A study of the physics of pellet injection in magnetically confined plasmas in stellarators
- Autores: Nerea Panadero Álvarez
- Directores de la Tesis: Kieran Joseph McCarthy (dir. tes.), José Ramón Martín Solis (tut. tes.)
- Lectura: En la Universidad Carlos III de Madrid ( España ) en 2018
- Idioma: español
- Tribunal Calificador de la Tesis: Elena de la Luna Gargantilla (presid.), Luis Raul Sánchez Fernández (secret.), Axel Lorenz (voc.)
- Programa de doctorado: Programa de Doctorado en Plasmas y Fusión Nuclear por la Universidad Carlos III de Madrid
- Materias:
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- Resumen
Life quality and energy consume are closely related. However, the large amount of energy expended nowadays plus the related environmental, health and economical problems imply that real and sustainable alternatives to fossil fuels are mandatory, i.e., it is necessary to change the energy production system. One of the strongest long-term candidates to replace fossil fuels is nuclear fusion, the energy source of the stars, which is an intrinsically safe process of energy production with a high energy density. Moreover, it is a relatively clean energy source with no greenhouse-gas emissions and reduced radioactive waste. However, many technological and physics related problems are still unresolved. Therefore, fusion energy is a key research topic on the path to a clean and sustainable energy that does not damage the environment or health and that, at the same time, is economically feasible.
Two nuclei, in order to fuse together, need to overcome the repulsive Coulomb force between their positive charges. For this, the energy of these reacting nuclei needs to be high enough to exceed the Coulomb barrier; that means temperatures of the order of 108 K. In addition, to employ fusion as a means to produce electricity, it is also necessary that the density of these nuclei is sufficient, so that the reaction rate is high enough that the net power is positive, and that the nuclei are confined for an adequate time. Atoms, deuterium and tritium in this case, at temperatures that fulfil these requirements (summarized in the Triple Product criterion) are ionized, i.e., they are in the plasma state. Plasma has some characteristics that differentiate it from the gas state, such as collective behaviour and electrical conductivity. Strong gravitational forces in the innermost part of stars enable nuclei to overcome the repulsive electrostatic forces. Since such strong gravitational forces are absent on Earth, an alternative needs to be found. Moreover, a way to confine a material at hundreds of millions of Kelvin needs to be developed.
At present, there are two main research lines, inertial and magnetic-confined fusion. In the case of this thesis, magnetic-confined fusion, which takes advantage of the particular properties of plasma to confine it, is the concept under consideration. In effect, the fact that charge particles describe a helical trajectory along magnetic field lines can be used to trap plasma electrons and ions if an appropriate magnetic field geometry is chosen. This magnetic field geometry is the result of a toroidal field, and a poloidal field added to compensate the ExB drift that displaces plasma particles in the major-radius direction of the torus. Hence, the resultant helical field, which must have nested magnetic surfaces, is able to confine the plasma and isolate it from the wall of the vessel. The simplest way to create a poloidal magnetic field in a torus is to induce a toroidal current in the plasma that, in turn, generates a poloidal magnetic field. In addition, a second approach, technically more complex, uses external coils with the appropriate shape to create the helical magnetic field, hence no induced current is necessary to confine the plasma. Devices that confine plasma by the former method are called “tokamaks”, while those whose use the latter are called “stellarators”.
The steady-state operation of magnetically confined fusion plasma is still an enormous challenge, since highly complex physics must be combined with the steady-state technological constraints. In order to achieve steady-state burning fusion plasma, it is necessary to establish, and maintain, simultaneously under stable conditions, the magnetic configuration, the kinetic configuration, the device safety and a solution for the fuel cycle. Achieving the desire kinetic configuration includes attaining the pertinent density, temperature and rotation profiles. Thus, maintaining the appropriate plasma density profile to achieve the expected fusion power, i.e., a highly peaked density profile, is of high relevance for the steady-state operation of a fusion reactor. Hence, an efficient fuelling capability is mandatory; this being of primary importance for helical devices, since neoclassical theory predicts that on-axis electron and/or ion cyclotron resonance heating (ECRH, ICRH) leads to strongly hollow profiles, which degrade the central energy confinement, thereby leading to plasma collapse. The injection of cryogenic hydrogen pellets is currently the best candidate to refuel the plasma core in large fusion devices, since the achieved fuel penetrations are deeper than those achieved with other techniques. Thus, efficient and reliable pellet injection technology that allows density profile control is one of the requirements to achieve steady-state operation in fusion devices. However, further experimental and theoretical studies are necessary to fully understand all the mechanisms involved in pellet ablation and in the subsequent particle deposition, since a complete understanding of experimental results from non-axisymmetric devices remains outstanding.
When a cryogenic hydrogen pellet is injected into magnetically confined plasma, plasma particles (thermal and non-thermal electrons and ions) transfer their energy flux to the pellet, thereby ablating it. The rate at which the incident particles ablate a pellet is given by the balance between the energy flux of the incoming particles and the energy required to ablate, dissociate, ionize and accelerate the pellet particles. The ablated particles expand around the pellet, protecting it from further interactions with the ambient plasma. Therefore, the pellet lifetime is increased, thus allowing it to penetrate deeper into the plasma. There are three different phenomena that protect the pellet, the dynamics of the cloud being the most important. Indeed, the heat flux reaching the solid pellet is strongly reduced due to collisions with the surrounding cloud particles, thereby shielding it almost completely. The second mechanism, known as electrostatic shielding, is related to the fact that the cloud is negatively charged with respect to the background plasma; thus, there is an associated negative potential that accelerates plasma ions and decelerates electrons. Since ions dissipate their energy in the shielding cloud, the heat flux at the pellet surface is significantly reduced by this negative sheath at the plasma-cloud interface. Finally, the ionized fraction of the cloud, or plasmoid, partially expels the magnetic field. Thus, the incident heat flux is also reduced by magnetic shielding.
Once the pellet material has been ablated and ionized, several phenomena take place until, finally, plasma temperature and density radial profiles recover. During this homogenization phase, the ionized material expands in the direction parallel to magnetic field lines until plasma and plasmoid pressures are equilibrated. During this expansion, the plasma potential distribution is modified, as is the poloidal rotation profile. At the same time, this material drifts down the magnetic field gradient. The origin of the latter phenomenon, the drift of the ionized material, is the vertical motion of plasmoid electrons and ions in the non-uniform magnetic field, which generates an uncompensated current.
In this work, pellet ablation and fuelling efficiency experiments, using a pipe-gun type cryogenic pellet injector (PI), are carried out in ECRH and neutral beam injection (NBI) heated hydrogen plasmas of the stellarator TJ-II. Here, all injections are made from the outer plasma side (inner plasma side injections are not possible for technical reasons). In order to increase the flexibility of the system, different pellet sizes were chosen for each of the four barrels; 42 mm (Type-1 pellet, containing ≤ 4x1018 hydrogen atoms), 0.66 mm (Type-2 pellet, containing ≤ 1.2x1019 hydrogen atoms), 0.76 mm (Type-3 pellet, containing ≤ 1.8x1019 H atoms) and 1 mm (Type-4 pellet, containing ≤ 4.1x1019 H atoms). These pellets are accelerated to 800–1200 m/s. In addition, the four injection lines are equipped with two diagnostics that provide timing signals and allow for particle accountability: a light-gate and a microwave cavity. Moreover, the PI system is equipped with two diagnostics that follow the time evolution of the light emitted by the cloud surrounding ablating pellets. The first one is a set of silicon photodiodes that follow, from above and behind the pellet injection path, the Balmer Hα light emitted by the neutral cloud surrounding a pellet. The second system consists of an ultra-fast CMOS camera (monochrome FASTCAM APX-RS by Photron Inc., San Diego, CA, USA), a 4.5 m long coherent fibre bundle and machine-vision type camera lenses. This system also allows following the evolution of the light emitted by the ablated material, as well as the pellet acceleration and trajectory, from above or tangentially to the pellet flight path.
Analysis of the Balmer Hα emission followed by the photodiode system allows reconstructing the pellet ablation rate, assuming that such emission is loosely related to the ablation rate and that pellet radial acceleration in the plasma is negligible. For ECRH plasmas, it is found that significant ablation, which strongly depends on plasma temperature, occurs only after a pellet has penetrated a few centimetres into the plasma and that it increases moderately as it penetrates deeper into the plasma, until a maximum is achieved (usually close to the plasma core), before decreasing suddenly when the pellet is totally consumed. In addition, the lifetimes of pellets injected into ECRH plasma in TJ-II is short, and penetration is shallow (typically ≤~12 cm), due to the relatively high temperatures, ≤ 1.5 keV. On the other hand, pellets injected into low-temperature NBI plasma are ablated at a lower rate (about half), so their lifetimes, and hence their penetration depths, are longer. Regarding the ablation profile, emission increases suddenly around five centimetres from the plasma edge and remains approximately constant until the pellet crosses the magnetic axis; afterwards, the emission is reduced, and continuous at this lower rate until the complete consumption of the pellet. These differences are attributed to the shape of the suprathermal ion distribution in TJ-II.
Light emissions are also used to study the pellet penetration dependence on pellet and plasma parameters, such as pellet velocity, pellet mass, and plasma density for pellet injections from the outer plasma side of TJ-II. Pellet penetration in TJ-II, as in other magnetically confined plasma devices, increases with increasing pellet mass and velocity as well as for high plasma density and low temperature. However, if suprathermal electrons are present in the plasma core, they can limit pellet penetration due to sudden excess ablation. Therefore, plasma heating methods play a key role in the achievable pellet penetration, since they determine the plasma density and temperature profiles and the possible presence of suprathermal particles. In addition, pellet dynamics inside the plasma are analysed employing fast-camera images. First, it is concluded that radial acceleration is zero or negligible. Second, it is found that pellets injected into ECRH plasmas follow the original injection path. In contrast, it is found that pellets injected into unbalanced NBI-heated plasmas are deflected toroidally and poloidally (along the direction of the neutral beam ions). Observed toroidal accelerations lie between 106 and 107 m/s2; while poloidal accelerations are estimated to be 104 to 106 m/s2.
The drift direction and magnitude of the ionized fraction of the cloud, or plasmoid, is investigated using the fast-camera system for ECRH and NBI plasmas. Plasmoids drifting, at between 0.5 and 20 km/s, towards the outer and lower plasma edge are observed. However, when pellets penetrate beyond the magnetic axis, it is observed that plasmoids seem to drift towards the plasma centre (inward drift). This change could be an indication of the inward-directed drift predicted by current homogenization models, which implies deeper and more efficient fuelling for pellets of size and velocity. In addition, it should be noted that the obtained drift values strongly depend on the frame exposure time, since drift velocity decreases rapidly with time, i.e., there is significant deceleration. Moreover, a dependence between plasmoid drift and plasmoid detachment position, related to rational surfaces, is observed. Indeed, reduced drifts are observed in the vicinity of rational surfaces.
Fuelling efficiency studies have been carried out in TJ-II. For this, pellet particle deposition profiles and fuelling efficiency are determined using pre- and post-injection density profiles provided by a Thomson Scattering (TS) system. Moreover, the influence of plasma heating methods on pellet ablation and material deposition is considered. It is found that fuelling efficiency increases with increasing target density and with increasing pellet penetration depth. This is especially noted for NBI plasmas, since pellets penetrate beyond the magnetic axis. Therefore, fuelling efficiencies are lower for ECRH plasma (≤ 40%), while higher for NBI plasmas (≤ 85%). On the contrary, injections into plasmas where a core-localized population of suprathermal electrons is present, result in higher fuelling efficiencies, although fast-electron over-ablation in the plasma core limits pellet penetration. This is attributed to two different mechanisms. On the one hand, the outwards-directed drift acceleration in the core region is expected to be small or negligible, and, in addition, to rapidly become inward-directed as the plasmoid expands. Thus, total drift is small and, hence, the amount of lost material due to plasmoid drift is reduced. On the other hand, the presence of suprathermal electrons appears to reduce the drift acceleration, and hence, the number of lost particles.
In order to attain a deeper understanding of pellet injection physics in the TJ-II, experimental results are compared with theoretical predictions. In first instance, a Neutral Gas Shielding-based (NGS) code is adapted for TJ-II to compare experimental ablation rates for pellets injected into both ECRH and NBI-heated plasmas with simulated rates. The NGS model was the first attempt to explain pellet ablation. Despite its simplicity, it succeeded in reproducing many of the experimental penetration depths and/or pellet lifetimes. In the model used here, the spatial distribution of the neutral part of the cloud is described by hydrodynamic conservation equations, assuming steady-state conditions and with the additional heat source of suprathermal ions. Simulated ablation rates reproduce fairly well experimental ablation profiles, and pellet penetration depths, within ≤ 15%, for ECRH TJ-II plasmas. On the other hand, results for injections into NBI TJ-II plasmas are less satisfactory; especially, the shape of the ablation profile is only approximately reproduced, while pellet penetration depths are reasonably well predicted (to 10%).
Next, the Hydrogen Pellet Injection (HPI2) code, in its stellarator version, is used to simulate pellet injections into ECRH plasmas in TJ-II. In contrast to the NGS-based code, HPI2 obtains pellet ablation with an enhanced version of the Neutral Gas and Plasma Shielding (NGPS) model, which not only takes into account the shielding provided by the cloud of neutral ablated particles that surrounds the pellet, but also the shielding provided by the ionized fraction of the ablatant, i.e., the plasmoid. In addition, the reduction of the incident flux due to electrostatic and magnetic shielding is included. Besides, the plasmoid time evolution is modelled by a 0-D, two-cell (plasmoid and background plasma) four-fluid Lagrangian system. Additionally, plasmoid ExB drift, whose dynamics is determined by plasmoid pressure relaxation with the background plasma, is calculated using an equation for the averaged acceleration of a plasmoid particle that is integrated to obtain the total average particle drift. The drift acceleration is obtained from the compensation of the curvature current by the polarization current.
With this code, using TS electron density and temperature profiles as input, ablation and material deposition predictions are compared with experimental measurements for ECRH plasmas for the TJ-II standard configuration. The agreement between the recorded Hα and the predicted ablation profile is reasonably good, considering that Hα emission is not directly proportional to ablation rate. This agreement improves when considering an averaged Hα emission profile for a complete series of reproducible discharges or the light profile obtained from the montage of snap-shot fast camera images, if available, are considered. Pellet penetration depths are also well predicted by the HPI2 code. Regarding post-injection plasma density profiles, HPI2 predictions are found to be shifted towards outer radii when compared to the experimental profiles from TS measurements. Thus, since experimental profiles are obtained several milliseconds after injections (HPI2 code predictions are for 0.3 ms after injection), it has been necessary to use a transport code to follow the temporal evolution of the simulate profiles. For this a neoclassical code is used (DKES). As a result, predicted density profiles that include neoclassical transport are closer to the corresponding TS profiles than those estimated by HPI2 only. However, the quantitative agreement can be considered reasonably good for on-axis ECRH plasmas but poorer for the off-axis ECRH cases, due to the presence of suprathermal electrons, which is not considered in the code. This agreement gives confidence in codes for stellarators, allowing predictions to be made with some confidence for the large W7-X device, providing suprathermal electron effects are not important.
The HPI2 code is then used to predict ablation and deposition profiles for pellets injected into relevant ECRH plasma scenarios in the stellarator W7-X, in particular corresponding to the second part of its initial operational phase, OP 1.2. It is predicted that better fuelling can be attained for HFS injections due to the inwards drift, since it leads to deeper deposition and less particle losses. In particular, the best result is predicted for HFS injections into X2-mode ECRH plasmas, due to higher temperature that increases ablation i.e., increases the difference between plasmoid and plasma pressures, and, hence, enhances plasmoid drift. Furthermore, comparisons with preliminary experimental results from OP 1.2 are presented. Predicted density profiles cannot reproduced experimental results, this being mainly attributed to the presence of suprathermal electrons. In addition, it is possible that turbulent transport is relevant. Finally, the HPI2 code is also used to simulate ablation and deposition profiles for pellets of different sizes and velocities injected into future relevant W7-X plasma scenarios, while estimating the plasmoid drift and the fuelling efficiency of injections made from two W7-X ports. These simulations allow identifying an advantageous port for efficient pellet injections into W7-X.
