Stellarator equilibria with reactor relevant energetic particle losses

Abstract

Stellarator configurations with reactor relevant energetic particle losses are constructed by simultaneously optimizing for quasisymmetry and an analytically derived metric ( $\unicode[STIX]{x1D6E4}_{c}$ ), which attempts to align contours of the second adiabatic invariant, $J_{\Vert }$ with magnetic surfaces. Results show that with this optimization scheme it is possible to generate quasihelically symmetric equilibria on the scale of ARIES-CS which completely eliminate all collisionless alpha particle losses within normalized radius $r/a=0.3$ . We show that the best performance is obtained by reducing losses at the trapped–passing boundary. Energetic particle transport can be improved even when neoclassical transport, as calculated using the metric $\unicode[STIX]{x1D716}_{\text{eff}}$ , is degraded. Several quasihelically symmetric equilibria with different aspect ratios are presented, all with excellent energetic particle confinement.

Accelerated methods for direct computation of fusion alpha particle losses within, stellarator optimization

“…It has, however, some disadvantage if the starting surface is close to a low-order rational surface such that one needs a very long field line to cover it. In that case, the method of Bader et al (2019) for flux coordinate systems would be preferable.…”

“…Direct computation of such losses with usual numerical methods is relatively time consuming compared to other calculations within the optimization loop, in particular computation of three-dimensional (3-D) magnetohydrodynamic equilibria. This is why 2 C. G. Albert, S. V. Kasilov and W. Kernbichler fusion alpha loss estimation is often performed via faster proxy models (Nemov et al 2005(Nemov et al , 2008Bader et al 2019) that, however, cannot capture the full physics of drift orbits and, therefore, are suited only for the initial stage of optimization. The reason for this is the high alpha energy of 3.5 MeV, leading to the following consequences.…”

Advancing the physics basis for quasi-helically symmetric stellarators

“…In brief, this metric seeks to align contours of the second adiabatic invariant J with flux surfaces. Its viability in producing configurations with excellent energetic ion confinement was demonstrated in Bader et al (2019). (iii) A magnetic well (Greene 1997), where present, provides stability against interchange modes.…”

“…In both cases, 5000 particles are included in the evaluation for each flux surface for 200 ms, which corresponds to 2 alpha slowing down times at the core ARIES-CS density (n e = 5 × 10 20 m −3 ) and temperature (T e = 12 keV) and to 10 alpha slowing down times at the mid-radius density (n e = 5 × 10 20 m −3 ) and temperature (T e = 4 keV). Previous calculations indicated that 5000 particles per flux surface were sufficient for Monte Carlo statistical purposes (Bader et al 2019). These calculations only consider the vacuum fields, and improvements with finite pressure and plasma currents are left for future optimization studies.…”

“…These advances come in several forms including the identification of new quasi-axisymmetric configurations (Henneberg et al 2019b). Advances in theoretical understanding have produced mechanisms for optimization in the areas of turbulent transport (Mynick, Pomphrey & Xanthopoulos 2010;Xanthopoulos et al 2014;, energetic particle transport (Bader et al 2019;Henneberg, Drevlak & Helander 2019a) and non-resonant divertors (Bader et al 2018). Also, construction of optimized equilibria from first principles has been demonstrated for quasi-symmetric stellarators (Landreman & Sengupta 2018;Landreman, Sengupta & Plunk 2019) and quasi-omnigenous stellarators .…”