Engineering topics

Kallinikos, N.

Publications and source records attributed to Kallinikos, N..

3 records

DOE OSTI2025

Characterization of admissible quasisymmetries

We solve ‘half’ the problem of finding three-dimensional quasisymmetric magnetic fields that do not necessarily satisfy magnetohydrostatic force balance. This involves determining which hidden symmetries are admissible as quasisymmetries, and then showing explicitly how to construct quasisymmetric magnetic fields given an admissible symmetry. The admissibility conditions take the form of a system of overdetermined nonlinear partial differential equations involving second derivatives of the symmetry's infinitesimal generator.

Burby, J. W. (ORCID:0000000317727647)↗

DOE OSTI2021

Approximate symmetries of guiding-centre motion

In a strong, inhomogeneous magnetic field, charged particle dynamics may be studied in the guiding-centre approximation, which is known to be Hamiltonian. When the magnetic field is quasisymmetric, the first-order guiding-centre (FGC) Hamiltonian structure admits a continuous symmetry, and therefore a conserved quantity in addition to the energy. Since the FGC system is only an approximation, it is also interesting to consider approximate symmetries of the guiding-centre Hamiltonian structure. We find that any approximate spatial symmetry coincides with quasisymmetry to leading order. For approximate phase-space symmetries, we derive weaker conditions than quasisymmetry. The latter include 'weak quasisymmetry' as a subcase, recently proposed by Rodríguez et al. Our results, however, show that weak quasisymmetry is necessarily non-spatial at first order. Finally, we demonstrate that if the magnetic field is constrained to satisfy magnetohydrostatic force balance then an approximate symmetry must agree with quasisymmetry to leading order.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Generalized Grad–Shafranov equation for non-axisymmetric MHD equilibria

The structure of static MHD equilibria that admit continuous families of Euclidean symmetries is well understood. Such field configurations are governed by the classical Grad–Shafranov equation, which is a single elliptic partial differential equation in two space dimensions. By revealing a hidden symmetry, here we show that in fact all smooth solutions of the equilibrium equations with non-vanishing pressure gradients away from the magnetic axis satisfy a generalization of the Grad–Shafranov equation. In contrast to solutions of the classical Grad–Shafranov equation, solutions of the generalized equation are not automatically equilibria, but instead only satisfy force balance averaged over the one-parameter hidden symmetry. We then explain how the generalized Grad–Shafranov equation can be used to reformulate the problem of finding exact three-dimensional smooth solutions of the equilibrium equations as finding an optimal volume-preserving symmetry.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗