Analytic scaling relations are derived for a phenomenological model of the plasmoid instability in an evolving current sheet, including the effects of reconnection outflow. Two scenarios are considered, where the plasmoid instability can be triggered either by an injected initial perturbation or by the natural noise of the system (here…

Quasi-symmetry of a steady magnetic field means integrability of first-order guiding-center motion by a spatial symmetry. Here, we derive many restrictions on the possibilities for a quasi-symmetry. We also derive an analog of the Grad–Shafranov equation for the flux function in a quasi-symmetric magnetohydrostatic field.

In this work, we consider optimal control problems constrained by elliptic partial differential equations (PDEs) with lognormal random coefficients, which are represented by a countably infinite-dimensional random parameter with i.i.d. normal distribution. We approximate the optimal solution by a suitable truncation of its Hermite polynomial…

Recently designed optimized stellarator experiments have suffered from very tight construction tolerances, but some level of deviation of the coil system is unavoidable during fabrication of the coils and assembly of the coil system. In this paper, we present a new approach that incorporates reduced sensitivity to construction tolerances of…

A systematic theory of the asymptotic expansion of the magnetohydrostatics (MHS) equilibrium in the distance from the magnetic axis is developed to include arbitrary smooth currents near the magnetic axis. Compared with the vacuum and the force-free system, an additional magnetic differential equation must be solved to obtain the pressure…

Good magnetic surfaces, as opposed to magnetic islands and chaotic field lines, are generally desirable for stellarators. In previous work, Landreman et al. [Phys. of Plasmas 28, 092505 (2021)] showed that equilibria computed by the Stepped-Pressure Equilibrium Code (SPEC) [Hudson et al.,…

This paper is focused on three points: (1) overcoming obstacles to tokamak power plants may require a configuration modification as large as that of a stellarator. (2) The demonstrated reliability of the computational design of stellarators should change fusion strategy. (3) Deployment of carbon-free energy sources is mandated by the thirty…

It is shown that the magnetic-field coils of a stellarator can, at least in principle, be substantially simplified by the use of permanent magnets. Such magnets cannot create toroidal magnetic flux but they can be used to shape the plasma and thus to create poloidal flux and rotational transform, thereby easing the requirements on the magnetic…

The Multi-region Relaxed MHD (MRxMHD) has been successful in the construction of equilibria in three-dimensional (3D) configurations. In MRxMHD, the plasma is sliced into sub-volumes separated by ideal interfaces, each undergoing relaxation, allowing the formation of islands and chaos. The resulting equilibrium has a stepped pressure profile…