arXiv subjects

Per Helander

Publications and source records attributed to Per Helander.

At least 19 recordsLinked to original sources

arXiv2026

On the Shafranov shift in stellarators

As first shown by Shafranov, toroidal plasmas in magnetohydrodynamic equilibrium tend to expand in major radius when the pressure is increased. Here, an average measure of the resulting Shafranov shift is introduced, and its properties are discussed for various classes of optimised stellarator configurations. It is shown to be particularly small in quasi-helical and quasi-isodynamic stellarators with a large number of field periods, which are thus particularly robust to variations in the plasma pressure.

physics.plasm-ph↗

arXiv2026

Optical analogy for stellarators: Ridges as caustics and coils as singularities

A common feature of most numerically optimized stellarator geometries is the presence of sharp ridges on outer flux surfaces, irrespective of the rotational transform. Despite their importance, an analytical theory for their existence has been lacking. In this work, we demonstrate that ridges are not artifacts but mathematical necessities. We develop such a theory for devices with quasisymmetry (QS). We demonstrate that QS exhibits close connections with the theory of geometrical optics, following Parker's ``optical analogy" (E.N. Parker, Geophys. Astrophys. Fluid Dyn, 1989). By mapping vacuum QS to the eikonal equation of geometrical optics, we derive the conditions for ridge formation, identified as field line caustics where magnetic field lines focus. Furthermore, we prove a geometric theorem for stellarator coil design: both ridges and filamentary coils must lie on the zero-determinant manifold of the magnetic gradient tensor. This topological constraint unifies the description of plasma ridges and external coils, providing a precise criterion for identifying valid coil locations and explaining the efficacy of the magnetic gradient lengthscale (J. Kappel et al., Plasma Phys. Control. Fusion, 2024) as a coil optimization parameter. We demonstrate that as the device becomes more compact, sharp ridges naturally form on the inboard side in quasiaxisymmetry. We support our analytical theory with extensive numerical evidence.

physics.plasm-ph↗

arXiv2025

Runaway electrons during a coil quench in stellarators

It is shown that avalanches of runaway electrons can arise in stellarators, even if there is no net toroidal current in the plasma or the magnetic-field coils, if the current in the latter varies rapidly enough, e.g. due to a superconductor quench. In present-day devices such as W7-X, significant runaway generation is theoretically possible only at very low gas or plasma density in the vacuum vessel, e.g. between discharges, if a seed population of free electrons is present. In reactor-scale stellarators, more dangerous runaway generation may occur both between discharges and during low-density plasma operation. Since a radiation-induced seed population is necessarily present in an activated device, an accidental coil ramp-down could convert substantial magnetic energy into wall-damaging runaway currents. There is however much more time to mitigate such events than in tokamaks disruptions.

physics.plasm-ph↗

arXiv2025

Piecewise omnigenous stellarators with zero bootstrap current

Until now, quasi-isodynamic magnetic fields have been the only known stellarator configurations that, at low collisionality, give small radial neoclassical transport and zero bootstrap current for arbitrary plasma profiles, the latter facilitating control of the magnetic configuration. The recently introduced notion of piecewise omnigenous fields has enormously broadened the space of stellarator configurations with small radial neoclassical transport. In this Letter, the existence of piecewise omnigenous fields that give zero bootstrap current is proven analytically and confirmed numerically. These results establish piecewise omnigenity as an alternative approach to stellarator reactor design.

physics.plasm-ph↗

arXiv2024

The pellet rocket effect in magnetic confinement fusion plasmas

Pellets of frozen material travelling into a magnetically confined fusion plasma are accelerated by the so-called pellet rocket effect. The non-uniform plasma heats the pellet ablation cloud asymmetrically, producing pressure-driven, rocket-like propulsion of the pellet. We present a semi-analytical model of this process by perturbing a spherically symmetric ablation model. Predicted pellet accelerations match experimental estimates in current tokamaks ($\sim 10^5 \;\rm m/s^2$). Projections for ITER high-confinement scenarios ($\sim 10^6 \;\rm m/s^2$) indicate significantly shorter pellet penetration than expected without this effect, which could limit the effectiveness of disruption mitigation.

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↗

arXiv2024

Optimised stellarators with a positive radial electric field

We draw attention to an interesting possibility in the design and operation of stellarator fusion reactors, which has hitherto been considered unrealistic under burning-plasma conditions. Thanks to recent advances in stellarator optimisation theory, it appears possible to create a positive (outward-pointing) radial electric field in the plasma core by carefully tailoring the geometry of the magnetic field. This electric field is likely to expel highly charged impurities from the centre of the plasma through neoclassical transport and thus eliminate, or at least mitigate, a long-standing problem in stellarator physics. Further out, the electric field is expected to suddenly change sign from positive to negative, thus creating a region of strongly sheared flow, which could locally suppress turbulent transport and enhance overall energy confinement.

physics.plasm-ph↗

arXiv2022

Constructing precisely quasi-isodynamic magnetic fields

We present a novel method for numerically finding quasi-isodynamic stellarator magnetic fields with excellent fast-particle confinement and extremely small neoclassical transport. The method works particularly well in configurations with only one field period. We examine the properties of these newfound quasi-isodynamic configurations, including their bootstrap currents, particle confinement, and available energy for trapped-electron driven turbulence, as well as the degree to which they change when a finite pressure profile is added. We finally discuss the differences between the magnetic axes of the optimized solutions and their respective initial conditions, and conclude with the prospects for future quasi-isodynamic optimization.

physics.plasm-ph↗

arXiv2022

Energetic bounds on gyrokinetic instabilities. Part II. Modes of optimal growth

We introduce modes of instantaneous optimal growth of free energy for the fully electromagnetic gyrokinetic equations. We demonstrate how these "optimal modes" arise naturally from the free energy balance equation, allowing its convenient decomposition, and yielding a simple picture of energy flows. Optimal modes have a number of other favorable features, such as their low-dimensionality, efficiency of computation, and the fact that their growth rates provide a rigorous and "tight" upper bound on both the nonlinear growth rate of energy, and the linear growth rate of traditional gyrokinetic (normal mode) instabilities. We provide simple closed form solutions for the optimal growth rates in a number of asymptotic limits, and compare these with our previous bounds.

physics.plasm-ph↗

arXiv2021

Heat conduction in an irregular magnetic field: Part II. Heat transport as a measure of the effective non-integrable volume

Given the large anisotropy of transport processes in magnetized plasmas, the magnetic field structure can strongly impact heat diffusion: magnetic surfaces and cantori form barriers to transport while chaotic layers and island structures can degrade confinement. When a small but non-zero amount of perpendicular diffusion is included, the structure of the magnetic field becomes less important, allowing pressure gradients to be supported across chaotic regions and island chains. We introduce a metric for the effective volume over which the local parallel diffusion dominates based on the solution to the anisotropic heat diffusion equation. To validate this metric, we consider model fields with a single island chain and a strongly chaotic layer for which analytic predictions of the relative parallel and perpendicular transport can be made. We also analyze critically chaotic fields produced from different sets of perturbations, highlighting the impact of the mode number spectrum on the heat transport. Our results indicate that this metric coincides with the effective volume of non-integrability in the limit $\kappa_{\perp} \rightarrow 0$. We propose that this metric be used to assess the impact of non-integrability on the heat transport in stellarator equilibria.

physics.plasm-ph↗

arXiv2021

Representing the boundary of stellarator plasmas

In stellarator optimization studies, the boundary of the plasma is usually described by Fourier series that are not unique: several sets of Fourier coefficients describe approximately the same boundary shape. A simple method for eliminating this arbitrariness is proposed and shown to work well in practice.

physics.plasm-ph↗

arXiv2020

Combined plasma-coil optimization algorithms

Combined plasma-coil optimization approaches for designing stellarators are discussed and a new method for calculating free-boundary equilibria is proposed. Four distinct categories of stellarator optimization, two of which are novel approaches, are the fixed-boundary optimization, the generalized fixed-boundary optimization, the quasi free-boundary optimization, and the free-boundary (coil) optimization. These are described using the multi-region relaxed magnetohydrodynmics (MRxMHD) energy functional, the Biot-Savart integral, the coil-penalty functional and the virtual casing integral, and their derivatives. The proposed free-boundary equilibrium calculation differs from existing methods in how the boundary-value problem is posed, and for the new approach it seems that there is not an associated energy minimization principle because a non-symmetric functional arises. We propose to solve the weak formulation of this problem using a spectral-Galerkin method, and this will reduce the free-boundary equilibrium calculation to something comparable to a fixed-boundary calculation. In our discussion of combined plasma-coil optimization algorithms, we emphasize the importance of the stability matrix.

physics.plasm-ph↗

arXiv2020

Coulomb collisions in strongly anisotropic plasmas I. Cyclotron cooling in electron-ion plasmas

The behaviour of a collisional plasma which is optically thin to cyclotron radiation is considered, and the distribution functions accessible to it on the various timescales in the system are calculated. Particular attention is paid to the limit in which the collision time exceeds the radiation emission time, making the electron distribution function strongly anisotropic. Unusually for plasma physics, the collision operator can nevertheless be calculated analytically although the plasma is far from Maxwellian. The rate of radiation emission is calculated and found to be governed by the collision frequency multiplied by a factor that only depends logarithmically on plasma parameters.

physics.plasm-ph↗

arXiv2020

Coulomb collisions in strongly anisotropic plasmas II. Cyclotron cooling in laboratory pair plasmas

The behaviour of a strongly-magnetized collisional electron-positron plasma which is optically thin to cyclotron radiation is considered, and the distribution functions accessible to it on the various timescales in the system are calculated. Particular attention is paid to the limit in which the collision time exceeds the radiation emission time, making the electron distribution function strongly anisotropic. Indeed, these are the exact conditions likely to be attained in the first laboratory electron-positron plasma experiments currently being developed, which will typically have very low densities and be confined in very strong magnetic fields. The constraint of strong-magnetization adds an additional complication in that long-range Coulomb collisions, which are usually negligible, must now be considered. A rigorous collision operator for these long-range collisions has never been written down. Nevertheless, we show that the collisional scattering can be accounted for without knowing the explicit form of this collision operator. The rate of radiation emission is calculated and it is found that the loss of energy from the plasma is proportional to the parallel collision frequency multiplied by a factor that only depends logarithmically on plasma parameters. That is, this is a self-accelerating process, meaning that the bulk of the energy will be lost in a few collision times. We show that in a simple case, that of straight field-line geometry, there are no unstable drift waves in such plasmas, despite being far from Maxwellian.

physics.plasm-ph↗

arXiv2020

Necessary and Sufficient Conditions for Quasisymmetry

A necessary and sufficient set of conditions for a quasisymmetric magnetic field in the form of constraint equations is derived from first principles. Without any assumption regarding the magnetohydrodynamic (MHD) equilibrium of the plasma, conditions for quasisymmetry are constructed starting from the single-particle Lagrangian to leading order. The conditions presented in the paper are less restrictive than the set recently obtained by Burby et al. [arXiv:1912.06468], and could facilitate ongoing efforts towards investigating the existence of global quasisymmetric MHD equilibria. It is also shown that quasisymmetry implies the existence of flux surfaces, regardless of whether the field corresponds to an MHD equilibrium.

physics.plasm-ph↗

arXiv2020

Effects of collisions on impurity transport driven by electrostatic modes

The turbulence-induced quasi-linear particle flux of a highly-charged, collisional impurity species is calculated from the electrostatic gyrokinetic equation including collisions with the bulk ions and the impurities themselves. The equation is solved by an expansion in powers of the impurity charge number $Z$. In this formalism, the collision operator only affects the impurity flux through the dynamics of the impurities in the direction parallel to the magnetic field. At reactor-relevant collisionality, the parallel dynamics is dominated by the parallel electric field, and collisions have a minor effect on the turbulent particle flux of highly-charged, collisional impurities.

physics.plasm-ph↗

arXiv2020

Available energy of magnetically confined plasmas

The concept of available energy of a collisionless plasma is discussed in the context of magnetic confinement. The available energy quantifies how much of the plasma energy can be converted into fluctuations (including nonlinear ones) and is thus a measure of plasma stability, which can be used to derive linear and nonlinear stability criteria without solving an eigenvalue problem. In a magnetically confined plasma, the available energy is determined by the density and temperature profiles as well as the magnetic geometry. It also depends on what constraints limit the possible forms of plasma motion, such as the conservation of adiabatic invariants and the requirement that the transport be ambipolar. A general method based on Lagrange multipliers is devised to incorporate such constraints in the calculation of the available energy, and several particular cases are discussed. In particular, it is shown that it is impossible to confine a plasma in a Maxwellian ground state relative to perturbations with frequencies exceeding the ion bounce frequency.

physics.plasm-ph↗

arXiv2018

Quasilinear particle transport from gyrokinetic instabilities in general magnetic geometry

The quasilinear particle flux arising from gyrokinetic instabilities is calculated in the electrostatic and collisionless approximation, keeping the geometry of the magnetic field arbitrary. In particular, the flux of electrons and heavy impurity ions is studied in the limit where the former move quickly, and the latter slowly, along the field compared with the mode frequency. Conclusions are drawn about how the particle fluxes of these species depend on the magnetic-field geometry, mode structure and frequency of the instability. Under some conditions, such as everywhere favourable or unfavourable magnetic curvature and modest temperature gradients, it is possible to make general statements about the fluxes independently of the details of the instability. In quasi-isodynamic stellarators with favourable bounce-averaged curvature for most particles, the particle flux is always outward if the temperature gradient is not too large, suggesting that it might be difficult to fuel such devices with gas puffing from the wall. In devices with predominantly unfavourable magnetic curvature, the particle flux can be inward, resulting in spontaneous density peaking in the centre of the plasma. In the limit of highly charged impurities, ordinary diffusion (proportional to the density gradient) dominates over other transport channels and the diffusion coefficient becomes independent of mass and charge. An estimate for the level of transport caused by magnetic-field fluctuations arising from ion-temperature-gradient instabilities is also given and is shown to be small compared with the electrostatic component.

physics.plasm-ph↗