In the last recent years, we have obtained analytical results on stellarator neoclassical theory that are the basis for the goals of this task and for some of the numerical goals of task (2).

In [Calvo-17], we derived orbit averaged low collisionality neoclassical equations that rigorously retain the component of the magnetic drift tangent to magnetic surfaces, so that they capture the so called superbanana-plateau regime, and are therefore valid for very low collisionality and small value of the radial electric field. These equations also incorporate the component of the electric field tangent to magnetic surfaces and allow to determine it self-consistently. The set of equations, consisting of the drift-kinetic and quasineutrality equations, is linear and radially local, and has been implemented in the new code KNOSOS (see task (2)), that for the moment can treat model magnetic fields corresponding to sufficiently optimized stellarators. In [Calvo-18], we derived analytical scalings of the tangential electric field in different asymptotic regimes and validated them with KNOSOS for model optimized configurations.

In [Calvo-18b], we studied the impact of the tangential electric field on radial impurity transport in stellarators when the impurities are collisional and the main ions have low collisionality. We gave an analytical expression for the impurity flux when impurities are diluted and proved that even for small values of the tangential electric field, its effect on impurity transport can be large.

The objectives of this proposal under this task are:

- Employ the techniques used in [Calvo-18b] to derive analytical expressions for the impurity flux in other potentially relevant situations. For example, when the pressure anisotropy of the main ions cannot be neglected. We will also explore the possibility to generalize these calculations to the case in which impurities are non-trace (i.e. they are not diluted in the main plasma).

Go to the bibliography.