Following the recent theoretical results discussed in the theory section, we have developed the numerical code KNOSOS (KiNetic Orbit-averaging SOlver for Stellarators) [Velasco-18, Calvo-18]. KNOSOS is the first radially-local code to rigorously retain the tangential magnetic drift in the calculation of ion neoclassical transport. In [Velasco-18] we proved that this is crucial in order to calculate accurately the tangential electric field created by the bulk ions, and the corresponding radial impurity transport, especially in the case of plasmas close to impurity screening [Velasco-17], such as scenarios displaying impurity hole of the Large Helical Device [Ida-09].

However, in its current version, KNOSOS solves the set of equations with some approximations. First, it solves the equations for the simplified case of a model magnetic configuration close enough to omnigeneity. Second, it solves only the ion drift kinetic equation, and considers adiabatic electrons in the ambipolarity and quasineutrality equations. Third, it employs a pitch-angle-scattering collision operator.

The objectives of this proposal under this task are:

- Extend and benchmark KNOSOS so that it can treat general stellarator geometries. Some first calculations of the drift kinetic equation without tangential magnetic drift and tangential electric field have been done and compared with the neoclassical code DKES [Velasco-18b]. We will include the tangential magnetic drift and we will solve consistently the ambipolar and quasineutrality equations.
- Extend and benchmark KNOSOS so that it becomes a multispecies code. First, the electron drift kinetic equation will be solved in parallel to that of the ions. For some plasma regimes, this may require upgrading the collision operator. Second, the electrons will be included in the ambipolarity and quasineutrality equations. Depending upon other results, so will the collisional impurities in the non-trace limit.
- Fine tune KNOSOS so that it can provide very fast accurate neoclassical estimations of transport. The set of equations solved by KNOSOS is suited to a very high degree of parallelization (in species, radial position, value of the pitch-angle variable at which the bounce-averages are calculated, value of the radial electric field, etc.). Furthermore, for each calculation, depending on the quantity of interest and the plasma parameters, a different level of sophistication may be required (e.g., the electrons may or not be considered adiabatic, or the tangential electric field may or not be neglected, etc). We will try to obtain systematic rules that speed up calculations.

Go to the bibliography.