arXiv subjects

A. A. Kaptanoglu

Publications and source records attributed to A. A. Kaptanoglu.

4 recordsLinked to original sources

arXiv2026

Periodic Korteweg-de Vries soliton potentials generate quasisymmetric magnetic fields

Quasisymmetry (QS) is a hidden symmetry of the magnetic field strength, B, that effectively confines charged particles in a three-dimensional toroidal plasma equilibrium. Here, we show that QS has a deep connection to the underlying symmetry that makes solitons possible. Our approach uncovers a hidden lower dimensionality of B on a magnetic flux surface, which could make stellarator optimization schemes significantly more efficient. Recent numerical breakthroughs (M. Landreman and E. Paul, Phys. Rev. Lett. 128, 035001 (2022)) have yielded configurations with excellent volumetric QS and surprisingly low magnetic shear. Given B, it may be possible to deduce an upper bound on the maximum quasisymmetric toroidal volume which depends only on the properties of B. This has been verified for the Landreman-Paul precise quasiaxisymmetric (QA) stellarator configuration. In the neighborhood of the outermost surface, we show that B approaches the form of the 1-soliton reflectionless potential (I. Gjaja and A. Bhattacharjee, Phys. Rev. Lett. 68, 2413 (1992)). The connection length diverges, indicating the possible presence of an X-point or cusp that could potentially be used as a basis for a divertor. We present a non-perturbative approach based on ensuring single-valuedness of B, which directly leads to its Painleve property and the KdV and Gardner's equations. Finally, we use an approach based on machine learning, trained on a large dataset of numerically optimized quasisymmetric stellarators. We robustly recover the KdV and Gardner's equations from the data.

physics.plasm-ph↗

arXiv2025

Periodic Korteweg-de Vries soliton potentials generate quasisymmetric magnetic field strength in a finite plasma-beta equilibrium

Quasisymmetry (QS) is a hidden symmetry of the magnetic field strength, B, that enables effective confinement of charged particles in a fully three-dimensional (3D) toroidal plasma equilibrium. Such equilibria are typically modeled by the ideal magnetohydrostatic (MHS) equation. The nonlinear, overdetermined nature of the quasisymmetric MHS equations severely complicates our understanding of the interplay between 3D shaping, equilibrium properties such as pressure and rotational transform, and B. Progress has been made through expansions near the magnetic axis; however, a more comprehensive theory is desirable. Using a combination of analysis and regression on a large dataset of numerically optimized quasisymmetric stellarators, we demonstrate that there is a hidden lower dimensionality of B on a magnetic flux surface with connections to the theory of periodic solitons. We show that $B$ on a flux surface is determined by three or at most four flux functions, each of which is a critical value of the derivative of B along the field line. While being consistent with the near-axis models, our results are global and hold even on the last closed flux surface.

physics.plasm-ph↗

arXiv2024

Improved stellarator permanent magnet designs through combined discrete and continuous optimizations

A common optimization problem in the areas of magnetized plasmas and fusion energy is the design of magnets to produce a given three-dimensional magnetic field distribution to high precision. When designing arrays of permanent magnets for stellarator plasma confinement, such problems have tens of thousands of degrees of freedom whose solutions, for practical reasons, should be constrained to discrete spaces. We perform a direct comparison between two algorithms that have been developed previously for this purpose, and demonstrate that composite procedures that apply both algorithms in sequence can produce substantially improved results. One approach uses a continuous, quasi-Newton procedure to optimize the dipole moments of a set of magnets and then projects the solution onto a discrete space. The second uses an inherently discrete greedy optimization procedure that has been enhanced and generalized for this work. The approaches are both applied to design arrays cubic rare-Earth permanent magnets to confine a quasi-axisymmetric plasma with a magnetic field on axis of 0.5 T. The first approach tends to find solutions with higher field accuracy, whereas the second can find solutions with substantially (up to 30%) fewer magnets. When the approaches are combined, they can obtain solutions with magnet quantities comparable to the second approach while matching the field accuracy of the first.

physics.plasm-ph↗

arXiv2022

A comparison of Fourier and POD mode decomposition methods for high-speed Hall thruster video

Hall thrusters are susceptible to large-amplitude plasma oscillations that impact thruster performance and lifetime and are also difficult to model. High-speed cameras are a popular tool to study these dynamics due to their spatial resolution and are a popular, nonintrusive complement to in-situ probes. High-speed video of thruster oscillations can be isolated (decomposed) into coherent structures (modes) with algorithms that help us better understand the evolution and interactions of each. This work provides an introduction, comparison, and step-by-step tutorial on established Fourier and newer Proper Orthogonal Decomposition (POD) algorithms as applied to high-speed video of the unshielded H6 6-kW laboratory model Hall thruster. From this dataset, both sets of algorithms identify and characterize $m=0$ and $m>0$ modes in the discharge channel and cathode regions of the thruster plume, as well as mode hopping between the $m=3$ and $m=4$ rotating spokes in the channel. The Fourier methods are ideal for characterizing linear modal structures and also provide intuitive dispersion relationships. By contrast, the POD method tailors a basis set using energy minimization techniques that better captures the nonlinear nature of these structures and with a simpler implementation. Together, the Fourier and POD methods provide a more complete toolkit for studying Hall thruster plasma instabilities and mode dynamics. Specifically, we recommend first applying POD first to quickly identify the nature and location of global dynamics and then using Fourier methods to isolate dispersion plots and other wave-based physics.

physics.plasm-ph↗