Good confinement of fusion-generated alpha particles is one of the basic properties of a fusion reactor. On the one hand, these alpha particles are expected to contribute to heat the plasma, which requires their confinement time to be comparable to the time that it takes them to thermalize by giving their energy to the bulk plasma. This is the so called slowing-down-time. Specifically, the widely-employed figure of merit for energetic ion confinement is the accumulated fraction of alphas that are lost between their birth and one slowing-down time. An even more restrictive criterion may be set by the heat loads on the walls: alphas that are promptly lost, and that therefore retain most of their original energy, could damage the plasma facing components (the degree to which this happens will depend to some extent on the details of the magnetic configuration beyond the last closed flux-surface, as well as on the design of the facing components themselves). This issue turns the fraction of alphas that are promptly lost (i.e. that are lost in a time scale much shorter than the slowing-down time) into an itional quantity to be targeted in the design of a magnetic configuration.

In stellarators, due to their three-dimensional configuration, neoclassical processes are the main concern with respect to energetic ion confinement, and they need to be studied and, in future reactors, optimized, as they have been to some extent in the stellarator Wendelstein 7-X.

We have developed a model that classifies orbits and succeeds in predicting configuration-dependent aspects of the prompt losses of energetic ions in stellarators:

- J. L. Velasco, I. Calvo, S. Mulas, E. Sánchez, F.I. Parra, Á. Cappa, and the W7- X Team. A model for the fast evaluation of prompt losses of energetic ions in stellarators. 61(11):116059, 2021. arxiv / PDF

This model has been successfully employed in the optimization of CIEMAT-QI, a stellarator configuration with (among other properties) fast ion confinement at low plasma pressure.

It has also been used to predict escenarios of good fast ion confinement in the stellarator W7-X:

- Theoretical prediction of improved energetic ion confinement in low-β Wendelstein 7-X plasmas with reduced turbulence. Invited talk at the
*23rd International Setellarator-Heliotron Workshop,*Warsaw, Poland, 2022.

Finally, it has been employed to characterize fast ion confinement in quasi-symmetric stellarators:

- E.J. Paul, A. Bhattacharjee, M. Landreman, D. Alex, J.L. Velasco, and R. Nies. Energetic particle loss mechanisms in reactor-scale equilibria close to quasisymmetry. Nuclear Fusion, 62(12):126054, 2022. arxiv / PDF

In a more recent paper, we have developed more general criteria for the good confinement of energetic particles in a stellarator:

- J.L. Velasco, I. Calvo, E. Sánchez, and F.I. Parra. Robust stellarator optimization via flat mirror magnetic fields. Nuclear Fusion, 63(12):126038, 2023. arxiv / PDF

Other work espefically related to energetic ions can be found in:

- Á. Cappa, J. Varela, D. López Bruna, E. Ascasíbar, M. Liniers, L.G. Eliseev, J.M. Fontdecaba, J.M. García-Regaña, A. González-Jerez, N.K. Kharchev, F. Medina, A.V. Melnikov, S. Mulas, M. Ochando, D. Spong, J L Velasco, and TJ-II Team. Stability analysis of TJ-II stellarator NBI driven alfvén eigenmodes in ECRH and ECCD experiments. Nuclear Fusion, 61(6):066019, 2021. PDF
- S. Yamamoto, K. Nagasaki, K. Nagaoka, J. Varela, Á. Cappa, E. Ascasíbar, F. Castejón, J.M. Fontdecaba, J.M. García-Regaña, Á. González-Jerez, K. Ida, A. Ishizawa, M. Isobe, S. Kado, S. Kobayashi, M. Liniers, D. López-Bruna, N. Marushchenko, F. Medina, A. Melnikov, T. Minami, T. Mizuuchi, Y. Nakamura, M. Ochando, K. Ogawa, S. Ohshima, H. Okada, M. Osakabe, M. Sanders, J L Velasco, G. M. Weir, and M. Yoshinuma. Effect of ECH/ECCD on energetic-particle-driven MHD modes in helical plasmas. Nuclear Fusion, 60(6):066018, 2020. PDF
- S Mulas, A Cappa, J Martínez-Fernández, D Lopez-Bruna, Teresa J. L. Velasco, T Estrada, J M Gómez-Manchón, M Liniers, K J McCarthy, I Pastor, F Medina, and E Ascasibar. Validating neutral-beam current drive simulations in the TJ-II stellarator. Nuclear Fusion, 2023. arxiv / PDF