Determination of the nature of radial transport in quasi-poloidal stellarator configurations

Mención Internacional en el título de doctorNuclear fusion is one of the most promising solutions to the long-term energy needs of the world. Nevertheless, bringing the source of energy of stars to Earth is not easy. From the different options explored to produce fusion, magnetic confinement is the most developed one and, probably, the first that will be available. Tokamaks and Stellarators are the two most important configuration concepts of this kind, both having a toroidal shape. The main problem magnetic confinement fusion suffers is that all configurations have important losses of energy and particles along the radial direction that makes achieving the required conditions a challenge. Traditionally, those losses have been modelled using neoclassical and turbulent descriptions that assume the existence of an underlying transport of diffusive characteristics. As a result, effective transport coefficients (diffusivities, viscosities, conductivities, etc.) have been estimated to describe the transport processes inside the plasmas confined in these magnetic configurations. Recently, it has been however suggested that there are several important regimes in these devices in which such an assumption may be wrong. As a result, these diffusive-like models may importantly misrepresent the transport dynamics and compromise the performance predictions of larger devices. Among the situations identified where the nature of the radial transport may be fundamentally non-diffusive, there are two particularly meaningful for magnetic confinement devices (see Ref. [1] for a review). The first one is the case of near-marginal transport, in which the plasma profiles (for pressure, temperature, etc) wander locally very close to the thresholds for the excitation of instabilities. In such cases, radial avalanching may become the dominant form of transport, instead of diffusion [2, 3]. In next-generation tokamaks, such as ITER [4], predictions have been made for an almost near-marginal operation in some profiles, due to the fact that turbulent fl uxes scale with a large power of the plasma temperature. Thus, at the much hotter plasmas expected in ITER, this might certainly be an issue to consider. Another example, closer to what we are going to study in this thesis, is the case of radial transport across strong, radially-sheared zonal flows, as shown recently in tokamaks [5, 6, 7]. The problem studied in this thesis, however, refers to transport in stellarators, not tokamaks. Stellarators have seen a recent revival by improving the confinement properties of neoclassical guiding centre orbits by endowing the confining magnetic field with a hidden symmetry usually referred to as quasi-symmetry. Several types of quasi-symmetries exist. The most important ones are quasi-poloidal, quasi-helical and quasiaxisymmetric. We will discuss them in detail in later chapters but, for now, it suffices with saying that quasi-symmetric configurations have a better neoclassical confinement compared to that of standard stellarators. Experimental results from the HSX (helically quasi-symmetric) stellarator [8] have already provided evidence supporting an improved neoclassical confinement [9]. They also have smaller viscosities in the direction of the symmetry, which should in principle facilitate an easier excitation of flows, either by the turbulence itself or externally. Experimental evidence supporting this reduction is also available from HSX [10]. In this context, it is therefore a natural question to ask whether the reduction of losses and better confinement in quasi-symmetric configurations are a mere reduction of turbulent transport levels, or whether there is something more fundamental being changed. The investigation of the latter is where this thesis is centered, focusing in particular on quasi-poloidal configurations. The reduction of the neoclassical poloidal viscosity expected for poloidally quasi-symmetric configuration should facilitate the self-generation of poloidal zonal flows, which are particularly important in terms of affecting radial transport [11]. From the previously mentioned tokamak evidence, it is therefore expected that nondiffusive features of transport might appear more strongly in poloidal quasi-symmetric configurations. Thus, the present thesis investigates whether this is the case or not. Or, more precisely, we will quantify the changes in the nature of radial turbulent transport and attempt to establish whether these changes are (or not) correlated to the level of quasi-poloidal symmetry of the configuration. In order to do it, many gyrokinetic turbulent simulations have been carried out, in a selected configuration with quasi-poloidal symmetry, using the Gene [12] gyrokinetic code (see Chapter 2). The degree of quasi-symmetry of the selected configuration varies, however, strongly with radius. We have used this to our advantage by carrying out local simulations around different radial locations of the same configuration, which has yielded the plethora of data with which the comparative study previously described has been carried out. The characterization of the nature or turbulent transport has been done by means of a methodology that employs tracked particles. These particles may be massless (i.e., tracers) or possess mass and charge. Either way, these particles are tracked as they are advected by the underlying turbulence (previously calculated by Gene ) and, if massive, the different magnetic and parallel drifts that might be present. The temporal dispersion of an initial population of these particles can be used to determine the nature of radial transport rather easily, as we discuss in Chapter 3. However, advecting tracked particles within the advance loop of modern Vlasov gyrokinetic codes is very ine cient and highly unpractical. Gyrokinetic codes have high complexity, strong parallelization and a extremely delicate internal balance. For that reason, we have developed a new and independent tracking code, TRACER, that we have used to carry out all the studies in this thesis. The inner details of this new code are discussed at length in Chapter 4. The discussion of the results of the comparative study previously mentioned is eshed out in Chapter 5. The main conclusion we have drawn is that there is indeed a correlation between the level of quasisymmetry and the nature of radial transport, which becomes more subdi ffusive the larger the level of quasi-symmetry is. The nature of this change is also shown to be connected with the larger ability of the quasisymmetric plasma to excite poloidal flows with strong radial shear, which is very reminiscent of what is found in tokamaks [7]. We have carried out this study both for tracers and massive ions, and very similar results are found in the long-term limit, which makes us believe that the conclusions of this thesis are of importance for the confinement of the thermally confined plasma. The main results of this thesis have been presented in several international conferences and workshops, and have also seen publication in the international journal Physics of Plasmas. A complete list of these publications and presentations can be found in Appendix C. As a last note it is worth saying that, throughout the document, most of the variables will be expressed in Gene units. A very few variables, mostly related with the description of the QPS-configuration, will be however expressed in the International System of Units. The abbreviations used in the document are always introduced and they are part of the general terminology used by the fusion community.Programa Oficial de Doctorado en Plasmas y Fusión NuclearPresidente: Edilberto Sánchez González.- Secretario: José Ramón Martin Solis.- Vocal: Guilhem Dif-Pradalie

Quasi-symmetry and the nature of radial turbulent transport in quasi-poloidal stellarators

Quasi-symmetric configurations have a better neoclassical confinement compared to that of standard stellarators. The reduction of the neoclassical viscosity along the direction of quasi-symmetry should facilitate the self-generation of zonal flows and, consequently, the mitigation of turbulent fluctuations and the ensuing radial transport. Therefore, it is expected that quasi-symmetries should also result in better confinement properties regarding radial turbulent transport. In this paper we show that, at least for quasi-poloidal configurations, the influence of quasi-symmetry on radial transport exceeds the expected reduction of fluctuation levels and associated effective transport coefficients, and that the intimate nature of transport itself is affected. In particular, radial turbulent transport becomes increasingly subdiffusive as the degree of quasi-symmetry becomes larger. This behavior is somewhat reminiscent of what has been previously reported in tokamaks with strong radially sheared zonal flows. Published by AIP Publishing.Research funded in part by the Spanish National Project Nos. ENE2012-33219 and ENE2012-31753. Research supported in part by the DOE Office of Science Grant No. DE-FG02-04ER5741 at the University of Alaska. Research carried out in part at the Institüt für Plasmaphysik of the Max-Planck Institüt in Greifswald (Germany), whose hospitality is gratefully acknowledged. Fruitful interactions with members of the ABIGMAP research network, funded by the Spanish National Project No. MAT2015-69777-REDT, is also acknowledged. Gene simulations have been possible thanks in part to a continued grant (Nos. FI-2014-1-0021, FI-2014-2-0026, FI-2014-3-0012, and FI-2015-1-0011) to use resources from the MareNostrum supercomputer at BSC (Barcelona, Spain). Gene and TRACER runs have also been carried out in Uranus, a supercomputer cluster located at Universidad Carlos III de Madrid (Spain) funded jointly by EU FEDER funds and by the Spanish Government via the National Project Nos. UNC313-4E-2361, ENE2009-12213-C03-03, ENE2012-33219, and ENE2012-31753

Confinement in electron heated plasmas in Wendelstein 7-X and ASDEX Upgrade; the necessity to control turbulent transport

In electron (cyclotron) heated plasmas, in both ASDEX Upgrade (L-mode) and Wendelstein 7-X, clamping of the ion temperature occurs at Ti ∼ 1.5 keV independent of magnetic configuration. The ions in such plasmas are heated through the energy exchange power as ${n}_{\mathrm{e}}^{2}({T}_{\mathrm{e}}-{T}_{\mathrm{i}})/{T}_{\mathrm{e}}^{3/2}$, which offers a broad ion heating profile, similar to that offered by alpha heating in future thermonuclear fusion reactors. However, the predominant electron heating may put an additional constraint on the ion heat transport, as the ratio Te/Ti > 1 can exacerbates ITG/TEM core turbulence. Therefore, in practical terms the strongly 'stiff' core transport translates into Ti-clamping in electron heated plasmas. Due to this clamping, electron heated L-mode scenarios, with standard gas fueling, in either tokamaks or stellarators may struggle to reach high normalized ion temperature gradients required in a compact fusion reactor. The comparison shows that core heat transport in neoclassically optimized stellarators is driven by the same mechanisms as in tokamaks. The absence of a strong H-mode temperature edge pedestal in stellarators, sofar (which, like in tokamaks, could lift the clamped temperature-gradients in the core), puts a strong requirement on reliable and sustainable core turbulence suppression techniques in stellarators.EC/H2020/633053/EU/Implementation of activities described in the Roadmap to Fusion during Horizon 2020 through a Joint programme of the members of the EUROfusion consortium/Eurato

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