Stellarators are an alternative to tokamaks in the quest for a fusion reactor based on magnetic confinement. Their most prominent advantage is that their magnetic field is created almost entirely by external coils. No time-dependent current is thus needed inside the plasma, which enables steady- state operation and makes stellarators less prone to large- scale instabilities than tokamaks. On the other hand, the magnetic configuration of the stellarator is three-dimensional, which generally worsens their neoclassical confinement (the one associated to the inhomogeneity of the magnetic field and inter-particle collisions) of both reactants and fusion-born alpha particles to a level incompatible with reactor operation.

This has historically left the stellarator concept at a disadvantage with respect to the tokamak, whose axial symmetry makes neoclassical transport negligible at the low collisionalities relevant for the core of a reactor. The strategy employed to mitigate this problem is stellarator optimization: the magnetic configuration is carefully tailored in order to have (among other criteria) a neoclassical transport as low as that of the axisymmetric tokamak. A stellarator configuration that fulfils this criterion is called omnigeneous. Quasi-isodynamic (QI) and quasi-symmetric configurations (QS) are specific types of omnigenous stellarator.

More specifically, optimization criteria include low energy transport, lack of core density depletion or impurity accumulation and reduced fast ion losses and parallel flows. At CIEMAT, we have developed the neoclassical code KNOSOS with this purpose. Wendelstein 7-X is a stellarator whose neoclassical optimization is under experimental validation.

We have introduced the notion of robust optimization via a flat mirror term:

- 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

A quasi-isodynamic configuration with sufficiently small radial variation of the mirror term can achieve the maximum-J property at low plasma β. This results in small radial transport of energy and good confinement of bulk and fast ions even if the configuration is not very close to perfect omnigeneity, and for a wide range of plasma scenarios, including low β and small radial electric field. Reactors based on this concept would be easier to design, as they would be more robust against arror fields, and operate.

As a result of this approach we have obtained CIEMAT-QI:

- E. Sánchez, J.L. Velasco, I. Calvo, and S. Mulas. A quasi-isodynamic configuration with good confinement of fast ions at low plasma . Nuclear Fusion, 63(6):066037, 2023. arxiv / PDF

This is a new quasi-isodynamic (QI) stellarator configuration optimized for the confinement of energetic ions at low plasma β. The new configuration has poloidally closed contours of magnetic field strength, low magnetic shear and a rotational transform profile allowing an island divertor. It shows ideal and ballooning magnetohydrodynamic stability up to β = 5%, reduced effective ripple, below 0.5% in the plasma core. Even at low β, the configuration approximately satisfies the maximum-J property, and the confinement of fast ions is good at β ∼ 1.5% and becomes excellent at reactor values, β ∼ 4%. An evaluation of the D31 neoclassical mono-energetic coefficient supports the expectation of a reduced bootstrap current for plasmas confined in QI configurations. A set of filamentary coils that preserve the good confinement of fast ions in the core is presented.

Related work 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
- 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
- J.A.Alonso,I.Calvo,D.Carralero,J.L.Velasco,J.M.Garc ́ıa-Regan ̃a,I.Palermo, and D. Rapisarda. Physics design point of high-field stellarator reactors. Nuclear Fusion, 62(3):036024, 2022. arxiv / PDF