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AbstractFluctuations of electron cyclotron emission (ECE) signals are analyzed for differently heated Wendelstein 7-X plasmas. The fluctuations appear to travel predominantly on flux surfaces and are used as ‘tracers’ in multivariate time series. Different statistical techniques are assessed to reveal the coupling and information entropy-based coupling analysis are conducted. All these techniques provide evidence that the fluctuation analysis allows one to check the consistency of magneto-hydrodynamic (MHD) equilibrium calculations. Expanding the suite of techniques applied in fusion data analysis, partial mutual information (PMI) analysis is introduced. PMI generalizes traditional partial correlation (Frenzel and Pompe Phys. Rev. Lett.
99 204101) and also Schreiber’s transfer entropy (Schreiber 2000 Phys. Rev. Lett.
85 461). The main additional capability of PMI is to allow one to discount for specific spurious data. Since PMI analysis allows one to study the effect of common drivers, the influence of the electron cyclotron resonance heating on the mutual dependencies of simultaneous ECE measurements was assessed. Additionally, MHD mode activity was found to be coupled in a limited volume in the plasma core for different plasmas. The study reveals an experimental test for equilibrium calculations and ECE radiation transport.
Particle and heat transport in fusion devices often exceed the neoclassical prediction. This anomalous transport is thought to be produced by turbulence caused by microinstabilities such as ion and electron-temperature-gradient (ITG/ETG) and trapped-electron-mode (TEM) instabilities, the latter ones known for being strongly influenced by collisions. Additionally, in stellarators, the neoclassical transport can be important in the core, and therefore investigation of the effects of collisions is an important field of study. Prior to this thesis, however, no gyrokinetic simulations retaining collisions had been performed in stellarator geometry. In this work, collisional effects were added to EUTERPE, a previously collisionless gyrokinetic code which utilizes the δ f method. To simulate the collisions, a pitch-angle scattering operator was employed, and its implementation was carried out following the methods proposed in [Takizuka & Abe 1977, Vernay Master's thesis 2008]. To test this implementation, the evolution of the distribution function in a homogeneous plasma was first simulated, where Legendre polynomials constitute eigenfunctions of the collision operator. Also, the solution of the Spitzer problem was reproduced for a cylinder and a tokamak. Both these tests showed that collisions were correctly implemented and that the code is suited for more complex simulations. As a next step, the code was used to calculate the neoclassical radial particle flux by neglecting any turbulent fluctuations in the distribution function and the electric field. Particle fluxes in the neoclassical analytical regimes were simulated for tokamak and stellarator (LHD) configurations. In addition to the comparison with analytical fluxes, a successful benchmark with the DKES code was presented for the tokamak case, which further validates the code for neoclassical simulations. In the final part of the work, the effects of collisions were investigated for slab and toroidal ITGs and TEMs in a tokamak configuration. The results show that collisions reduce the growth rate of slab ITGs in cylinder geometry, whereas they do not affect ITGs in a tokamak, which are mainly curvature-driven. However it is important to note that the pitch-angle scattering operator does not conserve momentum, which is most critical in the parallel direction. Therefore, the damping found in a cylinder could be the consequence of this missing feature and not a physical result [Dimits & Cohen 1994]. Nonetheless, the results are useful to determine whether the instability is mainly being driven by a slab or toroidal ITG mode. EUTERPE also has the feature of including kinetic electrons, which made simulations of TEMs with collisions possible. The combination of collisions and kinetic electrons made the numerical calculations extremely time-consuming, since the time step had to be small enough to resolve the fast electron motion. In contrast to the ITG results, it was observed that collisions are extremely important for TEMs in a tokamak, and in some special cases, depending on whether they were mainly driven by density or temperature gradients, collisions could even suppress the mode (in agreement with [Angioni et al. 2005, Connor et al. 2006]). In the case of stellarators it was found that ITGs are highly dependent on the device configuration. For LHD it was shown that collisions slightly reduce the growth rate of the instability, but for Wendelstein 7-X they do not affect it and the growth rate showed a similar trend with collisionality to that of the tokamak case. Collisions also tend to make the ballooning structure of the modes less pronounced.
In this work, studies with respect to the exhaust problem were performed
in the stellarator experiment Wendelstein 7-X with different target concepts and different magnetic field geometries. Different infrared cameras were used to study the heat flux from the plasma onto the PFC. In the first publication, the limiter set-up was used with a simpler magnetic topology in the plasma edge. The radial fall-off of the parallel heat flux for inboard limiters in W7-X shows, similar to inboard limiters in tokamaks, two different radial fall-off lengths, a short (narrow) one, characterizing the near-SOL, and a long (broad) characterizing the far-SOL. For the far-SOL, the heating power and connection length have been identified as the main scaling parameters, while for the near-SOL, the electron temperature close to the LCFS has been identified as the main scaling parameter. The two fall-off lengths differ by a factor 10, and the found scalings for both regimes differ from known models and experimental scalings in tokamaks. A turbulent-driven feature was discussed in the publication as a possible explanation for the behavior of the fall-off length in W7-X.
The gained information and data have been further used to support many
other publications, covering the symmetry of the heat loads, the
energy balance of the machine, and seeding experiments.
The heat exhaust in W7-X with an island divertor was studied in the second
and third publication. Definitions of parameters such as peaking factor and
wetted area were applied for the heterogeneous heat flux pattern on the
W7-X divertor. It was shown that the island divertor concept is capable
of spreading out the heat efficiently, resulting in large wetted areas of up to 1.5 m2. The reached values for the wetted area are comparable to the ones of the larger tokamak JET but with a much smaller ratio of wetted
area to the area of the last closed flux surface. Furthermore, a positive
scaling of the wetted area with the power in the SOL was observed. This
scaling is beneficial for future reactors but needs further investigation of the involved transport processes. The peaking factor (discussed in the second publication) describes how concentrated the heat load is within the region of the strike line. It was shown that this factor is decreasing for increasing densities without affecting the wetted area. The present work paves the way for further analysis of the transport processes of the heat flux towards the island divertor of Wendelstein 7-X.
The confinement of energy has always been a challenge in magnetic confinement fusion devices. Due to their toroidal shape there exist regions of high and low magnetic field, so that the particles are divided into two classes - trapped ones that are periodically reflected in regions of high magnetic field with a characteristic frequency, and passing particles, whose parallel velocity is high enough that they largely follow a magnetic field line around the torus without being reflected. The radial drift that a particle experiences due to the field inhomogeneity depends strongly on its position, and the net drift therefore depends on the path taken by the particle. While the radial drift is close to zero for passing particles, trapped particles experience a finite radial net drift and are therefore lost in classical stellarators. These losses are described by the so-called neoclassical transport theory. Recent optimised stellarator geometries, however, in which the trapped particles precess around the torus poloidally and do not experience any net drift, promise to reduce the neoclassical transport down to the level of tokamaks. In these optimised stellarators, the neoclassical transport becomes small enough so that turbulent transport may limit the confinement instead. The turbulence is driven by small-scale-instabilities, which tap the free energy of density or temperature gradients in the plasma. Some of these instabilities are driven by the trapped particles and therefore depend strongly on the magnetic geometry, so the question arises how the optimisation affects the stability. In this thesis, collisionless electrostatic microinstabilities are studied both analytically and numerically. Magnetic configurations where the action integral of trapped-particle bounce motion, J, only depends on the radial position in the plasma and where its maximum is in the plasma centre, so-called maximum-J configurations, are of special interest. This condition can be achieved approximately in quasi-isodynamic stellarators, for example Wendelstein 7-X. In such configurations the precessional drift of the trapped particles is in the opposite direction from the direction of propagation of drift waves. Instabilities that are driven by the trapped particles usually rely on a resonance between these two frequencies. Here it is shown analytically by analysing the electrostatic energy transfer between the particles and the instability that, thanks to the absence of the resonance, a particle species draws energy from the mode if the frequency of the mode is well below the charateristic bounce frequency. Due to the low electron mass and the fast bounce motion, electrons are almost always found to be stabilising. Most of the trapped-particle instabilities are therefore predicted to be absent in maximum- J configurations in large parts of parameter space. Analytical theory thus predicts enhanced linear stability of trapped-particle modes in quasi-isodynamic stellarators compared with tokamaks. Moreover, since the electrons are expected to be stabilising, or at least less destabilising, for all instabilities whose frequency lies below the trapped-electron bounce frequency, other modes might benefit from the enhanced stability as well. In reality, however, stellarators are never perfectly quasi-isodynamic, and the question thus arises whether they still benefit from enhanced stability. Here the stability properties of Wendelstein 7-X and a more quasi-isodynamic configuration, QIPC, are investigated numerically and compared with another, non-quasiisodynamic stellarator, the National Compact Stellarator Experiment (NCSX) and a typical tokamak. In gyrokinetic simulations, performed with the gyrokinetic code GENE in the electrostatic and collisionless approximation, several microinstabilities, driven by the density as well as both ion and electron temperature gradients, are studied. Wendelstein 7-X and QIPC exhibit significantly reduced growth rates for all simulations that include kinetic electrons, and the latter are indeed found to be stabilising when the electrostatic energy transfer is analysed. In contrast, if only the ions are treated kinetically but the electrons are taken to be in thermodynamic equilibrium, no such stabilising effect is observed. These results suggest that imperfectly optimised stellarators can retain most of the stabilising properties predicted for perfect maximum-J configurations. Quasi-isodynamic stellarators, in addition to having reduced neoclassical transport, might therefore also show reduced turbulent transport, at least in certain regions of parameter space.