Session NI02: Invited: Rosenbluth Award and MFE IV - Stellarators

Rosenbluth Dissertation Award: Quasisymmetry: a modern perspective on the stellarator concept

Quasisymmetry (QS) is a property of magnetic field-plasma systems that enables the containment of the plasma, necessary to undergo thermonuclear fusion. The concept originated in the 80s, when a generalisation of the working principle of the axisymmetric tokamak was sought. Here we revisit the concept from the ground up, providing a renewed perspective and exploring previously unexplored questions.

In this presentation we shall start by building QS from the most fundamental level: the behaviour of charged particles, and the attempt to confine them. This allows the conceptualisation of QS without any assumptions on the nature of the underlying equilibrium. This will make it clear an underlying tension between the symmetry and force balance, which makes the construction of QS equilibrium fields in a typical isotropic pressure equilibrium challenging. Anisotropic pressure solutions appear as a more natural option.

Under a more practical prism, we are interested in finding explicit examples of QS fields. Solving the governing partial differential equations governing the problem directly is too complex. Thus, the problem is often addressed through optimisation. To gain additional insight and control,we consider an asymptotic description of solutions around their core, the so-called near-axis expansion. We focus on this in this talk. A systematic construction of quasisymmetric fields within such a framework is here presented, which unveils an ordered structured topological phase space of quasisymmetric fields, providing an opportunity to understand properties and exhaust possibilities of quasisymmetric configurations.   

Recent Experimental and Modeling Results from the HSX Stellarator

The Helically Symmetric eXperiment (HSX) is an optimized stellarator with a major radius of 1.2 m and a 1 Tesla magnetic field. Previous work has shown that the unique quasi-helical magnetic field configuration of HSX allows for large intrinsic flows in the direction of symmetry [1] and reduces neoclassical transport [2] so that transport is predominantly driven by trapped electron mode turbulence [3].HSX is equipped with a set of auxiliary coils which are used to study the effects of magnetic field geometry on plasma confinement.

Excellent plasma performance has been achieved  following an intensive first wall reset, which involved removing coatings deposited on the plasma facing stainless steel wall, combined with a new vessel baking system and extensive glow discharge cleaning. The resulting reduction in impurity content has driven substantial improvements in plasma profiles, including core electron temperatures well above 2 keV and higher overall energy confinement. 

During studies with different main-ion species, more pronounced pressure profile peaking has been measured in hydrogen fueled plasmas than with helium fueling. This is consistent with non-linear GENE [4] simulations which predict reduced turbulent heat fluxes in hydrogen plasmas. Although previous work suggested the strong electron temperature peaking observed in the core of HSX is a result of turbulent suppression by ExB flow shear, recent analysis of correlation ECE measurements have shown increased radiation temperature fluctuations in regions with high electron temperature gradients. These measurements show qualitative agreement with non-linear gyrokinetic flux tube simulations with GENE.

[1] A. Briesemeister et al., 2010 Contrib. Plasma Phys. 50 8

[2] J. Canik et al., 2007 Phys. Rev. Lett. 98 8

[3] W. Guttenfelder et al., 2008 Phys. Rev. Lett. 101 21

[4] F. Jenko et al., 2000 Phys. Plasmas 7 1904

[5] M.J. Gerard et al., 2023 Nucl. Fusion 63 056004   

High-fidelity turbulence modeling of W7-X discharges: Novel insights into transport physics

In recent years, the Wendelstein 7-X (W7-X) stellarator has demonstrated the feasibility of

neoclassical transport optimization. However, turbulent transport remains a significant obstacle in

the development of fusion power plants. It has been hypothesized that W7-X is largely resistant to

electron-scale turbulence induced by electron temperature gradient (ETG) modes [1]. Conversely, it

was argued in [2] that ETG transport alone could account for the experimental observations of

electron heat diffusivity in the core of certain discharges. Meanwhile, ion-scale transport is believed

to be predominantly influenced by ion temperature gradient (ITG) turbulence, with trapped electron

mode (TEM) turbulence ostensibly confined to the edge region, if present at all [3, 4, 5].

In this presentation, we scrutinize these perspectives through comprehensive gyrokinetic transport

studies of an experimental electron cyclotron resonance heating (ECRH) discharge from W7-X,

utilizing the GENE [6] and GENE-3D [7] simulation codes. By employing flux-tube, full-flux-

surface, and innovative radially global simulations that retain all pertinent physical effects, we

provide evidence for significant contributions to the turbulent fluxes from both ETG and TEM

turbulence. Notably, the latter is primarily driven by the electron temperature gradient - a

mechanism that has hitherto been underrepresented in stellarator research compared to its density-

gradient-driven counterpart.

These insights are poised to reconcile the discrepancy between qualitative theoretical predictions

and quantitative experimental data, informing the development of simplified turbulence models

essential for the design of a future turbulence-optimized stellarator.

References

[1] G. G. Plunk et al., PRL 122, (2019)

[2] G. M. Weir et al., NF 61 (2021)

[3] T. Klinger et al., NF 59, (2019)

[4] T. Wegner et al., NF 60, (2020)

[5] M. Beurskens et al., NF 62, (2021)

[6] F. Jenko et al., PoP 7, (2000)

[7] M. Maurer et al., JCP 420, (2020)   

Stable quasi-isodynamic stellarators with low turbulence as fusion reactor candidates

Quasi-isodynamic (QI) stellarators are uniquely attractive fusion reactor candidates due to their low neoclassical transport, excellent confinement of fusion-born alpha particles, and vanishingly small net toroidal currents [1]. To be a viable fusion reactor, a stellarator design must be MHD stable, have low enough turbulent heat losses to alleviate the temperature clamping present in the Wendelstein 7-X experiment [2], and include set of buildable electromagnetic coils. Combining the work in [3] with the findings from [4], we present a new approach to finding MHD stable QI stellarator geometries with superb fast-ion confinement and considerably lower turbulence than W7-X, which can be realized by a set of relatively simple electromagnetic coils. Their small net toroidal currents, along with their optimised rotational transform profiles, make these configurations compatible with an edge island divertor. We have additionally found that these configurations can be designed to have an electron root — a region of outward-pointing radial electric field — which provides an elegant solution to the problem of impurity accumulation [5]. As such, these designs are alluring candidates for future stellarator experiments and reactors.

References

[1] P. Helander and J. Nuhrenberg. Bootstrap current and neoclassical transport in quasi-isodynamic stellarators. Plasma Physics and Controlled Fusion, 51(5):055004, Feb 2009.

[2] M. N. A. Beurskens and et al. Ion temperature clamping in Wendelstein 7-X electron cyclotron heated plasmas. Nuclear Fusion, 61(11):116072, Oct 2021.

[3] A. G. Goodman, et al. Quasi-isodynamic stellarators with low turbulence as fusion reactor candidates. PRX Energy 3, 023010, Jun 2024.

[4] J. Kappel, M. Landreman, and D. Malholtra. The magnetic gradient scale length explains why certain plasmas require close external magnetic coils. Plasma Physics and Controlled Fusion, 66, Jan 2024.

[5] C. D. Beidler, M. Drevlak, J. Geiger, P. Helander, H. M. Smith, and Y. Turkin. Reduction of neoclassical bulk-ion transport to avoid helium ash retention in stellarator reactor. Submitted to Nuclear Fusion, Jan 2024.   

Validation of a Comprehensive First-Principles-Based Framework for Predicting the Performance of Future Stellarators

Turbulence remains a significant obstacle for stellarator confinement. Using the most powerful supercomputers, it is now feasible to analyze turbulence across the plasma volume with gyrokinetic codes. Before using such codes, validation studies are necessary to ensure accuracy relative to experimental results.

In this talk, we showcase the results of the successful comprehensive validation of the GENE(-3D)-KNOSOS-Tango framework for predicting the steady-state plasma profiles in a stellarator. This extensive validation study is a first-of-a-kind for stellarators. This framework couples the gyrokinetic turbulence codes GENE and GENE-3D, the neoclassical transport code KNOSOS, and the transport code Tango in a multiple-timescale simulation loop.

We selected four OP1.2b W7-X scenarios with different turbulence characteristics. We perform ion-scale kinetic-electron and electron-scale adiabatic-ion simulations to evolve the density and temperature profiles. The simulated profiles agree very well with experimental data while turbulence properties, such as density fluctuations and heat diffusivities, mirror the observed trends. Key effects are also touched upon, such as electron-scale turbulence and the neoclassical radial electric field shear.

The validation of the GENE(-3D)-KNOSOS-Tango framework enables us to make credible predictions of physical phenomena in stellarators and reactor performance. This is of utmost importance today, when fusion start-ups worldwide are using simulation codes to design power-generating machines for the near future.   

Fast and Accurate Stellarator Optimization for Novel Physics Metrics

The stellarator is a promising fusion reactor concept that can avoid many limitations of tokamaks, such as operating without current drive and softer stability limits. However, the large design space and lack of guaranteed confinement means significant numerical optimization is required of any feasible stellarator design. We present an overview of the new stellarator design and analysis results made possible by the DESC code suite. This software package couples equilibrium and optimization codes together to efficiently solve the numerical optimization problems required for next-generation stellarator designs. Unlike finite differences or adjoint methods, automatic differentiation provides access to exact derivatives of any objective function and allows the inclusion of more physics constraints, such as metrics for particle confinement and stability. We demonstrate optimization of MHD equilibria for omnigenity, mercier and ballooning stability, alpha particle confinement, neoclassical and turbulent transport, and coil feasibility metrics. We also show new results from coil and winding surface optimization along with free boundary equilibria and single stage optimization of coils and equilibrium simultaneously.