Ion-temperature-gradient stability near the magnetic axis of quasisymmetric stellarators

Abstract

The stability of the ion-temperature gradient mode in quasisymmetric stellarators is assessed. This is performed using a set of analytical estimates together with linear gyrokinetic simulations. The peak growth rates, their corresponding real frequencies and wave-vectors are identified. A comparison is made between a first-order near-axis expansion model and eleven realistic designs obtained using numerical optimization methods. It is found that while the near-axis expansion is able to replicate the growth rates, real frequencies and perpendicular wave-vector at the inner core (both using simplified dispersion relations and first-principle gyrokinetic simulations), it leads to an overestimation of the growth rate at larger radii. An approximate analytic solution of the ITG dispersion relation for the non-resonant limit suggests growth rates could be systematically higher in quasi-axisymmetric (QA) configurations compared to quasi-helically (QH) symmetric ones. However except for very close to the axis, linear gyrokinetic simulations do not show systematic differences between QA and QH configurations.

Coarse-grained gyrokinetics for the critical ion temperature gradient in stellarators

“…As usual, the temperature gradient scale length is measured relative to the minor radius, a/L T = −(a/T )dT /dr. To study the most unstable ITG mode conditions, we neglect certain stabilizing factors such as the density gradient [22,23] and plasma beta (electromagnetic effects) [24].…”

Energetic particle tracing in optimized quasi-symmetric stellarator equilibria

“…higher values of the major radius to obtain a better behaviour of this approximation, albeit at the cost of a less compact reactor. The effective minor radius in this work is given as an average of this quantity throughout the last closed surface, which can be written as πa 2 A = 1/2π 2π 0 S(φ) dφ, where S(φ) is the area of the surface cross-section at each point of the cylindrical angle φ (Jorge & Landreman 2021). We note that the minor radius value is substantially larger than the alpha particles' gyroradius as expected of this kind of fusion reactor.…”

“…However, as it is a compact device, its aspect ratio , the ratio between its major radius and its minor radius , may stretch the limit of applicability of the NAE to be effective all the way up to the boundary, so we take higher values of the major radius to obtain a better behaviour of this approximation, albeit at the cost of a less compact reactor. The effective minor radius in this work is given as an average of this quantity throughout the last closed surface, which can be written as , where is the area of the surface cross-section at each point of the cylindrical angle (Jorge & Landreman 2021). We note that the minor radius value is substantially larger than the alpha particles’ gyroradius as expected of this kind of fusion reactor.…”

Direct Microstability Optimization of Stellarator Devices

“…The remaining input parameters for GS2 were obtained by performing convergence tests for the initial and final equilibria of each optimization in a similar fashion to Ref. [34].…”