Neoclassical transport is a fundamental part of stellarator scenario development, since it is expected to account for most of the energy losses in a stellarator reactor. Therefore, its minimization is in the core or any process of stellarator optimization and design.

In a tokamak, the radial neoclassical transport is very small. The reason is that the average radial magnetic drift (the slow motion that separates particles from the original magnetic field lines) is zero: trapped particles move back and forth along the magnetic field lines and, while they do so, they drift outwards and inwards; in a tokamak, due to the exact axisymmetry of the magnetic configuration, this radial drift is zero on average. A generic stellarator is different: the value of the magnetic field on a flux surface lacks the simple symmetry existing in a tokamak. When a particle moves along the magnetic field line, it finds a complicated landscape of maxima and minima of the magnetic field strength, and the average magnetic drift is not zero. There are exceptions: one is the quasisymmetric stellarator, which as the tokamak has one direction of symmetry and, as a consequence of this, has equivalent transport properties. Quasisymmetric stellarators are a particular case of a class of devices whose average magnetic drift is zero: omnigenous stellarators. While perfect omnigenetiy is impossible to achieve, careful design of the magnetic coils may allow to obtain a magnetic configuration which is close enough to omnigeneity so that energy confinement is practically equivalent to that of a tokamak.

Neoclassical optimization is the process that, among other goals, tries to achieve magnetic configurations close enough to omnigeneity. The figure of merit in the optimization loop is usually the *effective ripple*, which is a proxy for the radial energy flux in a particular neoclassical transport regime at low collisionalities: the so-called 1/ν regime. This quantity goes to zero as the designed magnetic configuration approaches omnigeneity.

We have developed a code, the KiNetic Orbit-averaging Solver for Stellarators (KNOSOS) that is able to provide a fast and accurate estimate of neoclassical transport in several stellarator regimes apart from the 1/ν, and that can therefore be used for a more efficient stellarator optimization.

KNOSOS is freely available and open-source, and can be downloaded from https://github.com/joseluisvelasco/KNOSOS

First calculations were presented in:

- KNOSOS: a fast orbit-averaged neoclassical code for arbitrary stellarator geometry in the
*Kinetic Theory Working Group Meeting*, Madrid, Spain, 2018. - I Calvo, F I Parra, J L Velasco, and J M García-Regaña. Impact of main ion pressure anisotropy on stellarator impurity transport. Nuclear Fusion, 60(1):016035, 2019. arXiv / PDF

KNOSOS is the result of a line of research aimed at describing analytically optimized stellarators. Examples of this work can be found in:

- I Calvo, F I Parra,
__J L Velasco,__and J A Alonso. The effect of tangential drifts on neoclassical transport in stellarators close to omnigeneity.*Plasma Physics and Controlled Fusion*, 59(5):055014, 2017. arxiv / PDF

- I Calvo, F I Parra, J A Alonso, and
__J L Velasco__. Optimizing stellarators for large flows.*Plasma Physics and Controlled Fusion*, 56(9):094003, 2014. arxiv / PDF

- I Calvo, F I Parra,
__J L Velasco__, and J A Alonso. Flow damping in stellarators close to quasisymmetry. Plasma Physics and Controlled Fusion, 57(1):014014, 2015. arxiv / PDF

- I Calvo, F I Parra,
__J L Velasco__, J A Alonso. Stellarators close to quasisymmetry.*Plasma Physics and Controlled Fusion*, 55(12):125014, 2013. arxiv / PDF