arXiv subjects

M. Barnes

Publications and source records attributed to M. Barnes.

At least 19 recordsLinked to original sources

arXiv2026

Zonal-flow generation and saturation of electromagnetic ion-scale turbulence in tokamaks

Local flux-tube gyrokinetic simulations of ion-scale turbulence in tokamak plasmas at finite plasma beta are conducted to investigate the generation of zonal flows via turbulent stresses. A parameter scan in the safety factor $q$ and electron beta $\beta_e$ reveals a transition from low- to high-transport states when $\beta_{\mathrm{eff}} \equiv q^2\beta_e$ exceeds a certain critical value $C_{\mathrm{nl}}$. While the linear stability limits for kinetic and ideal ballooning modes also scale as $\beta_e \propto 1/q^2$, they lie above the observed transition, indicating that the effect is not due to linear instabilities but to nonlinear dynamics. At low $\beta_{\mathrm{eff}}$, Reynolds stress dominates and drives zonal flows. At higher values, Maxwell stress becomes comparable, suppressing zonal-flow formation and leading to divergent transport. This nonlinear-transition boundary is determined for both the Cyclone Base Case and a spherical tokamak (ST40) configuration, suggesting that the relation $\beta_{\mathrm{eff}} = C_{\mathrm{nl}}$ may have broader applicability, though $C_{\mathrm{nl}}$ appears to be configuration-dependent. For the Cyclone Base Case, the ratio of energy transfer rates into zonal flows due to Maxwell and Reynolds stresses is observed empirically to scale as $\beta_e$ for $\beta_e$ below a critical value $\beta_{e,\mathrm{sb}}$ (scaling breakdown). The value of $\beta_{e,\mathrm{sb}}$ is found to increase with decreasing aspect ratio, suggesting that the linear scaling remains valid over a wider range of $\beta_e$ for more compact magnetic equilibria. This low-$\beta_e$ scaling provides the basis for a practical method to predict the nonlinear-transition threshold with minimal reliance on highly electromagnetic nonlinear simulations.

physics.plasm-ph↗

arXiv2026

High-beta runaway transitions in a fluid model of electromagnetic ion-temperature-gradient turbulence

Gyrokinetic simulations of tokamak turbulence indicate that fluctuation levels increase abruptly and dramatically when the plasma beta exceeds a certain critical value. This increase in fluctuation levels coincides with a transition from a state dominated by zonal flow to one in which turbulent eddies form radially-elongated `streamers'. Here we derive from gyrokinetics a minimal fluid model for electromagnetic ion-temperature-gradient (ITG) turbulence that captures the key features of this transition. Due to the relative simplicity of the model, we are able to conduct a detailed numerical study of the interplay between the turbulence and the zonal flow across a broad range of values of the plasma beta and the ITG. We find that the transition occurs when the Reynolds stress, which tends to strengthen zonal flows, is overwhelmed by the Maxwell and diamagnetic stresses, which tend to weaken them. Power-law scalings of the stress ratios with plasma beta and ITG are obtained, indicating a possible means by which the location of the transition could be predicted with minimal computational cost.

physics.plasm-ph↗

arXiv2026

Scaling laws for the cutoff wavenumber of the short-wavelength ion-temperature-gradient mode in a Z-pinch

We use a heuristic fluid model to predict the dependence of the cutoff wave number for the short-wavelength ion temperature gradient (SWITG) mode on ion density gradient, ion temperature gradient (ITG) and ion-electron temperature ratio. In particular, we predict that the cutoff wave number increases linearly with increasing ITG for sufficiently large values of the ITG. Direct numerical solutions of the gyrokinetic dispersion relation using a purpose-built solver confirm the predicted scalings at large ITG values and find a weaker power-law scaling for intermediate ITG values. Combining these wave number scalings with a simple diffusive estimate for turbulent fluxes produces a scaling prediction for the ITG heat flux in SWITG-driven turbulence. Applying the critical balance conjecture additionally provides scalings for the aspect ratio of the SWITG turbulent eddies.

physics.plasm-ph↗

arXiv2026

Asymptotic scaling theory of electrostatic turbulent transport in magnetised fusion plasmas

Turbulent transport remains one of the principal obstacles to achieving efficient magnetic confinement in fusion devices. Two of the dominant drivers of the turbulence are microscale instabilities fuelled by electron- and ion-temperature gradients (ETG and ITG), whose nonlinear saturation determines the cross-field transport of particles and energy. We present a simple asymptotic scaling theory that unifies ETG- and ITG-driven turbulence within a common framework. By balancing the fundamental time scales of linear free energy injection, nonlinear decorrelation, and parallel propagation, the theory isolates the dependence of the heat flux on equilibrium parameters to two key quantities: the parallel system scale and the outer-scale aspect ratio. We show that these quantities encapsulate the essential physics of saturation, leading to distinct predictions for ETG and ITG transport: a cubic scaling with the temperature gradient in the electron channel, and a linear scaling in the ion channel, the latter recovering the ITG scaling recently proposed and numerically verified in axisymmetric geometry by Nies et al. [Phys. Rev. Res. 8, 013295 (2026)]. Extensive nonlinear gyrokinetic simulations confirm that these theoretical predictions in fact hold irrespective of the magnetic geometry (slab, tokamak, or stellarator), including the first numerical confirmation of the cubic ETG scaling anticipated by earlier studies. Our theory depends only on the parallel system scale and the outer-scale aspect ratio, and hence provides a physics-based foundation for fast, geometry-aware transport models, offering a pathway toward reactor optimisation in both tokamaks and stellarators.

physics.plasm-ph↗

arXiv2024

Suppression of temperature-gradient-driven turbulence by sheared flows in fusion plasmas

Starting from the assumption that saturation of plasma turbulence driven by temperature-gradient instabilities in fusion plasmas is achieved by a local energy cascade between a long-wavelength outer scale, where energy is injected into the fluctuations, and a small-wavelength dissipation scale, where fluctuation energy is thermalised by particle collisions, we formulate a detailed phenomenological theory for the influence of perpendicular flow shear on magnetised-plasma turbulence. Our theory introduces two distinct regimes, called the weak-shear and strong-shear regimes, each with its own set of scaling laws for the scale and amplitude of the fluctuations and for the level of turbulent heat transport. We discover that the ratio of the typical radial and poloidal wavenumbers of the fluctuations (i.e., their aspect ratio) at the outer scale plays a central role in determining the dependence of the turbulent transport on the imposed flow shear. Our theoretical predictions are found to be in excellent agreement with numerical simulations of two paradigmatic models of fusion-relevant plasma turbulence: (i) an electrostatic fluid model of slab electron-scale turbulence, and (ii) Cyclone-base-case gyrokinetic ion-scale turbulence. Additionally, our theory envisions a potential mechanism for the suppression of electron-scale turbulence by perpendicular ion-scale flows based on the role of the aforementioned aspect ratio of the electron-scale fluctuations.

physics.plasm-ph↗

arXiv2023

Electrostatic microturbulence in W7-X: comparison of local gyrokinetic simulations with Doppler reflectometry measurements

The first experimental campaigns of Wendelstein 7-X (W7-X) have shown that turbulence plays a decisive role in the performance of neoclassically optimized stellarators. This stresses the importance of understanding microturbulence from the theoretical and experimental points of view. To this end, this paper addresses a comprehensive characterization of the turbulent fluctuations by means of nonlinear gyrokinetic simulations performed with the code stella in two W7-X scenarios. In the first part of the paper, the amplitude of the density fluctuations is calculated and compared with measurements obtained by Doppler reflectometry (DR) in the OP1 experimental campaigns. It is found that the trend of the fluctuations along the radius is explained by the access of the DR system to different regions of the turbulence wavenumber spectrum. In the second part of the article, frequency spectra of the density fluctuations and the zonal component of the turbulent flow are numerically characterized for comparisons against future experimental analyses. Both quantities feature broad frequency spectra with dominant frequencies of O(1)-O(10) kHz.

physics.plasm-ph↗

arXiv2023

Ion temperature and density gradient driven instabilities and turbulence in Wendelstein 7-X close to the stability threshold

Electrostatic gyrokinetic instabilities and turbulence in the Wendelstein 7-X stellarator are studied. Particular attention is paid to the ion-temperature-gradient (ITG) instability and its character close to marginal stability [Floquet-type turbulence (Zocco et al. 2022) with no electron temperature gradient]. The flux-tube version of the $\delta$f code stella (Barnes et al. 2019) is used to run linear and nonlinear gyrokinetic simulations with kinetic electrons. The nature of the dominant instability depends on the wavelength perpendicular to the magnetic field, and the results are conveniently displayed in stability diagrams that take this dependence into account. This approach highlights the presence of universal instabilities, which are less unstable but have longer wavelengths than other modes. A quasi-linear estimate of the heat flux suggests they are relevant for transport. Close to the stability threshold, the linear eigenmodes and turbulence form highly extended structures along the computational domain if the magnetic shear is small. Numerical experiments and diagnostics are undertaken to assess the resulting radial localisation of the turbulence, which affects the interaction of the latter with zonal flows. Increasing the amplitude of the magnetic shear (e.g. through current drive) has a stabilising effect on the turbulence and thus reduces the nonlinear energy transport.

physics.plasm-ph↗

arXiv2022

Prevention of core particle depletion in stellarators by turbulence

In reactor-relevant plasmas, neoclassical transport drives an outward particle flux in the core of large stellarators and predicts strongly hollow density profiles. However, this theoretical prediction is contradicted by experiments. In particular, in Wendelstein 7-X, the first large optimized stellarator, flat or weakly peaked density profiles are generally measured, indicating that neoclassical theory is not sufficient and that an inward contribution to the particle flux is missing in the core. In this Research Letter, it is shown that the turbulent contribution to the particle flux can explain the difference between experimental measurements and neoclassical predictions. The results of this Research Letter also prove that theoretical and numerical tools are approaching the level of maturity needed for the prediction of equilibrium density profiles in stellarator plasmas, which is a fundamental requirement for the design of operation scenarios of present devices and future reactors.

physics.plasm-ph↗

arXiv2022

New linear stability parameter to describe low-$\beta$ electromagnetic microinstabilities driven by passing electrons in axisymmetric toroidal geometry

In magnetic confinement fusion devices, the ratio of the plasma pressure to the magnetic field energy, $\beta$, can become sufficiently large that electromagnetic microinstabilities become unstable, driving turbulence that distorts or reconnects the equilibrium magnetic field. In this paper, a theory is proposed for electromagnetic, electron-driven linear instabilities that have current layers localised to mode-rational surfaces and binormal wavelengths comparable to the ion gyroradius. The model retains axisymmetric toroidal geometry with arbitrary shaping, and consists of orbit-averaged equations for the mode-rational surface layer, with a ballooning space kinetic matching condition for passing electrons. The matching condition connects the current layer to the large scale electromagnetic fluctuations, and is derived in the limit that $\beta$ is comparable to the square root of the electron-to-ion-mass ratio. Electromagnetic fluctuations only enter through the matching condition, allowing for the identification of an effective $\beta$ that includes the effects of equilibrium flux surface shaping. The scaling predictions made by the asymptotic theory are tested with comparisons to results from linear simulations of micro-tearing and electrostatic microinstabilities in MAST discharge #6252, showing excellent agreement. In particular, it is demonstrated that the effective $\beta$ can explain the dependence of the local micro-tearing mode (MTM) growth rate on the ballooning parameter $\theta_0$ -- possibly providing a route to optimise local flux surfaces for reduced MTM-driven transport.

physics.plasm-ph↗

arXiv2022

A phase-shift-periodic parallel boundary condition for low-magnetic-shear scenarios

We formulate a generalized periodic boundary condition as a limit of the standard twist-and-shift parallel boundary condition that is suitable for simulations of plasmas with low magnetic shear. This is done by applying a phase shift in the binormal direction when crossing the parallel boundary. While this phase shift can be set to zero without loss of generality in the local flux-tube limit when employing the twist-and-shift boundary condition, we show that this is not the most general case when employing periodic parallel boundaries, and may not even be the most desirable. A non-zero phase shift can be used to avoid the convective cells that plague simulations of the three-dimensional Hasegawa-Wakatani system, and is shown to have measurable effects in periodic low-magnetic-shear gyrokinetic simulations. We propose a numerical program where a sampling of periodic simulations at random pseudo-irrational flux surfaces are used to determine physical observables in a statistical sense. This approach can serve as an alternative to applying the twist-and-shift boundary condition to low-magnetic-shear scenarios which, while more straightforward, can be computationally demanding.

physics.plasm-ph↗

arXiv2022

Three-Dimensional Inhomogeneity of Electron-Temperature-Gradient Turbulence in the Edge of Tokamak Plasmas

Nonlinear multiscale gyrokinetic simulations of a Joint European Torus edge pedestal are used to show that electron-temperature-gradient (ETG) turbulence has a rich three-dimensional structure, varying strongly according to the local magnetic-field configuration. In the plane normal to the magnetic field, the steep pedestal electron temperature gradient gives rise to anisotropic turbulence with a radial (normal) wavelength much shorter than in the binormal direction. In the parallel direction, the location and parallel extent of the turbulence are determined by the variation in the magnetic drifts and finite-Larmor-radius (FLR) effects. The magnetic drift and FLR topographies have a perpendicular-wavelength dependence, which permits turbulence intensity maxima near the flux-surface top and bottom at longer binormal scales, but constrains turbulence to the outboard midplane at shorter electron-gyroradius binormal scales. Our simulations show that long-wavelength ETG turbulence does not transport heat efficiently, and significantly decreases overall ETG transport -- in our case by $\sim$40 \% -- through multiscale interactions.

physics.plasm-ph↗

arXiv2022

Interpreting Radial Correlation Doppler Reflectometry using Gyrokinetic Simulations

A linear response, local model for the DBS amplitude applied to gyrokinetic simulations shows that radial correlation Doppler reflectometry measurements (RCDR, Schirmer et al., Plasma Phys. Control. Fusion 49 1019 (2007)) are not sensitive to the average turbulence radial correlation length, but to a correlation length that depends on the binormal wavenumber $k_\perp$ selected by the Doppler backscattering (DBS) signal. Nonlinear gyrokinetic simulations show that the turbulence naturally exhibits a non-separable power law spectrum in wavenumber space, leading to a power law dependence of the radial correlation length with binormal wavenumber $l_r \sim C k_\perp^{-\alpha} (\alpha \approx 1)$ which agrees with the inverse proportionality relationship between the measured $l_r$ and $k_\perp $ in experiments (Fernandez-Marina et al., Nucl. Fusion 54 072001 (2014)). This offers the possibility of characterizing the eddy aspect ratio in the perpendicular plane to the magnetic field and motivates future use of a non-separable turbulent spectrum to quantitatively interpret RCDR and potentially other turbulence diagnostics. The radial correlation length is only measurable when the radial resolution at the cutoff location $W_n$ satisfies $W_n \ll l_r$, while the measurement becomes dominated by $W_n$ for $W_n \gg l_r$. This suggests that $l_r$ is likely inaccessible for electron-scale DBS measurements ($k_\perp\rho_s > 1$). The effect of $W_n$ on ion-scale radial correlation lengths could be non-negligible.

physics.plasm-ph↗

arXiv2022

A novel approach to radially global gyrokinetic simulation using the flux-tube code $\texttt{stella}$

A novel approach to global gyrokinetic simulation is implemented in the flux-tube code $\texttt{stella}$. This is done by using a subsidiary expansion of the gyrokinetic equation in the perpendicular scale length of the turbulence, originally derived by Parra and Barnes [Plasma Phys. Controlled Fusion, $\textbf{57}$ 054003, 2015], which allows the use of Fourier basis functions while enabling the effect of radial profile variation to be included in a perturbative way. Radial variation of the magnetic geometry is included by utilizing a global extension of the Grad-Shafranov equation and the Miller equilibrium equations which is obtained through Taylor expansion. Radial boundary conditions that employ multiple flux-tube simulations are also developed, serving as a more physically motivated replacement to the conventional Dirichlet radial boundary conditions that are used in global simulation. It is shown that these new boundary conditions eliminate much of the numerical artefacts generated near the radial boundary when expressing a non-periodic function using a spectral basis. We then benchmark the new approach both linearly and nonlinearly using a number of standard test cases.

physics.plasm-ph↗

arXiv2021

Energy partition between Alfv\'enic and compressive fluctuations in magnetorotational turbulence with near-azimuthal mean magnetic field

The theory of magnetohydrodynamic (MHD) turbulence predicts that Alfv\'enic and slow-mode-like compressive fluctuations are energetically decoupled at small scales in the inertial range. The partition of energy between these fluctuations determines the nature of dissipation, which, in many astrophysical systems, happens on scales where plasma is collisionless. However, when the magnetorotational instability (MRI) drives the turbulence, it is difficult to resolve numerically the scale at which both types of fluctuations start to be decoupled because the MRI energy injection occurs in a broad range of wavenumbers, and both types of fluctuations are usually expected to be coupled even at relatively small scales. In this study, we focus on collisional MRI turbulence threaded by a near-azimuthal mean magnetic field, which is naturally produced by the differential rotation of a disc. We show that, in such a case, the decoupling scales are reachable using a reduced MHD model that includes differential-rotation effects. In our reduced MHD model, the Alfv\'enic and compressive fluctuations are coupled only through the linear terms that are proportional to the angular velocity of the accretion disc. We numerically solve for the turbulence in this model and show that the Alfv\'enic and compressive fluctuations are decoupled at the small scales of our simulations as the nonlinear energy transfer dominates the linear coupling below the MRI-injection scale. In the decoupling scales, the energy flux of compressive fluctuations contained in the small scales is almost double that of Alfv\'enic fluctuations. Finally, we discuss the application of this result to prescriptions of ion-to-electron heating ratio in hot accretion flows.

astro-ph.HE↗

arXiv2021

Extended electron tails in electrostatic microinstabilities and the nonadiabatic response of passing electrons

Ion-gyroradius-scale microinstabilities typically have a frequency comparable to the ion transit frequency. Due to the small electron-to-ion mass ratio and the large electron transit frequency, it is conventionally assumed that passing electrons respond adiabatically in ion-gyroradius-scale modes. However, in gyrokinetic simulations of ion-gyroradius-scale modes in axisymmetric toroidal magnetic fields, the nonadiabatic response of passing electrons can drive the mode, and generate fluctuations with narrow radial layers, which may have consequences for turbulent transport in a variety of circumstances. In flux tube simulations, in the ballooning representation, these instabilities reveal themselves as modes with extended tails. The small electron-to-ion mass ratio limit of linear gyrokinetics for electrostatic instabilities is presented, in axisymmetric toroidal magnetic geometry, including the nonadiabatic response of passing electrons and associated narrow radial layers. This theory reveals the existence of ion-gyroradius-scale modes driven solely by the nonadiabatic passing electron response, and recovers the usual ion-gyroradius-scale modes driven by the response of ions and trapped electrons, where the nonadiabatic response of passing electrons is small. The collisionless and collisional limits of the theory are considered, demonstrating parallels in structure and physical processes to neoclassical transport theory. By examining initial-value simulations of fastest-growing eigenmodes, the predictions for mass-ratio scaling are tested and verified numerically for a range of collision frequencies. Insights from the small electron-to-ion mass ratio theory may lead to a computationally efficient treatment of extended modes.

physics.plasm-ph↗

arXiv2021

Electrostatic gyrokinetic simulations in Wendelstein 7-X geometry: benchmark between the codes stella and GENE

The first experimental campaigns have proven that, due to the optimization of the magnetic configuration with respect to neoclassical transport, the contribution of turbulence is essential to understand and predict the total particle and energy transport in Wendelstein 7-X (W7-X). This has spurred much work on gyrokinetic modelling for the interpretation of the available experimental results and for the preparation of the next campaigns. At the same time, new stellarator gyrokinetic codes have just been or are being developed. It is therefore desirable to have a sufficiently complete, documented and verified set of gyrokinetic simulations in W7-X geometry against which new codes or upgrades of existing codes can be tested and benchmarked. This paper attemps to provide such a set of simulations in the form of a comprehensive benchmark between the recently developed code stella and the well-established code GENE. The benchmark consists of electrostatic gyrokinetic simulations in W7-X magnetic geometry and includes different flux tubes, linear ion-temperature-gradient (ITG) and trapped-electron-mode (TEM)} stability analyses, computation of linear zonal flow responses and calculation of ITG-driven heat fluxes.

physics.plasm-ph↗

arXiv2021

Turbulent transport of impurities in 3D devices

A large diffusive turbulent contribution to the radial impurity transport in Wendelstein 7-X (W7-X) plasmas has been experimentally inferred during the first campaigns and numerically confirmed by means of gyrokinetic simulations with the code stella. In general, the absence of strong impurity accumulation during the initial W7-X campaigns is attributed to this diffusive term. In the present work the diffusive contribution is also calculated in other stellarator plasmas. In particular, the diffusion (D) and convection (V) coefficients of carbon and iron impurities produced by ion-temperature-gradient (ITG) turbulence are obtained for W7-X, LHD, TJ-II and NCSX. The results show that, although the size of D and V can differ across the four devices, inward convection is found for all of them. For W7-X, TJ-II and NCSX the two coefficients are comparable and the turbulent peaking factor is surprisingly similar. In LHD, appreciably weaker diffusive and convective impurity transport and significantly larger turbulent peaking factor are predicted. All this suggests that ITG turbulence, although not strongly, would lead to negative impurity density gradients in stellarators. Then, considering mixed ITG/Trapped Electron Mode (TEM) turbulence for the specific case of W7-X, it has been quantitatively assessed to what degree pellet fueled reduced turbulence scenarios feature reduced turbulent transport of impurities as well. The results for trace iron impurities show that, although their turbulent transport is not entirely suppressed, a significant reduction of V and a stronger decrease of D are found. Although the diffusion is still above neoclassical levels, the neoclassical convection would gain under such conditions a greater specific weight on the dynamics of impurities in comparison with standard ECRH scenarios.

physics.plasm-ph↗

arXiv2021

Gyrokinetic simulations in stellarators using different computational domains

In this work, we compare gyrokinetic simulations in stellarators using different computational domains, namely, flux tube, full-flux-surface, and radially global domains. Two problems are studied: the linear relaxation of zonal flows and the linear stability of ion temperature gradient (ITG) modes. Simulations are carried out with the codes EUTERPE, GENE, GENE-3D, and stella in magnetic configurations of LHD and W7-X using adiabatic electrons. The zonal flow relaxation properties obtained in different flux tubes are found to differ with each other and with the radially global result, except for sufficiently long flux tubes, in general. The flux tube length required for convergence is configuration-dependent. Similarly, for ITG instabilities, different flux tubes provide different results, but the discrepancy between them diminishes with increasing flux tube length. Full-flux-surface and flux tube simulations show good agreement in the calculation of the growth rate and frequency of the most unstable modes in LHD, while for W7-X differences in the growth rates are found between the flux tube and the full-flux-surface domains. Radially global simulations provide results close to the full-flux-surface ones. The radial scale of unstable ITG modes is studied in global and flux tube simulations finding that in W7-X, the radial scale of the most unstable modes depends on the binormal wavenumber, while in LHD no clear dependency is found.

physics.plasm-ph↗