arXiv subjects

Gabriel G. Plunk

Publications and source records attributed to Gabriel G. Plunk.

9 recordsLinked to original sources

arXiv2026

Near-axis quasi-isodynamic database

In this work, we investigate the landscape of quasi-isodynamic stellarators using the near-axis expansion of the magnetic field. Building on recent theoretical developments, we construct a database of more than 800,000 stable, approximately quasi-isodynamic vacuum magnetic configurations. These configurations span a range of field period numbers and other geometric control parameters, including the magnetic axis shape and plasma elongation. To evaluate each configuration, we use a broad set of measures, including effective ripple, sensitivity of the Shafranov shift to changes in plasma beta, the prevalence of maximum-J trapped particles, and the Rosenbluth-Hinton residual, among others. This enables an exhaustive, thorough and quantitative characterization of the database. Statistical analysis and modern machine learning techniques are then employed to find correlations, and identify key descriptors and heuristics to help understand tendencies that govern the behaviour of numerical optimization. The database provides baseline configurations for further studies, and to serve as tailored initial conditions for optimization. With this work we initiate a long term program to complete a systematic exploration of quasi-isodynamic stellarator design space.

physics.plasm-ph↗

arXiv2025

Computing MHD equilibria of stellarators with a flexible coordinate frame

For the representation of axi-symmetric plasma configurations, it is natural to use cyl. coordinates (R,Z,$ϕ$), where $ϕ$ is an independent coordinate. The same cyl. coordinates have also been widely used for representing 3D MHD equilibria of non-axisymmetric configurations (stellarators), with cross-sections, defined in RZ-planes, that vary over $ϕ$. Stellarator equilibria have been found, however, for which cyl. coordinates are not at all a natural choice, for instance certain stellarators obtained using the near-axis expansion (NAE), defined by a magn. axis curve and its Frenet frame. In this contribution, we propose an alternative approach for representing the boundary in a fixed-boundary 3D MHD equil. solver, moving away from cyl. coordinates. Instead, we use planar cross-sections whose orientation is determined by a general coordinate frame (G-Frame). This frame is similar to the conventional Frenet frame, but more flexible. As an additional part of the boundary representation, it becomes an input to the equil. solve, along with the geometry of the cross-sections. We see two advantages: 1) the capability to easily represent configurations where the magn. axis is highly non-planar or even knotted 2) a reduction in the degrees of freedom needed for the boundary surface, and thus the equil. solver, enabling progress in optimization of these configurations. We discuss the properties of the G-Frame, starting from the conventional Frenet frame. Then we show two exemplary ways of constructing it, first from a NAE solution and also from a given boundary surface. We present the details of the implementation of the new frame in the 3D MHD equil. solver GVEC. Furthermore, we demonstrate for a highly shaped QI-optimized stellarator that far fewer degrees of freedom are necessary to find a high quality equil. solution, compared to the solution computed in cyl. coordinates.

physics.plasm-ph↗

arXiv2024

Near-axis description of stellarator-symmetric quasi-isodynamic stellarators to second order

The near-axis description of optimised stellarators, at second order in the expansion, provides important information about the field, both of physical and practical importance for stellarator optimisation. It however remains relatively underdeveloped for an important class of such stellarators, called quasi-isodynamic (QI). In this paper we develop the theoretical and numerical framework for the construction of such solutions. We find that the case of QI stellarators calls for the careful treatment of continuity, smoothness and periodicity of the various functions involved, especially for so-called half-helicity fields, which feature prominently in existing QI designs. The numerical implementation of necessary elements is described, and several examples are constructed and quantitatively verified in detail. This work establishes a basis for further systematic exploration of the space of QI stellarators, and the development of both theoretical and practical tools to facilitate effective optimisation of QI stellarators.

physics.plasm-ph↗

arXiv2024

Quasi-isodynamic stellarators with low turbulence as fusion reactor candidates

The stellarator is a type of fusion energy device that - if properly designed - could provide clean, safe, and abundant energy to the grid. To generate this energy, a stellarator must keep a hot mixture of charged particles (known as a plasma) sufficiently confined by using a fully shaped magnetic field. If this is achieved, the heat from fusion reactions within the plasma can be harvested as energy. We present a novel method for designing reactor-relevant stellarator magnetic fields, which combine several key physical properties. These include plasma stability, excellent confinement of the fast moving particles generated by fusion reactions, and reduction of the turbulence that is known to limit the performance of the most advanced stellarator experiment in the world, Wendelstein 7-X.

physics.plasm-ph↗

arXiv2023

Helicity of the magnetic axes of quasi-isodynamic stellarators

In this study, we explore the influence of the helicity of the magnetic axis-defined as the self-linking number of the curve-on the quality of quasi-isodynamic stellarator-symmetric configurations constructed using the near-axis expansion method (Camacho Mata et al. 2022; Plunk et al. 2019). A class of magnetic axes previously unexplored within this formalism is identified when analyzing the axis shape of the QIPC configuration (Subbotin et al. 2006): the case of half-helicity (per field period). We show these shapes are compatible with the near-axis formalism and how they can be used to construct near-axis stellarators with up-to 5 field-periods, $ε_{eff} \approx$ 1.3%, and similar rotational transform as existing conventionally optimized designs, without the need of a plasma boundary optimization.

physics.plasm-ph↗

arXiv2022

Direct construction of stellarator-symmetric quasi-isodynamic magnetic configurations

We develop the formalism of the first order near-axis expansion of the MHD equilibrium equations described in Garren & Boozer (1991), Plunk et al. (2019) and Plunk et al. (2021), for the case of a quasi-isodynamic, N-field period, stellarator symmetric, single-well magnetic field equilibrium. The importance of the magnetic axis shape is investigated, and we conclude that control of the curvature and torsion is crucial to obtain omnigenous configurations with finite aspect ratio and low effective ripple, especially for a higher number of field periods. For this reason a method is derived to construct classes of axis shapes with favourable curvature and torsion. Solutions are presented, including a three-field-period configuration constructed at an aspect ratio of A=20, with a maximum elongation of e=3.2 and an effective ripple under 1%, which demonstrates that high elongation is not a necessary feature of QI stellarators.

physics.plasm-ph↗

arXiv2015

Generalized universal instability: Transient linear amplification and subcritical turbulence

In this work we numerically demonstrate both significant transient (i.e. non-modal) linear amplification and sustained nonlinear turbulence in a kinetic plasma system with no unstable eigenmodes. The particular system considered is an electrostatic plasma slab with magnetic shear, kinetic electrons and ions, weak collisions, and a density gradient, but with no temperature gradient. In contrast to hydrodynamic examples of non-modal growth and subcritical turbulence, here there is no sheared flow in the equilibrium. Significant transient linear amplification is found when the magnetic shear and collisionality are weak. It is also demonstrated that nonlinear turbulence can be sustained if initialized at sufficient amplitude. We prove these two phenomena are related: when sustained turbulence occurs without unstable eigenmodes, states that are typical of the turbulence must yield transient linear amplification of the gyrokinetic free energy.

physics.plasm-ph↗

arXiv2011

Kuramoto model with coupling through an external medium

Synchronization of coupled oscillators is often described using the Kuramoto model. Here we study a generalization of the Kuramoto model where oscillators communicate with each other through an external medium. This generalized model exhibits interesting new phenomena such as bistability between synchronization and incoherence and a qualitatively new form of synchronization where the external medium exhibits small-amplitude oscillations. We conclude by discussing the relationship of the model to other variations of the Kuramoto model including the Kuramoto model with a bimodal frequency distribution and the Millennium Bridge problem.

nlin.CD↗

arXiv2009

The theory of gyrokinetic turbulence: A multiple-scales approach

Gyrokinetics is a rich and rewarding playground to study some of the mysteries of modern physics. In this thesis I present work, motivated by the quest for fusion energy, which seeks to uncover some of the inner workings of turbulence in magnetized plasmas. I begin with the fundamental theory of gyrokinetics, and a novel formulation of its extension to the equations for mean-scale transport -- the equations which must be solved to determine the performance of magnetically confined fusion devices. The second project presents gyrokinetic secondary instability theory as a mechanism to bring about saturation of the basic instabilities that drive gyrokinetic turbulence. Emphasis is put on the ability for this analytic theory to predict basic properties of the nonlinear state, which can be applied to a mixing length phenomenology of transport. The final project is an application of the methods from inertial range understanding of fluid turbulence, to describe the stationary state of fully developed two-dimensional gyrokinetic turbulence. This work explores the relatively new idea of a phase-space cascade, whereby fine scales are nonlinearly generated in both position space and velocity space, and ultimately smoothed by collisional entropy production. This process constitutes the thermodynamic balance which occurs in the true steady state of a turbulent plasma, including those found in fusion devices.

physics.plasm-ph↗