Under this task, we would like to understand what is the correct computational approach (perhaps depending on plasma parameters) to study stellarator plasma turbulence and zonal flow dynamics in multispecies plasmas.

*Influence of global effects on zonal flow dynamics*

The flows produced by the component of the turbulent fluctuating electric potential that is constant on each flux surface and varies across it on the gyro-radius legth scale are called zonal flows, and they are thought to play an important role in reducing turbulent transport. In [Mishchenko-08, Monreal-16, Monreal-17] the properties of long-term linear and collisionless zonal flow relaxation in stellarators were studied, deriving analytical expressions for the zonal flow residual level and the zonal flow oscillation frequency. In [Monreal-16, Monreal-17], those analytical expressions were evaluated numerically in several magnetic configurations and compared to gyrokinetic simulations with GENE (in full flux-surface domain) and EUTERPE (radially global), finding a very good agreement. A detailed comparison between calculations in radially global and flux-tube domains has not been carried out yet, but there are indications, both from theory [Monreal-16, Monreal-17] and also from simulations [Smoniewski-18], that the zonal flow properties cannot be properly accounted for in a flux-tube. Nevertheless, because of its numerical and computational advantages, this domain is often employed for simulating physics situations in which the zonal flow dynamics is considered important (see e.g. [Nakata-17], [Plunk-17]).

An intuitive explanation why flux-tube simulations might not be enough to determine either zonal flow dynamics of turbulence properties in stellarator geometry comes from noting that the radial electric field plays a key role in stellarators, with the associated ExB flow modifying the particle trajectories along the flux surface and moving the particles across field lines. This affects in particular the zonal flow linear properties [Sugama-09, Mishchenko-12] as well as the mode structure of microinstabilities [Riemann-15]. This suggests that at least a full flux surface domain is required to properly treat the electric field in a stellarator. Furthermore, the different boundary conditions imposed in each computational domain can also make a difference between radially local and global domains.

The objective of this activity is:

- Determine the minimal computational domain required for an accurate description of the linear zonal flow dynamics and characterize the effect of an insufficient domain in the non- linear turbulent fluxes.

*Influence of neoclassical transport on turbulence*

As explained in [Calvo-17], one can find stellarator magnetic configurations and plasma regimes in which the deviation of the main ion neoclassical distribution from a Maxwellian distribution is as large as the Maxwellian distribution itself. In these situations, the neoclassical equations are radially non-local, radial turbulent transport is negligible compared to radial neoclassical transport and the question about the influence of neoclassical effects on turbulence is also irrelevant. We are interested in situations in which the deviation of the main ion neoclassical distribution from a Maxwellian distribution is large, but not that large. The arguments of [Calvo-17] indicate that these situations exist, for example, in large aspect ratio stellarators (all stellarators in operation today have large aspect ratio).

It is also important to note that large neoclassical corrections to the distribution function do not necessarily imply a similarly large neoclassical flux. This is for example the case of the “deep √ν regime” (i.e. the √ν regime at sufficiently low collisionality): the neoclassicalcorrection to the Maxwellian is large (in particular, its size does not depend on the collisionality) but neoclassical transport gets smaller as the collisionality is decreased, and turbulent transport could therefore gain relevance.

Our objective can be summarized as follows:

- Characterize in what conditions, how and to what extent the neoclassical corrections to the Maxwellian distribution affect the linear mode spectrum and turbulence in stellarators. The expected outcome of this novel investigation is the identification of those conditions and the fundamental mechanisms of this interaction. Numerical tools will be developed that will be applied in other parts of this proposal and can potentially be used for the modelling of experiments at later stages.