The basic physics idea behind magnetic confinement fusion is relatively simple: it consists on extracting energy from well-known atomic reactions that take place once the appropriate conditions have been created. These conditions can be summarized by the so-called Lawson Criterion: the triple product nτET (where n is the plasma density, T the plasma temperature and τE the energy confinement time) must be above certain value.

Roughly speaking, the energy confinement time can be defined as the ratio between the energy content of the plasma over the net power input into the device by the external heating systems. Therefore, maximizing the triple product is equivalent to minimizing the input power needed to sustain a given plasma density and temperature. Since, in steady-state, the input power is basically equal to the energy flowing out of the plasma due to transport processes, undertanding and predicting energy transport in magnetic confinement devices is key for achieving fusion-relevant plasma parameters.

Neoclassical transport is caused by the combination of the motion of charged particles in an inhomogeneous magnetic field and particle collisions. In stellarators, the very unfavourable scaling of the neoclassical energy flux with the temperature makes it dominant in the core region in reactor-relevant scenarios. Therefore, predictive transport simulations with neoclassical transport at the core, complemented with simple models for turbulent transport in the edge, are typically used for estimating the confinement time, power load to the walls, needs of heating… of stellarators. This approach has to be supported by a step-by-step systematic validation of the predictions of neoclassical theory with experimental estimates of energy transport.

Examples of such validation studies are:

- A Dinklage, M Yokoyama, K Tanaka, J L Velasco, D López-Bruna, C D Beidler, S Satake, E Ascasíbar, J Arévalo, J Baldzuhn, Y Feng, D Gates, J Geiger, K Ida, M Jakubowski, A López- Fraguas, H Maassberg, J Miyazawa, T Morisaki, S Murakami, N Pablant, S Kobayashi, R Seki, C Suzuki, Y Suzuki, Yu Turkin, A Wakasa, R Wolf, H Yamada, M Yoshinuma, LHD Exp. Group, TJ-II Team, and W7-AS Team. Inter-Machine Validation Study of Neoclassical Transport Modeling in Medium- to High-Density Stellarator-Heliotron Plasmas.
*Nuclear Fusion*, 53(6):063022, 2013. PDF - Predicting the performance of existing stellarators and future reactors.
*Plasma Physics and fusion seminars (2016-2017),*Universidad Carlos III de Madrid, 2016.

Other related results can be found in:

- C D Beidler and the W7-X Team. Demonstration of reduced neoclassical energy transport in Wendelstein 7-X. Nature, 596(7871):221–226, 2021. PDF
- D. Carralero, T. Estrada, E. Maragkoudakis, T. Windisch, J.A. Alonso, M. Beurskens, S. Bozhenkov, I. Calvo, H. Damm, O. Ford, G. Fuchert, J.M. García-Regaña, N. Pablant, E. Sánchez, E. Pasch, J.L. Velasco, and the Wendelstein 7-X team. An experimental characterization of core turbulence regimes in Wendelstein 7-X. Nuclear Fusion, 61(9):096015, 2021. arxiv / PDF
- A. Murari, E. Peluso, J. Vega, J.M. García-Regaña, J.L. Velasco, G. Fuchert, and M. Gelfusa. Scaling laws of the energy confinement time in stellarators without renormalization factors. Nuclear Fusion, 61(9):096036, 2021. PDF
- Tallents, D López-Bruna,
__J L Velasco__, M A Ochando, B Ph Van Milligen, V I Vargas, J J Martinell, D Tafalla, J M Fontdecaba, J Herranz, E Blanco, F Tabarés, T Estrada, I Pastor and the TJ-II Team. Transport analysis in an ECH power scan of TJ-II plasmas.*Plasma Physics and Controlled Fusion*, 56(7):075024, 2014. PDF - Non-local NC simulations in stellarators/heliotrons using the FORTEC-3D code.
*Gyrokinetic Theory Working Group Meeting*, Madrid, Spain, 2014. - Validation of local and non-local neoclassical predictions for the radial transport of plasmas of low ion collisionallity.
*41th EPS Conference on Plasma Physics,*Berlin, Germany, 2014.