@phdthesis{Proll2014,
  author    = {Josefine Henriette Elise Proll},
  title     = {Trapped-particle instabilities in quasi-isodynamic stellarators},
  journal    = {Von gefangenen Teilchen angetriebene Instabilit{\"a}ten in quasi-isodynamischen Stellaratoren},
  url       = {https://nbn-resolving.org/urn:nbn:de:gbv:9-001733-4},
  year      = {2014},
  abstract  = {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.},
  language  = {en}
}