KNOSOS (KiNetic Orbit-averaging SOlver for Stellarators) is a freely available, open-source code that calculates neoclassical transport in low-collisionality plasmas of three-dimensional magnetic confinement devices by solving the radially local drift-kinetic and quasineutrality equations. The main feature of KNOSOS is that it relies on orbit-averaging to solve the drift-kinetic equation very fast. KNOSOS treats rigorously the effect of the component of the magnetic drift that is tangent to magnetic surfaces, and of the component of the electrostatic potential that varies on the flux surface. In these papers, we show several calculations for the stellarators W7-X, LHD, NCSX and TJ-II that provide benchmark with standard local codes and demonstrate the advantages of this approach.

In this work, we develop a model that, based on the radially-local bounce-averaged drift-kinetic equation, classifies orbits and succeeds in predicting configuration-dependent aspects of the prompt losses of energetic ions in stellarators. Such a model could in turn be employed in the optimization stage of the design of new devices.

W7-X has already been able to achieve high-temperature plasma conditions during its 2017 and 2018 experimental campaigns, producing record values of the fusion triple product for such stellarator plasmas. The triple,product of plasma density, ion temperature and energy confinement time is used in fusion research as a figure of merit, as it must attain a certain threshold value before net-energy-producing operation of a reactor becomes possible. Here we demonstrate that such record values provide evidence for reduced neoclassical energy transport in W7-X, as the plasma profiles that produced these results could not have been obtained in stellarators lacking a comparably high level of neoclassical optimization.

Achieving impurity and helium ash control is a crucial issue in the path towards fusion-grade magnetic confinement devices, and this is particularly the case of helical reactors, whose low- collisionality ion-root operation scenarios usually display a negative radial electric field which is expected to cause inwards impurity pinch. In this work we discuss, based on experimental measurements and standard predictions of neoclassical theory, how plasmas of very low ion collisionality, similar to those observed in the impurity hole of the large helical device can be an exception to this general rule, and how a negative radial electric field can coexist with an outward impurity flux.

  • J L Velasco, K McCarthy, N Panadero, S Satake, D López-Bruna, J A Alonso, I Calvo, T Estrada, J M Fontdecaba, J Hernández, R García, F Medina, M A Ochando, I Pastor, S Perfilov, E Sánchez, A Soleto, B Ph Van Milligen, A Zhezhera, and the TJ-II Team. Particle transport after pellet injection in the TJ-II stellarator. Plasma Physics and Controlled Fusion, 58(8):084004, 2016. arXiv / PDF

Core plasma fuelling and density control is a critical issue for developing steady-state scenarios in fusion reactors. In this work we study radial particle transport in stellarator plasmas using cryogenic pellet injection. By means of perturbative experiments, we estimate the experimental particle flux and compare it with neoclassical simulations. Experimental evidence is obtained of the fact that core depletion in helical devices can be slowed-down even by pellets that do not reach the core region. This phenomenon is well captured by neoclassical predictions.

  • J A Alonso, J L Velasco, I Calvo, T Estrada, J M Fontdecaba, J García-Regaña, J Geiger, M Landreman, K McCarthy, F Medina, B Ph Van Milligen, M A Ochando, and F I Parra. Parallel impurity dynamics in the TJ-II stellarator. Plasma Physics and Controlled Fusion, 58(7):074009, 2016. arXiv / PDF

We review in a tutorial fashion some of the causes of impurity density variations along field lines and radial impurity transport in the moment approach framework. We apply the fluid model including main ion-impurity friction and inertia to observations of asymmetric emissivity patterns in neutral beam heated plasmas of the TJ-II stellarator. The model is able to explain qualitatively several features of the radiation asymmetry, both in stationary and transient conditions, based on the calculated in-surface variations of the impurity density.

Direct observations of electrostatic potential variations along the flux surfaces of the TJ-II stellarator are presented. Its effect on and/or combination with impurity density variations can give rise to substantial changes of radial impurity fluxes. Measurements taken with two distant Langmuir probe arrays show differences in the edge floating potentials profiles of several tens of volts in electron-root wave-heated plasmas. Neoclassical Monte Carlo simulations estimate the correct order of magnitude for the overall variation in potential and predict the trend observed with the radial electric field.

Rotation is favorable for confinement, but a stellarator can rotate at high speeds if and only if it is sufficiently close to quasisymmetry. This article investigates how close it needs to be; it contains the first step towards a formulation to calculate the rotation profile of a stellarator close to quasisymmetry.

A comparative study of energy transport for medium- to high-density discharges in the stellarator-heliotrons TJ-II, W7-AS and LHD is carried out. The chosen discharges exhibit significant ion energy transport, and ion-root conditions, i.e. a small negative radial electric field, were found. Within a core region, the predicted neoclassical energy fluxes comply with experimental findings .

The drift kinetic equation is solved for low density TJ-II plasmas employing slowly varying, time-dependent profiles. This allows us to simulate density ramp-up experiments and describe from first principles the formation and physics of the radial electric field shear layer. The main features of the transition are perfectly captured by the calculation, and good quantitative agreement is also found. The results presented here, that should be valid for other non-quasisymmetric stellarators, provide a fundamental explanation for a wealth of experimental observations connected to the shear layer emergence in TJ-II.