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This thesis presents advancements in the understanding of the plasma conditions leading to the excitation and saturation of the Edge Harmonic Oscillations (EHOs) observed during QH-mode operation in tokamak plasmas. Such operations represent a safer alternative with respect to H-mode due to the absence of Edge Localised Modes (ELMs) while retaining high energy confinement and pedestal height. In this work, EHOs have been assumed to be the nonlinear evolution of linearly unstable external infernal (exfernal) modes. It is consistently found that exfernal modes can be excited and nonlinearly saturated in wide regions of the parameter space. Such regions have been identified through the use of various analytical and numerical tools developed within the ideal MHD model, including linear analytical modelling, linear stability software, and nonlinear equilibrium and initial value simulations. An expanded set of large aspect ratio equations describing the linear stability of exfernal modes is derived analytically, including higher order terms in the expansion of the safety factor around the rational surface, which allows for the effects of finite edge magnetic shear. Numerical solution of the equations provides the linearly unstable exfernal mode parameter space with respect to pedestal pressure gradient, pedestal width, edge safety factor and edge magnetic shear. Nonlinearly saturated exfernal modes calculated with the 3D VMEC free boundary code are found in regions of the parameter space where the exfernal modes are linearly unstable to the 2D VMEC neighbour state. The obtained critical value of the edge magnetic shear in the VMEC simulations is also recovered by the linear stability analysis. The parameter space is found to be reduced by the presence of a plasma separatrix due to a partial stabilisation of the external kink current-driven branch of the exfernal mode. An analytical estimation of the critical magnetic shear for the excitation of exfernal modes in diverted plasmas is also presented. Finally, it is shown that the parameter space for the saturation of external modes can be expanded through the application of non-axisymmetric Magnetic Perturbations (MPs). This is done analytically using a linear time-invariant perturbation of the 2D equilibrium assuming an external helical magnetic perturbation, and also in the VMEC code by the inclusion of non-axisymmetric coils in the calculation of the vacuum field. The approaches were applied to saturated external kink and exfernal modes. For the external kink case, quantitative agreement is found in the saturated amplitude obtained with the linear model and with the VMEC code for cases where the external kink is stable in the absence of MPs. For the case of saturated exfernal modes, only qualitative agreement is found, possibly due to the approximations taken in the calculation of the analytical model. Nevertheless, a significant expansion of the parameter space of saturated exfernal modes is obtained via the introduction of symmetry breaking coils, resulting in an appealing route for future reactor operations.

The effect of n = 1 magnetic perturbations (MPs) on prompt fast ion losses in DIII-D has been investigated using the light ion beam probe technique. The effect of normalized beta, β n, and the plasma response to the MPs is studied for several MP spectra. Magnetics data show a strong dependence of plasma response to β n that depends on the phase difference in perturbation coils, Δ ϕ U L . For most phases, the response increases with β n, however, the response is suppressed for phases between 180∘ and 240∘. Experimental data from scintillator based fast ion loss detectors shows that relative fluctuation of lost ions (20%-30% of the steady signal) does not diminish across the L- to H-mode transition for Δ ϕ U L = 240 ∘ , despite the 34% decrease in radial response field and 50% decrease in poloidal response field. Simulations of the DIII-D discharges using M3D-C1 and ASCOT5 find that prompt losses from neutral beam injection in each investigated case hit the first wall at several concentrated locations: the vessel floor, midplane diagnostic ports, vessel ceiling, and inner wall. Simulated losses from co-injection neutral beams are born outside the last closed flux surface, corresponding to radial orbit displacements of 3-6 cm due to the MPs. Department of Energy FC02-04ER54698, DE-SC0020337 Ministerio de Ciencia e Innovación FJC2019-041002-I

This paper studies the effect of 3D magnetic perturbations (MPs) on fast-ion confinement, and its impact on the toroidal rotation velocity profile. Two low collisionality H-mode experiments carried out at the ASDEX Upgrade tokamak have been analysed. The two discharges feature different magnetic field helicity (q95), and differences in the velocity-space and level of fast-ion losses are observed. A new analysis technique has been developed that sheds light on the dependencies between fast-ion losses and toroidal rotation, providing for the first time correlation patterns resolved in radius and velocity space of the lost fast-ions. The correlation intensifies towards the plasma edge and is strongly dependent on the orbit topology of the lost fast-ions. The ASCOT orbit following code has been used to characterize the fast-ion resonant transport and beam driven torques, using the vacuum approach and including plasma response (PR). The change of the toroidal canonical momentum, which serves as figure of merit for resonant fast-ion transport, has been calculated with ASCOT. The beam geometry and q95 are found to have a strong impact on the fast-ion transport and losses. The fast-ion transport induced by the MPs affects the beam driven torques. The effect of the changes of the j × B and collisional torques on plasma rotation is analysed using the torques simulated by ASCOT and simple momentum balance calculations. For the low q95 = 3.8 discharge, which benefits from a resonant amplification, we find excellent agreement with the measured variation of the toroidal velocity. For the high q95 = 5.5 discharge, the inclusion of the PR improves the comparison with experimental data with respect to the vacuum estimation, but still some differences with experiments are observed. This suggests that other non-resonant effects could play a role for the determination of the toroidal rotation profile.

The application of 3D fields might help in preventing and mitigating the avalanche generation of runaway electrons (RE) during disruption events in controlled fusion devices [1, 2]. The successful results recently obtained in ASDEX Upgrade [3] have motivated new experiments with this technique also in the COMPASS tokamak [4]. The resonant magnetic perturbation (RMP) coil system in COMPASS has been used to apply 3D fields with different amplitude and toroidal mode number (n=1 and n=2) to mitigate the RE beams generated during disruptions induced by impurity massive injection (Argon or Neon). Like in ASDEX Upgrade, the application of RMP results in a significantly higher decay rate and reduced lifetime of the generated RE beam.The strength of the observed effects strongly depends on the upper-to-lower coil phasing, i.e. on the poloidal spectrum of the applied perturbation, which has been reconstructed including the plasma response by the code MARS-F [5]. The RMP coils were powered both before and after the impurity gas puff, demonstrating that the RE deconfinement due to perturbation appears in the RE dominated disruption independently of the same effect on the hot plasma. The enhanced deconfinement of the RE seed population was observed as an increase of HXR signal immediately after energizing the RMP coils in the pre-disruption scenario. RMPs have a different impact in disruptions induced by Argon or Neon, indeed in the latter case a stronger reduction of the RE beam lifetime (down to -80%) has been observed. External perturbations also destabilize the RE radial beam position, increase the level of radial fluctuations and are correlated with the appearance of sudden HXR bursts for those coils phasing which maximize the predicted plasma response. Moreover, the configuration with n=2 RMP odd parity induces a MHD instability accompanied by a significant increase of the radial fluctuations resulting in a faster current decay rate.

This paper deals with helical self-organization in current-carrying toroidal pinches for the magnetic confinement of fusion plasmas. We perform our study in the framework of 3D nonlinear visco-resistive magnetofluid modelling, where a large set of simulations is now available. A global picture is derived about how visco-resistive transport coefficients and magnetic boundary conditions rule the self-organized helical states for the reversed-field pinch configuration. Decreasing visco-resistive dissipation causes a transition from steady ohmic helical equilibria to intermittent states (sawtoothing activity), while selected helical magnetic perturbations applied at the boundary favor steady global quasi-helical solutions. The sawtoothing frequency decreases together with visco-resistive dissipation, while sawtoothing amplitude decreases when applying non-resonant magnetic perturbations. Simulations of the tokamak configuration allow us to draw a tight parallelism with reversed-field pinches: a similar role of dissipation and magnetic boundary conditions on the dynamics of the internal kink mode is found, with decreasing sawtoothing frequency and amplitude by decreasing dissipation and by applying suitable helical boundary conditions. Magnetic chaos healing is the topological feature of the transition from intermittent to quasi-quiescent helical states in reversed-field pinches. Bundles of Lagrangian coherent structures (LCS) in the weakly stochastic region surrounding the helical core constitute the skeleton of chaos healing, and behave as barriers to the transport of magnetic field lines. In this work, they are detected during the whole temporal evolution and it is proved that they can withstand the nonlinear dynamics even during sawtoothing activity. Furthermore, we show that LCS are connected to regions with strong gradients of the connection length of magnetic field lines to the edge. This provides a further indication of their possible role in the formation of electron temperature barriers. As a final result it is shown that a reasonable value of plasma rotation can further enhance the intensity of the dominant helical mode.

In recent experiments at the ASDEX Upgrade tokamak the existence of an Edge Resonant Transport Layer (ERTL) was revealed as the main transport mechanism responsible for the measured fast-ion losses in the presence of externally applied 3D fields. The Monte Carlo orbit-following code ASCOT was used to study the fast-ion transport including the plasma response calculated with MARS-F, reproducing a strong correlation of fast-ion losses with the poloidal mode spectra of the 3D fields. In this work, a description of the physics underlying the ERTL is presented by means of numerical simulations together with an analytical model and experimental measurements to validate the results. The degradation of fast-ion confinement is calculated in terms of the variation of the toroidal canonical momentum (δP phgr ). This analysis reveals resonant patterns at the plasma edge activated by 3D perturbations and emphasizes the relevance of nonlinear resonances. The impact of collisions and the radial electric field on the ERTL is analysed.

Collisional particle transport in the presence of field perturbations originating from various MHD activity is examined theoretically on tokamaks (ITER, ASDEX Upgrade, NSTX and DIIID) and the reversed-field pinch RFX-mod [1]. For ITER and ASDEX Upgrade, modes typically leading to a disruption [2] are considered. On NSTX and DIII-D unstable Alfvén modes are investigated. Finally on RFX-mode the effect of saturated tearing modes is studied. The existence of subdiffusive transport [3] for electrons is found to occur in some cases at very low mode amplitudes. Subdiffusion is also found for ions of high energy. In fact, orbit resonances can produce long time correlations and dynamical traps [4] for particle trajectories at perturbation amplitudes much too small for the orbits to be represented as uniformly chaotic. Besides this, in all devices orbits show a high degree of anisotropy, especially when comparing the angular (toroidal and poloidal) and radial directions. As a consequence, in the presence of field perturbations produced by MHD modes, the use of a traditional diffusive-convective scheme for transport, which is expressed by the Fick's law~? = -D~?n+~v n, leading to the well known transport scalings, is questionable. The existence and nature of subdiffusive transport is difficult to determine from first-principle theories, since it is found to depend on the nature of the mode spectrum and frequency, as well as on the mode amplitudes: this fact is mirrored in the different value of the Kubo number found in the devices analyzed in this paper. The connection between subdiffusive transport, Kubo and nonlocal models of transport [5] is also discussed.

The plasma response from an external n = 2 magnetic perturbation field in ASDEX Upgrade has been measured using mainly electron cyclotron emission (ECE) diagnostics and a rigid rotating field. To interpret ECE and ECE-imaging (ECE-I) measurements accurately, forward modeling of the radiation transport has been combined with ray tracing. The measured data is compared to synthetic ECE data generated from a 3D ideal magnetohydrodynamics (MHD) equilibrium calculated by VMEC. The measured amplitudes of the helical displacement around the low field side midplane are in reasonable agreement with the one from the synthetic VMEC diagnostics. Both exceed the prediction from the vacuum field calculations and indicate the presence of a kink response at the edge, which amplifies the perturbation. VMEC and MARS-F have been used to calculate the properties of this kink mode. The poloidal mode structure of the magnetic perturbation of this kink mode at the edge peaks at poloidal mode numbers larger than the resonant components |m| > |nq|, whereas the poloidal mode structure of its displacement is almost resonant |m| ~ |nq|. This is expected from ideal MHD in the proximity of rational surfaces. The displacement measured by ECE-I confirms this resonant response., 34 pages, 19 figures. This is an author-created, un-copyedited version of an article submitted for publication in Plasma Physics and Controlled Fusion. IoP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it

The limits for the heat loads on the DEMO first wall are significantly stricter compared to those of ITER due to cooling and breeding blanket requirements. In addition to the thermal particle and radiation loads, fast particles in the form of fusion alphas and NBI ions with high energies can escape the confinement due to various magnetic perturbations and produce a significant heat load on the first wall. Previously, the losses of fusion alpha and NBI ions have been found to be manageable, with wall loads remaining below 10% of the limit of 1 MW/m2 envisaged for the DEMO first wall. This is primarily due to the plasma profiles that allow the 800 keV NBI ions to penetrate deep into the plasma before ionizing, and the generous gap of up to 20 cm between the separatrix and the first wall panels. Additionally, only losses due to toroidal field ripple were accounted for, while significant perturbations would be introduced by the possible addition of ELM control coils. In this contribution, we present ASCOT simulation results for fast ion confinement and losses under the effects of additional perturbations, including increased toroidal field ripple due to reduced ferritic inserts and reduced number of toroidal field coils, and the addition of resonant magnetic perturbations (RMP) due to ELM control coils. Additionally, the effect of NBI ionization in the scrape-off layer is discussed, which can introduce localized loads due to high-energy prompt losses.

Thanks to its advanced system for the control of magnetohydrodynamic modes, the RFX-mod device run as a tokamak is particularly suited to the study of the possible impact on runaway electron (RE) de-confinement in response to applied magnetic perturbations. This paper shows that during the flat-top phase in RFX-mod discharges, with a plasma current of I p ∼ 150 kA and a low density ( n e < 10 19 m−3), the amount of REs scales with the m = 2,n = 1 perturbation both in q(a) q(a) > 2 plasmas. Similar results have also been obtained in post-disruption phases, but still with limited statistics. The mechanisms generating REs and the effect of magnetic perturbation (MP) on their confinement are interpreted by numerical simulations with the relativistic guiding center code ORBIT. The role played by different magnetic equilibria on the energy of REs and on their loss rates is investigated. ORBIT simulations indicate that RE-enhanced losses are associated with a raised level of stochasticity, the effect being more pronounced when the MP amplitude is higher and internally resonant.

The magnetic topology of the stochastic edge of a helical reversed-field pinch, with helicity m/n, shows to be deeply influenced by higher harmonics (m +/- 1)/n, with the same n, due to toroidal coupling. As a consequence, by measuring kinetic quantities in a particular theta, phi location, one can incur in substantial errors or mis-interpretations of the kinetic plasma response: only a full 3D coverage of theta, phi angles can reveal the real topology of the plasma. This can be a caveat for MP application in tokamaks, because it shows that toroidal and poloidal sidebands, though smaller than the base mode by a factor similar to epsilon = a/R, can have a sizable effect on the kinetic response of the edge plasma, and thus on related issues (for example, ELM stabilization and suppression).

Filament or blob structures have been observed in all magnetic configurations with very similar features despite the difference in the magnetic geometry, and are believed to play an important role in convecting particles and energy towards the wall. Despite their different generation mechanism, turbulent structures and edge-localized mode (ELM) filaments share some common physical features. The electromagnetic effects on filament structures deserve particular interest, among others reasons for the implication they could have for ELM, related for instance to their dynamics in the transition region between closed and open field lines or to the possibility, at high beta regimes, of causing line bending which could enhance the interaction of blobs with the first wall. A direct characterization of the effects of active modification of the edge topology on EM turbulent filament structures is presented, comparing reversed field pinch and tokamak configurations. Measurements are obtained in the RFX-mod device, which allows operation in both configurations and with different equilibria. The RFX-mod experiment versatility is exploited also from the point of view of the active control of the edge magnetic topology, equipped with an advanced system for edge boundary feedback control. Three different case studies of actively controlled magnetic perturbations are shown, focusing on the filament interaction with local magnetic islands. High-frequency fluctuations, characterizing electrostatic and magnetic filament features, and the associated transport coefficients have been observed to be strongly affected by the island proximity and topology.

The response of the edge plasma to a magnetic perturbation (MP) is studied in the RFX-mod device, in both reversed field pinch (RFP) and tokamak discharges. The use of spatially distributed diagnostics, in particular along the poloidal direction, allows a direct 3D characterization of the plasma. It is shown that there is a difference between the spectrum of the MP and that of different properties of the edge plasma, such as the floating potential, the electron pressure and the flow, for both RFP and tokamak plasmas. In particular, for RFP cases, even if the magnetic perturbation is mainly m = 1, with the amplitude of the m = 0 and m = 2 sidebands negligible, the connection length to the wall of the magnetic field L cw has a more complex structure. The ergodic regions, with L cw larger than the Kolmogorov length, are due to the interaction of both m = 1 and m = 0 modes, showing a complex and non-monochromatic behaviour along the poloidal angle. This structure of L cw is responsible for the impure m = 1 behaviour of the plasma wall interaction, floating potential and electron pressure. Thus the helicity of the edge plasma is quite different from that of the dominant MP.

Experiments to balance the density pump-out effect during edge localized mode (ELM) control through the application of an n = 1 magnetic perturbation in type-I H-mode plasmas at JET are presented, describing the effect on T-e, n(e) and p(e) profiles. Reference discharges during H-mode with and without resonant magnetic perturbation are first considered, and compared with results obtained in previous work. Pellet and gas injection are the two applied techniques; on the basis of previous experience, various particle fuelling rates have been tested on two different divertor configurations, finding those for which the compensation takes place. In terms of plasma confinement, while core pressure is found to be almost unvaried with the particle fuelling, the edge pressure pedestal improves towards the value obtained during the H-mode without the application of the magnetic perturbation. The edge stability analysis shows that the mitigated edge plasma even with the addition of particle fuelling is in the stable region against the type-I ELM triggering peeling-ballooning modes.

The influence of a sinusoidal magnetic field on the effective viscosity of a magnetorheological dispersion in the low particle concentration regime is studied experimentally. When a sinusoidal magnetic field of low amplitude, conceived as perturbation, is applied transversally to the static field, a significant enhancement occurs in the measured effective viscosity. The magnitude of changes depends on a number of factors such as the amplitude and frequency of the perturbation, the particle concentration, the application time of the fields, and the shear rate. It has also been found that the behavior of the effective viscosity as a function of frequency presents a critical behavior. Therefore, an average Mason number is proposed, whose behavior as a function of frequency is similar to that shown by the effective viscosity.