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# 28th IAEA Fusion Energy Conference (FEC 2020)

May 10 – 15, 2021
Virtual Event
Europe/Vienna timezone
The Conference will be held virtually from 10-15 May 2021

## Improving Energetic Particle Confinement in Stellarator Reactors

May 11, 2021, 8:30 AM
4h
Virtual Event

#### Virtual Event

Regular Poster Magnetic Fusion Theory and Modelling

### Description

Improving Energetic Particle Confinement in Stellarator Reactors
A. Bader$^1$, M. Drevlak$^2$, D.T. Anderson$^1$, C.C. Hegna$^1$, S.A. Henneberg$^2$,
T.G. Kruger$^1$, A. Ware$^3$
1: University of Wisconsin-Madison, WI, USA,
2: Max-Planck Institut fur Plasmaphysik, Greifswald, Germany,
3: University of Montana, MT, USA

Energetic particle confinement is a key issue for the scalability of stellarators to fusion power plants. Prompt losses of alpha particles born from fusion reactions can cause significant material damage. Analytically derived proxies for collisionless energetic particle confinement (1) have been used for the first time to optimize quasihelically symmetric stellarator equilibria (2). This paper will expand on recently published results, along with inclusion of analysis to account for collisional alpha particle transport with reactor relevant alpha sourcing profiles.
A proxy for energetic particle transport, $\gamma_c$, accounts for both the net bounce-averaged radial particle drifts, a quantity to be minimized, and poloidal drift, a quantity to be maximized. Minimization of 𝛾c corresponds to aligning contours of the second adiabatic invariant, $J_\parallel$, to flux surfaces. This metric has been included in the ROSE optimization code (3) and used to optimize equilibria for good energetic and neoclassical particle transport. Previous results indicate that two classes of stellarators, quasihelically-symmetric stellarators, and maximum-J stellarators should have better energetic particle transport than other configurations (4). This paper focuses on optimizations of quasihelically symmetric stellarators. Results indicate the existence of equilibria which nearly eliminate all collisionless losses within the plasma mid-radius (figure 1a) for an ARIES-CS scale reactor (450 m3, 5.8 T). These configurations are obtained by optimizing simultaneously for $\gamma_c$ and a metric for quasihelical symmetry. Interestingly, configurations with improved energetic particle transport did not correlate with improvements to neoclassical transport in the 1/𝜈 regime as measured by $\epsilon_\mathrm{eff}$.

It is well known that the ripple associated with realistic plasma coils can negatively affect alpha particle confinement. However, using coil optimization codes REGCOIL (5) and FOCUS (6), we show that it is possible to reproduce configurations with high enough fidelity that the alpha particle confinement is not significantly degraded (figure 1b). A key feature for the coil optimization is the realization of the equilibria with coils placed farther from the plasma, thus reducing high order harmonics associated with the toroidal mode numbers equivalent to the coil number. These high order modes have been previously found to be deleterious to energetic particle confinement on both stellarators and tokamaks.
New results will be presented regarding alpha particle transport that include collisions with the background plasma. Collisional calculations require additional assumptions about configuration parameters, most importantly the density and temperature profiles which govern the collisional equations and the alpha particle source distribution. We show that when including collisions, configurations exist at the ARIES-CS scale and with ARIES-CS parameters with total energy loss below 4% (figure 2a) with most of the losses occurring from particles born outside the midradius (> r/a = 0.55) (figure 2b). Results will be presented that show energetic particle transport under a variety of density and temperature profile assumptions.

In light of these results, the outlook for energetic particle optimization for quasihelical stellarators is bright. The results presented here represent only a first attempt and with improved optimization algorithms better configurations may yet be found. Additionally, further improvements in stellarator coil design can help gain confidence that such configurations are realizable.

References:
(1) V. V. Nemov et al. Physics of Plasmas 15 052501 (2008)
(2) A. Bader et al. Journal of Plasma Physics 85 5 (2019)
(3) M. Drevlak et al. Nuclear Fusion 59 016010 (2018)
(4) W. Lotz et al. Plasma Phys. Control. Fusion 34 1037 (1992)
(5) M. Landreman Nuclear Fusion 57 046003 (2017)
(6) C. Zhu et al. Nuclear Fusion 58 016008 (2018)

Work supported by DE-FG02-93ER54222, DE-FG02-99ER54546 and UW2020 135AAD3116

Affiliation University of Wisconsin-Madison United States

### Primary authors

Aaron Bader (University of Wisconsin-Madison) Michael Drevlak (Max-Planck-Institut für Plasmaphysik) David Anderson (University of Wisconsin-Madison) T. Kruger (University of Wisconsin-Madison) Chris Hegna (University of WIsconsin-Madison) Sophia Henneberg (Max-Planck-Institut für Plasmaphysik) A. S. Ware (University of Montana)