorien. die Teilchen in magnetischen Spiegeln. Tokamaks und Stellaratoren durchlaufen können. Behandelt werden Führungszentrumsbahnen. die aus einer Überlagerung der Driften mit der Bewegung entlang der Feldlinien entstehen. Dabei spielt die Reflektion an magnetischen Spiegel eine wesentliche Rolle. Deshalb wollen wir uns zunächst die Bahnen in einer Spiegelmaschine anschauen, bevor wir Trajektorien im Tokamak und im Stellarator behandeln. Die Bahnen in toroidalen Plasmen sind eine wichtige Grundlage für das Verständnis von Transportvorgängen senkrecht zu den magnetischen Flächen, für den toroidalen elektri¬schen Strom und das Entstehen radialer elektrischerFelder.

Während die Plasmen im Weltraum oder in der Ionosphäre durch hochenergetische Teilchen erzeugt werden, verwendet man zur Plasmaerzeugung im Labor meistens elektrische Felder. Diese werden als Gleich-. Wechsel- oder Wellenfelder bereitgestellt. Die verschiedenen Techniken, elektrische Felder in Plasmen einzukoppeln. werden in diesem Kapitel beschrieben. In allen Fällen werden freie Elektronen soweit beschleunigt, bis ihre Energie der Ionisationsenergie der Neutralteilchen entspricht. Durch einen inelastischen Stoß entsteht ein zusätzliches Elektron-Ion-Paar. und der Prozess setzt sich mit verdoppelter Elektronenzahl fort. Die Vervielfältigung der Ladungsträger sättigt erst dann, wenn die Erzeugungsrate durch eine entsprechende Verlustrate ausgeglichen wird.

In Kapitel 8 haben wir Transportkoeffizienten für die Diffusion parallel und senkrecht zum Magnetfeld behandelt. Nach Tab. 8.3 liegen die Werte der Diffusionskoeffizienten für Ionen bei 10 bzw. 10 m/s. Man redet vonklassischem Transport, wenn man sich auf diese Koeffizienten beziehen. Wir werden sehen, dass die toroidale Geometrie von Fusionsexperimenten zu einer wesentlichen Erhöhung des Transports senkrecht zum Magnetfeld führt. Verantwortlich dafür sind Teilchendriften und Spiegeleffekte, wie sie in durch Toroidizität und. besonders beim Stellarator. diskrete Spulen erzeugten inhomogenen Magnetfeldern auftreten. Die Theorie desneoklassischen Transports berücksichtigt diese Effekte. Der unglücklich gewählte AusdruckNeoklassik umfasst also alle Einflüsse der toroidalen Magnetfeldkorifiguration auf den stoßbehafteten Transport sowie auf die Stabilität des Plasmas.

Trotz der Erhöhung der Diffusion durch nooklassische Effekte sind Teilchenstöße alleine nicht in der Lage, die in Fusionsplasmen gemessenen hohen Werte von Transportkoeffizienten zu erklären. Inzwischen ist es unbestritten, dassFluktuationen in den Plasmaparametern die Ursache für die beobachteten Transportverluste sind. Die Fluktuationen werden durch Plasmaturbulenz hervorgerufen. Daher spricht man vonturbulentem oder auchanomalem Transport. Man beobachtet Fluktuationen in Dichte. Temperatur und Plasmapotential. Fluktuationen im elektrischen Feld führen zu Driften und dadurch zu Transport. Man spricht vonelektrostatischer Turbulenz, wenn der Transport nur durch die E×B-Drift im fluktuierenden elektrischen Feld erzeugt wird. Zeitlich veränderliche elektrische Felder werden aber immer auch Magnetfeldstörungen hervorrufen. Wenn magnetische Fluktuationen zu einer wesentlichen Veränderung der magnetischen Flussflächen führen und damit zum Transport beitragen, so spricht man vomelektromagnetischer Turbulenz.

Stabile Plasmazustände treten in der Natur nur dann auf, wenn neben der Gleichge- wichtsbedingung noch eine Stabilitätsbedingung erfüllt ist. Ist das nicht der Fall, so führen kleinste Störungen des Gleichgewichtszustandes über eine Instabilität zu dessen Zerfall. In der Mechanik einzelner Körper ist das nicht anders. Ein Körper ist im Gleichgewicht, wenn die Summe der an ihm angreifenden Kräfte verschwindet oder der Gradient des konservativen Potentials, in dem er sich befindet, Null ist. Der Stabilitätsbegriff in der Mechanik ist in Abb. 4.1 erläutert. Die Gleichgewichtslage einer Kugel in einem Potential, wie es z. B. durch Gravitation hervorgerufen werden kann, ist nur dann stabil, wenn kleinste Auslenkungen der Position zu einer rücktreibenden Kraft führen. Die zweite Ableitung des Potentials muss also positiv sein. Dagegen ist die Lage instabil, wenn eine Auslenkung die potentielle Energie des Körpers absenkt, und damit die kinetische Energie erhöht.

Für ein sich ohne äußere Heizung selbständig erhaltendes Fusionsplasma muss dasTri- pelprodukt Open image in new window einen Wert von etwa 0,5 MJs/m überschreiten. Da der Wert des Magnetfeldes technisch noch oben begrenzt ist, bedeutet das nach (10.22), dass hohe Werte für den normierten Plasmadruckß und die EnergieeinschlusszeitTZ erreicht werden müssen. Aber auchß undTE sind physikalische Grenzen gesetzt, die wir in den folgenden Kapiteln behandeln wollen.

Understanding the transport processes that determine the plasma profile widths in the scrape-off layer (SOL) and divertor region of tokamaks is crucial for successful power and particle exhaust management in future devices. Plasma transport from the SOL into the private flux region (PFR) broadens the profiles and could mitigate the power exhaust challenge. Analysis of ion current profiles, measured by Langmuir probes in the ASDEX upgrade (AUG) tokamak, shows that the ion current width in the PFR, normalized by the flux expansion between outer target and midplane, is about 1.2 mm in L-mode and 0.9 mm in inter-ELM H-mode plasmas. The measured widths agree within a factor of two with predictions from an analytical model, based on Pfirsch-Schl & uuml;ter flows. According to the model, the ion PFR width increases with the distance Delta R between the outer target and X-point major radii, and scales inversely with the poloidal magnetic field Bp. For the tokamaks ITER and SPARC the model predicts PFR widths below 0.3 mm.

The physics governing the height of the X-point radiator (XPR) and the influence of the related radiation losses on the edge temperature profiles is studied with a reduced power balance model, which is an extension of a model developed to study XPR access. For ASDEX Upgrade parameters with a heating power of 10 MW, the model reproduces that the X-point radiator can be moved from the X-point up to 14 cm into the confined plasma, dissipating up to 70% of the heating power. The key parameter is the neutral density in the X-point region. A reduction of the edge kinetic pressure gradient of about 50% is found which could explain the suppression of edge localized modes observed in experiment. The calculated edge temperature response is consistent with experimental data.

On the basis of several recent breakthroughs in fusion research, many activities have been launched around the world to develop fusion power plants on the fastest possible time scale. In this context, high-fidelity simulations of the plasma behavior on large supercomputers provide one of the main pathways to accelerating progress by guiding crucial design decisions. When it comes to determining the energy confinement time of a magnetic confinement fusion device, which is a key quantity of interest, gyrokinetic turbulence simulations are considered the approach of choice - but the question, whether they are really able to reliably predict the plasma behavior is still open. The present study addresses this important issue by means of careful comparisons between state-of-the-art gyrokinetic turbulence simulations with the GENE code and experimental observations in the ASDEX Upgrade tokamak for an unprecedented number of simultaneous plasma observables.

The quasi-continuous exhaust (QCE) regime is a regime that is naturally type-I ELM-free. It combines the high density at the plasma edge needed for power exhaust with the high normalised energy confinement typical for H-mode operation. In the QCE regime large-scale ELMs are avoided and high-frequency, low-amplitude filaments are present leading to the name-giving quasi-continuous edge transport of particles and energy. This contribution reports that for the first time the QCE regime was successfully achieved in JET with a metal wall. Moreover, it was demonstrated in the recent JET deuterium-tritium campaign DTE3 that the regime is compatible with D-T operation. Porting the QCE regime to JET strongly benefited from the experimental and modelling efforts at the medium sized tokamaks ASDEX Upgrade and TCV. Using the physics picture developed from the ASDEX Upgrade experimental results, the route to the QCE regime in JET reported here is following closely the approach that was successful in ASDEX Upgrade. First, strong plasma shaping-large elongation and triangularity and the highly correlated closeness to double null-is developed. Second, sufficient fuelling to achieve high enough density at the pedestal foot, close to the separatrix, is applied. In addition, neon seeding proved to be very beneficial to avoid type-I ELMs when reducing the main ion fuelling.

After a long device enhancement phase, scientific operation resumed in 2022. The main new device components are the water cooling of all plasma facing components and the new water-cooled high heat flux divertor units. Water cooling allowed for the first long-pulse operation campaign. A maximum discharge length of 8 min was achieved with a total heating energy of 1.3 GJ. Safe divertor operation was demonstrated in attached and detached mode. Stable detachment is readily achieved in some magnetic configurations but requires impurity seeding in configurations with small magnetic pitch angle within the edge islands. Progress was made in the characterization of transport mechanisms across edge magnetic islands: Measurement of the potential distribution and flow pattern reveals that the islands are associated with a strong poloidal drift, which leads to rapid convection of energy and particles from the last closed flux surface into the scrape-off layer. Using the upgraded plasma heating systems, advanced heating scenarios were developed, which provide improved energy confinement comparable to the scenario, in which the record triple product for stellarators was achieved in the previous operation campaign. However, a magnetic configuration-dependent critical heating power limit of the electron cyclotron resonance heating was observed. Exceeding the respective power limit leads to a degradation of the confinement.

The temperature decay length ( λ T e ) in the near scrape-off layer (SOL) reflects the ratio between the transport parallel to the magnetic field lines via Spitzer–Härm electron conduction and the perpendicular mechanisms involving neoclassical and anomalous transport. The implementation of the thermal helium beam diagnostic on ASDEX Upgrade has enabled an excellent spatiotemporal study of the structure of the electron temperature profile ( T e ) around the separatrix and the derivation of the near SOL decay lengths. From the analysis of the T e profile structure of attached H- and L-mode discharges, a self-consistent correspondence between the extrema of the electron temperature curvature profile ( ∂ R 2 T e ) and the position of the separatrix ( R s e p ) is revealed. A 1.5 D model for the power balance from closed to open field lines, including the escaping heat flux from the confined region and the parallel losses to the divertor, as well as results from the plasma edge code GRILLIX, support these experimental results. The evaluation shows that the temperature decay length is not constant over the plasma edge and SOL region, so that the absolute value of λ T e strongly depends on the analyzed region. Independent of the exact location and in agreement with edge Thomson scattering evaluations, the decay lengths show the known inverse relation to the plasma current ( I p ).

The improved energy confinement mode (I-mode) is a potential candidate for future fusion power plants, as it combines ELM-free operation with good confinement. The unusual edge transport and turbulence in this regime is still not fully understood. This study analyzes the turbulent structure of the weakly coherent mode (WCM) in ASDEX Upgrade. Measurements from Doppler back-scattering and a thermal helium beam diagnostic are used to determine velocities of the background plasma and the WCM over multiple discharges. A phase velocity of the WCM of the order of 2–5 km s ^−1 in the electron diamagnetic drift direction is found, quantitatively close to a drift wave assuming negligible temperature fluctuations. A good agreement with a previously proposed mechanism behind the I-mode regime is observed. This marks the first experimental verification of a specific understanding of the WCM and the I-mode regime.

The quasi-coherent mode (QCM), appearing in enhanced D alpha high confinement mode (EDA H-mode) and quasi-continuous exhaust (QCE) plasmas has been analysed in detail at ASDEX Upgrade via thermal helium beam spectroscopy under various discharge parameters. In both scenarios the QCM appears to be localized close to the separatrix and to propagate in ion diamagnetic direction in the plasma frame. The poloidal wavenumber of the QCM is about 0.025<k theta rho s<0.075 and the radial wavenumber is kr approximate to 0 cm-1 . It was found that the plasmas are generally below the ideal MHD limit at the separatrix. All the properties are consistent with ideal, resistive or kinetic ballooning modes. Simultaneous to the appearance of the QCM, higher harmonic modes can be observed in EDA H-modes, which are exclusively visible in magnetic pick-up coils and have toroidal mode numbers of up to n = 10. By performing a bicoherence analysis it was found that the higher harmonic modes and the QCM are coupling, but are disjoint phenomena. Qualitatively, the bandwidth of the QCM serves as a promising distinctive feature between QCE plasmas and EDA H-modes.

A novel experimental method is applied to localize the initial suppression of turbulence, in the form of density fluctuations, at the transition from the low (L-) to the high (H-) confinement mode in toroidal magnetic fusion plasmas. The high radial and temporal resolution, combined with the unprecedented statistical significance, provided the awaited information on a possible dominant ExB shear layer in L-H transition physics. We show, for the first time, that the H-mode turbulence suppression is initiated at the inner ExB shear layer in the ASDEX Upgrade tokamak possibly shedding light on the causality behind the L-H transition process.

This study employs the established momentum transport analysis at ASDEX Upgrade [Zimmermann et al., Nucl. Fusion 63, 124003 (2023)] to investigate the parametric variations of the momentum transport coefficients in the core of H-mode plasmas. These experimental results are compared to a comprehensive database of gyrokinetic calculations. Generally, good agreement between predicted and measured diffusive and convective transport coefficients is found. The predicted and measured Prandtl numbers correlate most dominantly with the magnetically trapped particle fraction. The experimentally inferred pinch numbers strongly depend on the logarithmic density gradient and magnetic shear, consistent with the theoretical predictions of the Coriolis pinch. The intrinsic torque from residual stress in the inner core is small, scales with the local logarithmic density gradient, and the data indicate a possible sign reversal. In the outer periphery of the core, the intrinsic torque is always co-current-directed and scales with the pressure gradient. This is consistent with prior experimental findings and global, non-linear gyrokinetic predictions. It suggests that profile shearing effects generate the intrinsic torque in the inner core. Toward the outer core, most likely, effects from E×B-shearing become more influential. These results offer the first comprehensive picture of this transport channel in the core plasma and contribute to validating the corresponding theoretical understanding. The derived scaling laws are used to construct a reduced momentum transport model, which has been validated against an additional dataset. This demonstrates that the model captures the essential contributions to momentum transport in the core of H-mode plasmas.

In tokamaks, radial transport is ballooning, meaning it is enhanced at the low-field side (LFS). This work investigates the effect of the magnetic configuration on the high-field side (HFS) scrape-off layer. Our experiments involved L-mode and H-mode discharges at ASDEX Upgrade, in which we scanned the magnetic configuration from a lower to an upper single-null shape, thus varying the location of the secondary separatrix. We show that the secondary separatrix determines the width of the HFS scrape-off layer, meaning that the density is much lower in the region that is magnetically disconnected from the LFS scrape-off layer, outside the secondary separatrix. Furthermore, we observe that the large density often seen in the HFS divertor drastically decreases as the separation between the primary and secondary separatrices falls below a particular value. This value is different for L-mode and H-mode plasmas and closely matches the power decay length measured at the LFS midplane. We also show how the HFS scrape-off layer density is smaller in an upper single-null than in a lower single-null, when the ionic grad-B drift points down. This difference is likely caused by reversing the E x B drifts in the active divertor when switching the active X-point from the bottom to the top. We further observe that the neutral density in the lower divertor also correlates with the plasma shape and the high-density region in the HFS scrape-off layer. During the shape scans analyzed here, the HFS divertor remained partially detached throughout, with transitory reattachment modulated by ELM activity in H-mode. This work provides novel experimental data that can be leveraged to further the modeling capabilities and understanding of scrape-off layer physics in highly shaped plasmas.