Constructing precisely quasi-isodynamic magnetic fields

Abstract

We present a novel method for numerically finding quasi-isodynamic stellarator magnetic fields with excellent fast-particle confinement and extremely small neoclassical transport. The method works particularly well in configurations with only one field period. We examine the properties of these newfound quasi-isodynamic configurations, including their transport coefficients, particle confinement and available energy for trapped-electron-instability-driven turbulence, as well as the degree to which they change when a finite pressure profile is added. We finally discuss the differences between the magnetic axes of the optimized solutions and their respective initial conditions, and conclude with the prospects for future quasi-isodynamic optimization.

Magnetic fields with general omnigenity

“…The optimization function penalizes the difference between the equilibrium magnetic field B eq and the constructed omnigenous field B, similar to the approach used by Goodman et al (2023). The errors are evaluated at a series of collocation points in the computational coordinates as…”

“…Moreover, Garren & Boozer (1991) suggested from a near-axis expansion that exact quasi-symmetry cannot be satisfied beyond a single flux surface. This is not a significant restriction in practice, however, QA and QH solutions have been found with good QS throughout a volume (Nührenberg & Zille 1988;Zarnstorff et al 2001;Henneberg et al 2019;Bader et al 2020;Landreman & Paul 2022), and many solutions have been discovered that approach OP while being far from QS (Camacho Mata, Jorge et al 2022;Sánchez et al 2023;Goodman et al 2023). The performance of QH and OP have also been experimentally verified by the HSX and W7-X stellarators, respectively.…”

“…This omnigenous field is generalized to any helicity, as was also done by Landreman & Catto (2012). The difference between the actual equilibrium magnetic field and the constructed target field is then penalized, like the technique devised by Goodman et al (2023).…”

Energetic particle tracing in optimized quasi-symmetric stellarator equilibria

“…Although perfectly omnigenous (Cary & Shasharina 1997) and quasi-symmetric (Garren & Boozer 1991 a ) devices have been conjectured not to exist, it has been shown that very precise approximations can be obtained (Landreman & Paul 2022; Goodman et al. 2023).…”

Helicity of the magnetic axes of quasi-isodynamic stellarators

“…Optimization within these parameters has resulted in remarkably low neoclassical transport, as measured by the effective neoclassical ripple metric eff (Jorge et al 2022). Boundary optimization using NAE configurations as initial points has also allowed the discovery of novel QI stellarators with excellent fast-particle confinement (Goodman et al 2023). However, these methods have only led to configurations with a small number of field periods (N<3), in stark contrast to traditionally optimized QI configurations, like W7-X, QIPC (Subbotin et al 2006) or Shafranov et al (2004) with N = 5, 6 and 9, respectively.…”