Resumen de Electromagnetic turbulence in the edge of fusion plasmas: spontaneous and actively modulated features
This thesis aims to study the properties of turbulence and how its arising affects cross-field transport in the periphery of fusion devices. Such knowledge is fundamental for understanding the mechanisms responsible for energy exhaustion from the plasma core to the divertor in those devices, as well as it determines the level of plasma-wall interaction during current ramp-up in present and future devices [1], and flat-top when the plasma density approaches to the density limit [2], where the enhanced cross-field particle transport might lead to the damage of plasma-facing components and impurity influx.
Turbulence appears naturally in many physical systems and presents a universal behavior that is shared by most of them [3]. That is also true for plasma systems where turbulence controls the transport, and thus the plasma confinement time. Understanding and controlling cross-field transport in magnetically confined plasma is a requirement for achieving a commercial fusion reactor. On that account, in this thesis, we compare the turbulent properties of different magnetic configurations, fusion devices, and plasma regimes. Turbulent transport plays a crucial role in both tokamak and stellarator, while shear flows can impact turbulence growth and development. The improved confinement regime, called H-mode, happens when the ExB shearing rate becomes comparable to the growth rate of the dominant instability [4]. Such an effect has a beneficial impact on the overall plasma confinement, leading to an improvement in the plasma confinement time, but it is detrimental for the energy exhaustion since it ultimately decreases the power deposition area on the divertor plates.
Recent scaling law obtained from data of several tokamaks in H-mode in attached divertor conditions has shown that the power width (λq) decreases approximately with the strength of the poloidal magnetic field or plasma current, λ_q∝B_p^(-1)∝I_p^(-1) [5], where the divertor heat flux width is determined in first approximation by the competition between cross-field and parallel transport in the scrape-off layer (SOL). By extrapolating such scale for ITER Q = 10 standard scenario, one gets λ_q≈1 mm, which would exceed the power threshold in stationary condition set by the materials intended to be used in the ITER divertor. Whether this scale is applicable for ITER and beyond (DEMO), it is still a matter of discussion in the fusion community. Meanwhile, alternative solutions have been proposed. The possibility of ITER operates in partial or full detachment [6] condition, i.e., when the plasma pressure along the field lines and the deposition power on the divertor reduce substantially, has become feasible and promisor scenario. Such a regime is typically obtained by seeding impurities in the SOL, which in turn, induces an increase of the radiation power, cooling down the plasma and raising the level of collisionality along the field lines. That regime, however, is followed by a substantial increase of the separatrix density, close to the density limit where plasma disruption can occur. In addition, advanced magnetic divertors configurations offer a potential solution for this issue by spreading the heat over a broader area. This is achieved by tailoring the magnetic field geometry in configurations such as the ’snowflake’ and the Super-X [7]. While these configurations would demand major modifications in ITER, recent turbulent simulations [8,9] have shown that the turbulent cross-field transport contribution in the SOL of ITER and beyond might be larger than in the current devices, and so λq. The latter phenomenon seems to be, to a large extent, determined by the turbulent coupling between the plasma edge and the scrape-off layer (SOL). The penetration of streamers into SOL generated by instabilities such the trapping electron mode (TEM) in the pedestal region, combined with a wider and relaxed ExB shear layer, seems to be behind this effect [8] that ultimately would lead to the widening of the heat flux width. Besides, a possible leading role of electromagnetic instabilities that typically generate more resilient turbulent structures to the background, e.g., edge-localized mode (ELM) filaments, can enlarge λq [9]. The propagation of turbulence from the edge to the SOL, a phenomenon known as turbulence spreading, is believed to be responsible for a large turbulence level and transport in the near SOL, i.e., around the separatrix. Therefore, according to this approach, turbulence in the SOL would come from elsewhere (e.g., plasma edge), rather than created locally. Fluctuations in the SOL are governed by travelling turbulent filaments. These structures share some features with the edge-localized mode (ELM) filaments that, in turn, typically result in a large transient heat flux on the plasma-facing components. While the existence of ELMs in future fusion reactors is a concern since they might reduce the device life-time, grassy ELMs, streamers, or big blobs can help to enlarge the power deposition area in future devices without being a great risk for the plasma-facing components. For that reason, the proper understanding of the turbulence characteristics and dynamics is fundamental, so we can make safe predictions for ITER and beyond. This thesis aims to shed light on this subject by focusing on the experimental characterization of turbulence in the plasma edge and SOL of three different devices. The main results of the thesis are presented in four chapters: 5,6,7, and 8. Chapter 5 presents some experimental evidence of the turbulence spreading phenomenon in the TJ-II stellarator and how ExB shear can control it. The local effective turbulence growth and the rate of turbulence spreading, both obtained from a K – \epsilon model [10], are computed from the edge to the SOL with a set of electrostatic sensors, poloidally and radially displaced. In addition, some relevant plasma parameters such as the poloidal phase velocity, the radial particle flux, and the turbulent correlation time (from the autocorrelation of the floating potential) are obtained. The results show that the local turbulence growth reduces once a shear layer is formed in the plasma edge induced by an external electrode biasing. A similar result is also verified when the dominant external heating power is switched from electron cyclotron resonance heating (ECRH) to neutral beam injectors (NBI). Such transition is followed by a flip of the sign of the radial electric field in the plasma edge and the development of a poloidal phase shear layer. Besides, the turbulence spreading rate is mainly activated in the SOL, decreasing when the ExB shearing rate becomes comparable to the inverse of the turbulence correlation time, thus leading to an edge-SOL decoupling. Therefore, one can think that the turbulence is created in the plasma edge and then propagates into the SOL, thus increasing the level of turbulence in this region. Besides, in the far SOL (approximately 2 cm away from the last closed flux surface – LCFS), the rate of turbulence drive becomes comparable to the rate of turbulence spreading, suggesting that 1) the spreading is an important source of turbulence in this region; 2) the local drive can be fed by the spreading. Nevertheless, the presence of a transport barrier reduces this effect. The role of radial electric fields in regulating turbulence propagation is further confirmed in chapter 6 in spontaneous neoclassical electron-ion root transition experiments in TJ-II. During this process, the edge radial electric field flips sign continuously from positive to negative values. This stellarator property makes these devices good laboratories to study the interplay between radial electric fields and turbulence. Through the measurements of two electrostatic probes remotely separated (toroidally), the zonal flows have been shown to be amplified during the transition. This result is based on the spatial-temporal decomposition of floating potential signals from both probes in orthogonal modes. It has been shown that the dominant mode presents a low-frequency response (≈ 1 kHz) and long-range correlation, which are precisely the properties of zonal flows [11]. For that reason, the amplitude of the dominant mode was used as a proxy for the rise and fall of the zonal flow. During the ion root phase, the effective turbulent correlation length drops sharply. Such a result indicates the turbulence does not penetrate so easy the SOL as in the electron root phase. It is worth noting that this result was obtained from the maximum cross-correlation of radially displaced floating potential signals, instead of the correlation at zero delay, in order to take into account for the fact that turbulence is propagating in this region. Furthermore, the turbulence propagation or turbulence spreading was computed using the transfer entropy (TE) technique. TE measures the information flow between two events and so the causal relationship between them. From two floating potential signals radially displaced in the plasma edge, it is shown from TE that turbulence propagates radially outward at ⁓1 km/s during the electron root, reducing to virtually zero in the ion root phase. Using multiple pins around the LCFS, the propagation appears as plume starting from the reference point in the plasma edge (r – r0 ≈ -10 mm) to the near SOL in the electron root phase, while it almost disappears in the ion root phase. This result presents a further confirmation of turbulence spreading and how radial electric fields can affect it. Although this result is obtained for a stellarator, a similar effect is expected to happen also in tokamaks, as suggested by simulations [9]. The electromagnetic properties of turbulent filaments are investigated in RFX-mod operating as tokamak in the single-null configuration in chapters 7 and 8. In chapter 7, filament properties in L and H-mode (ELM-free) are compared. H-mode in RFX-mod is obtained by the aid of an external electrode biasing placed in the plasma edge from the bottom [12]. Such a configuration induces an improvement in the plasma confinement by suppressing turbulence after the arising of a shear layer in the plasma edge. The plasma boundary was monitored with a set of electrostatic and magnetic sensors with good spatial-temporal resolution. When biasing is on, the floating and ion saturation current profiles become steeper, while a shear layer around the LCFS develops. Radial turbulent particle flux reduces in this location as well as an effective turbulent correlation length in the SOL, suggesting that turbulence coming from the LCFS does not penetrate SOL as in L-mode. Through advanced statistical techniques, filaments are detected and tracked from the edge to the SOL in a two-dimension floating potential map together with their associated plasma density and current density parallel to the equilibrium magnetic field. Filaments or blobs are defined from the extreme events from a reference ion saturation signal in the SOL close to the LCFS. This analysis reveals a dipole potential around the ion saturation peak (proportional to density), in agreement with the classical blob view [13]. By considering the negative pole as reference for the blob properties (e.g., size and velocity), the filament dynamics is tracked from the edge to the SOL. While in L-mode, they travel almost freely with an average velocity approximately 3 km/s, during H-mode, their motion becomes restricted to the near SOL. The higher ExB shear in the latter regime is pointed out to be the reason for this effect. By comparing the ExB shearing rate with the inverse of the local turbulence characteristic time [14], one can see that the latter is always larger (or at least comparable) to the former in L-mode, therefore filaments in this regime are not expected to be suppressed by the background. On the other hand, this trend is reversed in H-mode, where the shearing rate largely overcomes the inverse of the local turbulence characteristic time. In this regime, however, filaments are not suppressed instantaneously; they instead remain ‘trapped’ in the SOL until fade away. This result seems to be in qualitative agreement with the vortex selection mechanism often observed in fluids [15]. The ExB background shear selects vortex according to its polarity, while those with opposite polarity are unstable if their vorticities are comparable in amplitude with background vorticity. The negative monopole in H-mode has vorticity with the same polarity as the background in the same location. Consequently, the blob would spin around it rather than radially propagates. In addition, filament dynamics in the two scenarios are discussed in the framework of analytical models and velocity scaling. During L-mode, filaments are better described by the sheath connected regime, in which filament is connected along the field lines to a material surface (e.g., limiter or divertor). The parallel current density and potential structure are shown to be roughly synchronized in agreement with that. However, due to the variations of the parallel connection length along the radial direction, filaments near the LCFS scale differently from those further out (in the limiter shadow), in a good agreement with actual connection length in these two zones. In H-mode, filaments near the last closed flux surface (LCFS) scale roughly as the inertial regime. However, the higher electromagnetic activity during this phase could also contribute to that [16]. Edge-localized mode (ELM) is an electromagnetic instability that arises in H-mode, and it is responsible for ejecting particles and energy towards the SOL [17], representing a risk for plasma-facing components in the present and future devices. The plasma is ejected from the edge as filaments, similar to those observed in L-mode, but with larger magnetic perturbation [18]. In chapter 8, ELM filaments are investigated in RFX-mod running as tokamak, where they appear spontaneously during the biasing H-mode in RFX-mod. The properties of these structures are compared with the type I ELMs observed in the COMPASS tokamak. In both devices, the ELM filaments carry a substantial current towards the SOL. The current density fluctuation associated with the ELMs in COMPASS is up to ten times larger than L-mode filaments. Statistical analysis reveals a complex and rich fine structure within the ELM cycles. Four phases during one ELM cycle is defined based on the evolution of an ion saturation current signal at the SOL of RFX-mod. Before the ELM crash, a quasicoherent fluctuation (100 < f < 200 kHz) is observed in the plasma edge from the magnetic coils. After the crash, the quasicoherent mode becomes broader, while larger parallel current density fluctuation is observed. Besides, filaments are expelled towards the SOL, while the background ExB flow, floating potential, and ion saturation profiles become less steep. In contrast, before and right after the ELM crash, filaments are observed to be restricted to the near SOL (i.e., close to the LCFS), similar to the H-mode filaments studied in chapter 7. During the filamentary phase of the ELM cycle, the fine structure is studied by employing the wavelet decomposition and the local intermittency measurement (LIM) to detect blobs at different time scales. The analyses reveal that blobs at different scales behave differently, with smaller blobs showing higher radial velocity than the bigger ones, in qualitative agreement with the sheath connected regime. Similar analyses applied to the inter-ELM phase indicate that filaments were blocked in the near SOL regardless of the time scale. In light of this result, it is evident that the relaxed shear flow layer during the ELM favors the propagation of filaments at a broad range of scales. The onset of the crash, however, is not identified here. Previous studies suggested that field line stochastization can lead to fast profile relaxation since plasma is exhausted rapidly along the reconnected field lines [19]. The presence of ELM precursors and quasicoherent modes are also observed in COMPASS, suggesting that these oscillations are fundamental for the ELM arising and development.
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