arXiv subjects

M. Barnes

Publications and source records attributed to M. Barnes.

At least 37 records · Page 2Linked to original sources

arXiv2020

Impact of plasma shaping on tokamak microstability

We have used the local-$δ{f}$ gyrokinetic code GS2 to perform studies of the effect of flux-surface shaping on two highly-shaped, low- and high-$β$ JT-60SA-relevant equilibria, including a successful benchmark with the GKV code. We find a novel destabilization of electrostatic fluctuations with increased elongation for plasma with a strongly peaked pressure profile. We explain the results as a competition between the local magnetic shear and finite-Larmor-radius (FLR) stabilization. Electromagnetic studies indicate that kinetic ballooning modes are stabilized by increased shaping due to an increased sensitivity to FLR effects, relative to the ion-temperature-gradient instability. Nevertheless, at high enough $β$, increased elongation degrades the local magnetic shear stabilization that enables access to the region of ballooning second-stability.

physics.plasm-ph↗

arXiv2020

Ion versus electron heating in compressively driven astrophysical gyrokinetic turbulence

The partition of irreversible heating between ions and electrons in compressively driven (but subsonic) collisionless turbulence is investigated by means of nonlinear hybrid gyrokinetic simulations. We derive a prescription for the ion-to-electron heating ratio $Q_\rmi/Q_\rme$ as a function of the compressive-to-Alfvénic driving power ratio $P_\compr/P_\AW$, of the ratio of ion thermal pressure to magnetic pressure $β_\rmi$, and of the ratio of ion-to-electron background temperatures $T_\rmi/T_\rme$. It is shown that $Q_\rmi/Q_\rme$ is an increasing function of $P_\compr/P_\AW$. When the compressive driving is sufficiently large, $Q_\rmi/Q_\rme$ approaches $\simeq P_\compr/P_\AW$. This indicates that, in turbulence with large compressive fluctuations, the partition of heating is decided at the injection scales, rather than at kinetic scales. Analysis of phase-space spectra shows that the energy transfer from inertial-range compressive fluctuations to sub-Larmor-scale kinetic Alfvén waves is absent for both low and high $β_\rmi$, meaning that the compressive driving is directly connected to the ion entropy fluctuations, which are converted into ion thermal energy. This result suggests that preferential electron heating is a very special case requiring low $β_\rmi$ and no, or weak, compressive driving. Our heating prescription has wide-ranging applications, including to the solar wind and to hot accretion disks such as M87 and Sgr A*.

physics.plasm-ph↗

arXiv2020

Turbulent impurity transport simulations in Wendelstein 7-X plasmas

A study of turbulent impurity transport by means of quasilinear and nonlinear gyrokinetic simulations is presented for Wendelstein 7-X (W7-X). The calculations have been carried out with the recently developed gyrokinetic code stella. Different impurity species are considered in the presence of various types of background instabilities: ITG, TEM and ETG modes for the quasilinear part of the work; ITG and TEM for the nonlinear results. While the quasilinear approach allows one to draw qualitative conclusions about the sign or relative importance of the various contributions to the flux, the nonlinear simulations quantitatively determine the size of the turbulent flux and check the extent to which the quasilinear conclusions hold. Although the bulk of the nonlinear simulations are performed at trace impurity concentration, nonlinear simulations are also carried out at realistic effective charge values, in order to know to what degree the conclusions based on the simulations performed for trace impurities can be extrapolated to realistic impurity concentrations. The presented results conclude that the turbulent radial impurity transport in W7-X is mainly dominated by ordinary diffusion, which is close to that measured during the recent W7-X experimental campaigns. It is also confirmed that thermo-diffusion adds a weak inward flux contribution and that, in the absence of impurity temperature and density gradients, ITG- and TEM-driven turbulence push the impurities inwards and outwards, respectively.

physics.plasm-ph↗

arXiv2020

Stabilisation of short-wavelength instabilities by parallel-to-the-field shear in long-wavelength $\mathbf{E} \times \mathbf{B}$ flows

Magnetised plasma turbulence can have a multiscale character: instabilities driven by mean temperature gradients drive turbulence at the disparate scales of the ion and the electron gyroradii. Simulations of multiscale turbulence, using equations valid in the limit of infinite scale separation, reveal novel cross-scale interaction mechanisms in these plasmas. In the case that both long-wavelength (ion-gyroradius-scale) and short-wavelength (electron-gyroradius-scale) linear instabilities are driven far from marginal stability, we show that the short-wavelength instabilities are suppressed by interactions with long-wavelength turbulence. The observed suppression is a result of two effects: parallel-to-the-field-line shearing by the long wavelength $\mathbf{E} \times \mathbf{B}$ flows, and the modification of the background density gradient by long-wavelength fluctuations. In contrast, simulations of multiscale turbulence where instabilities at both scales are driven near marginal stability demonstrate that when the long-wavelength turbulence is sufficiently collisional and zonally dominated the effect of cross-scale interaction can be parameterised solely in terms of the local modifications to the mean density and temperature gradients. We discuss physical arguments that qualitatively explain how a change in equilibrium drive leads to the observed transition in the impact of the cross-scale interactions.

physics.plasm-ph↗

arXiv2019

A Scale-Separated Approach for Studying Coupled Ion and Electron Scale Turbulence

Multiple space and time scales arise in plasma turbulence in magnetic confinement fusion devices because of the smallness of the square root of the electron-to-ion mass ratio $(m_e/m_i)^{1/2}$ and the consequent disparity of the ion and electron thermal gyroradii and thermal speeds. Direct simulations of this turbulence that include both ion and electron space-time scales indicate that there can be significant interactions between the two scales. The extreme computational expense and complexity of these direct simulations motivates the desire for reduced treatment. By exploiting the scale separation between ion and electron scales,and expanding the gyrokinetic equations for the turbulence in $(m_e/m_i)^{1/2}$, we derive such a reduced system of gyrokinetic equations that describes cross-scale interactions. The coupled gyrokinetic equations contain novel terms which provide candidate mechanisms for the observed cross-scale interaction. The electron scale turbulence experiences a modified drive due to gradients in the ion scale distribution function, and is advected by the ion scale $E \times B$ drift, which varies in the direction parallel to the magnetic field line. The largest possible cross-scale term in the ion scale equations is sub-dominant in our $(m_e/m_i)^{1/2}$ expansion. Hence, in our model the ion scale turbulence evolves independently of the electron scale turbulence. To complete the scale-separated approach, we provide and justify a parallel boundary condition for the coupled gyrokinetic equations in axisymmetric equilibria based on the standard "twist-and-shift" boundary condition. This approach allows one to simulate multi-scale turbulence using electron scale flux tubes nested within an ion scale flux tube.

physics.plasm-ph↗

arXiv2018

Optimisation of confinement in a fusion reactor using a nonlinear turbulence model

The confinement of heat in the core of a magnetic fusion reactor is optimised using a multidimensional optimisation algorithm. For the first time in such a study, the loss of heat due to turbulence is modelled at every stage using first-principles nonlinear simulations which accurately capture the turbulent cascade and large-scale zonal flows. The simulations utilise a novel approach, with gyrofluid treatment of the small-scale drift waves and gyrokinetic treatment of the large-scale zonal flows. A simple near-circular equilibrium with standard parameters is chosen as the initial condition. The figure of merit, fusion power per unit volume, is calculated, and then two control parameters, the elongation and triangularity of the outer flux surface, are varied, with the algorithm seeking to optimise the chosen figure of merit. A two-fold increase in the plasma power per unit volume is achieved by moving to higher elongation and strongly negative triangularity.

physics.plasm-ph↗

arXiv2018

A Hybrid Gyrokinetic Ion and Isothermal Electron Fluid Code for Astrophysical Plasma

This paper describes a new code for simulating astrophysical plasmas that solves a hybrid model composed of gyrokinetic ions (GKI) and an isothermal electron fluid (ITEF) [A. Schekochihin et al., Astrophys. J. Suppl. \textbf{182}, 310 (2009)]. This model captures ion kinetic effects that are important near the ion gyro-radius scale while electron kinetic effects are ordered out by an electron-ion mass ratio expansion. The code is developed by incorporating the ITEF approximation into {\tt AstroGK}, an Eulerian $δf$ gyrokinetics code specialized to a slab geometry [R. Numata et al., J. Compute. Pays. \textbf{229}, 9347 (2010)]. The new code treats the linear terms in the ITEF equations implicitly while the nonlinear terms are treated explicitly. We show linear and nonlinear benchmark tests to prove the validity and applicability of the simulation code. Since the fast electron timescale is eliminated by the mass ratio expansion, the Courant--Friedrichs--Lewy condition is much less restrictive than in full gyrokinetic codes; the present hybrid code runs $\sim 2\sqrt{m_\mathrm{i}/m_\mathrm{e}} \sim 100$ times faster than {\tt AstroGK}\ with a single ion species and kinetic electrons where $m_\mathrm{i}/m_\mathrm{e}$ is the ion-electron mass ratio. The improvement of the computational time makes it feasible to execute ion scale gyrokinetic simulations with a high velocity space resolution and to run multiple simulations to determine the dependence of turbulent dynamics on parameters such as electron--ion temperature ratio and plasma beta.

physics.plasm-ph↗

arXiv2018

Turbulent heating in an inhomogeneous, magnetised plasma slab

Observational evidence in space and astrophysical plasmas with long collisional mean free path suggests that more massive charged particles may be preferentially heated. One possible mechanism for this is the turbulent cascade of energy from injection to dissipation scales, where the energy is converted to heat. Here we consider a simple system consisting of a magnetized plasma slab of electrons and a single ion species with a cross-field density gradient. We show that such a system is subject to an electron drift wave instability, known as the universal instability, which is stabilized only when the electron and ion thermal speeds are equal. For unequal thermal speeds, we find that the instability gives rise to turbulent energy exchange between ions and electrons that acts to equalize the thermal speeds. Consequently, this turbulent heating tends to equalize the component temperatures of pair plasmas and to heat ions to much higher temperatures than electrons for conventional mass-ratio plasmas.

physics.plasm-ph↗

arXiv2015

Dependence of intrinsic rotation reversals on collisionality in MAST

Tokamak plasmas rotate even without external injection of momentum. A Doppler backscattering system installed at MAST has allowed this intrinsic rotation to be studied in Ohmic L-mode and H-mode plasmas, including the first observation of intrinsic rotation reversals in a spherical tokamak. Experimental results are compared to a novel 1D model, which captures the collisionality dependence of the radial transport of toroidal angular momentum due to the effect of neoclassical flows on turbulent fluctuations. The model is able to accurately reproduce the change in sign of core toroidal rotation, using experimental density and temperature profiles from shots with rotation reversals as inputs and no free parameters fit to experimental data.

physics.plasm-ph↗

arXiv2014

High-m Kink/Tearing Modes in Cylindrical Geometry

The global ideal kink equation, for cylindrical geometry and zero beta, is simplified in the high poloidal mode number limit and used to determine the tearing stability parameter, $Δ^\prime$. In the presence of a steep monotonic current gradient, $Δ^\prime$ becomes a function of a parameter, $σ_0$, characterising the ratio of the maximum current gradient to magnetic shear, and $x_s$, characterising the separation of the resonant surface from the maximum of the current gradient. In equilibria containing a current "spike", so that there is a non-monotonic current profile, $Δ^\prime$ also depends on two parameters: $κ$, related to the ratio of the curvature of the current density at its maximum to the magnetic shear, and $x_s$, which now represents the separation of the resonance from the point of maximum current density. The relation of our results to earlier studies of tearing modes and to recent gyro-kinetic calculations of current driven instabilities, is discussed, together with potential implications for the stability of the tokamak pedestal.

physics.plasm-ph↗

arXiv2013

Multiscale Gyrokinetics for Rotating Tokamak Plasmas: Fluctuations, Transport and Energy Flows

This paper presents a complete theoretical framework for plasma turbulence and transport in tokamak plasmas. The fundamental scale separations present in plasma turbulence are codified as an asymptotic expansion in the ratio of the gyroradius to the equilibrium scale length. Proceeding order-by-order in this expansion, a framework for plasma turbulence is developed. It comprises an instantaneous equilibrium, the fluctuations driven by gradients in the equilibrium quantities, and the transport-timescale evolution of mean profiles of these quantities driven by the fluctuations. The equilibrium distribution functions are local Maxwellians with each flux surface rotating toroidally as a rigid body. The magnetic equillibrium is obtained from the Grad-Shafranov equation for a rotating plasma and the slow (resistive) evolution of the magnetic field is given by an evolution equation for the safety factor q. Large-scale deviations of the distribution function from a Maxwellian are given by neoclassical theory. The fluctuations are determined by the high-flow gyrokinetic equation, from which we derive the governing principle for gyrokinetic turbulence in tokamaks: the conservation and local cascade of free energy. Transport equations for the evolution of the mean density, temperature and flow velocity profiles are derived. These transport equations show how the neoclassical corrections and the fluctuations act back upon the mean profiles through fluxes and heating. The energy and entropy conservation laws for the mean profiles are derived. Total energy is conserved and there is no net turbulent heating. Entropy is produced by the action of fluxes flattening gradients, Ohmic heating, and the equilibration of mean temperatures. Finally, this framework is condensed, in the low-Mach-number limit, to a concise set of equations suitable for numerical implementation.

physics.plasm-ph↗

arXiv2013

Intrinsic rotation driven by non-Maxwellian equilibria in tokamak plasmas

The effect of small deviations from a Maxwellian equilibrium on turbulent momentum transport in tokamak plasmas is considered. These non-Maxwellian features, arising from diamagnetic effects, introduce a strong dependence of the radial flux of co-current toroidal angular momentum on collisionality: As the plasma goes from nearly collisionless to weakly collisional, the flux reverses direction from radially inward to outward. This indicates a collisionality-dependent transition from peaked to hollow rotation profiles, consistent with experimental observations of intrinsic rotation.

physics.plasm-ph↗

arXiv2012

Freely decaying turbulence in two-dimensional electrostatic gyrokinetics

In magnetized plasmas, a turbulent cascade occurs in phase space at scales smaller than the thermal Larmor radius ("sub-Larmor scales") [Phys. Rev. Lett. 103, 015003 (2009)]. When the turbulence is restricted to two spatial dimensions perpendicular to the background magnetic field, two independent cascades may take place simultaneously because of the presence of two collisionless invariants. In the present work, freely decaying turbulence of two-dimensional electrostatic gyrokinetics is investigated by means of phenomenological theory and direct numerical simulations. A dual cascade (forward and inverse cascades) is observed in velocity space as well as in position space, which we diagnose by means of nonlinear transfer functions for the collisionless invariants. We find that the turbulence tends to a time-asymptotic state, dominated by a single scale that grows in time. A theory of this asymptotic state is derived in the form of decay laws. Each case that we study falls into one of three regimes (weakly collisional, marginal, and strongly collisional), determined by a dimensionless number D*, a quantity analogous to the Reynolds number. The marginal state is marked by a critical number D* = D0 that is preserved in time. Turbulence initialized above this value become increasingly inertial in time, evolving toward larger and larger D*; turbulence initialized below D0 become more and more collisional, decaying to progressively smaller D*.

physics.plasm-ph↗

arXiv2012

Experimental Signatures of Critically Balanced Turbulence in MAST

Beam Emission Spectroscopy (BES) measurements of ion-scale density fluctuations in the MAST tokamak are used to show that the turbulence correlation time, the drift time associated with ion temperature or density gradients, the particle (ion) streaming time along the magnetic field and the magnetic drift time are consistently comparable, suggesting a "critically balanced" turbulence determined by the local equilibrium. The resulting scalings of the poloidal and radial correlation lengths are derived and tested. The nonlinear time inferred from the density fluctuations is longer than the other times; its ratio to the correlation time scales as $ν_{*i}^{-0.8\pm0.1}$, where $ν_{*i}=$ ion collision rate/streaming rate. This is consistent with turbulent decorrelation being controlled by a zonal component, invisible to the BES, with an amplitude exceeding the drift waves' by $\sim ν_{*i}^{-0.8}$.

physics.plasm-ph↗

arXiv2012

Turbulent transport and heating of trace heavy ions in hot, magnetized plasmas

Scaling laws for the transport and heating of trace heavy ions in low-frequency, magnetized plasma turbulence are derived and compared with direct numerical simulations. The predicted dependences of turbulent fluxes and heating on ion charge and mass number are found to agree with numerical results for both stationary and differentially rotating plasmas. Heavy ion momentum transport is found to increase with mass, and heavy ions are found to be preferentially heated, implying a mass-dependent ion temperature for very weakly collisional plasmas and for partially-ionized heavy ions in strongly rotating plasmas.

physics.plasm-ph↗

arXiv2012

Zero-Turbulence Manifold in a Toroidal Plasma

Sheared toroidal flows can cause bifurcations to zero-turbulent-transport states in tokamak plasmas. The maximum temperature gradients that can be reached are limited by subcritical turbulence driven by the parallel velocity gradient. Here it is shown that q/ε(magnetic field pitch/inverse aspect ratio) is a critical control parameter for sheared tokamak turbulence. By reducing q/ε, far higher temperature gradients can be achieved without triggering turbulence, in some instances comparable to those found experimentally in transport barriers. The zero-turbulence manifold is mapped out, in the zero-magnetic-shear limit, over the parameter space (γ_E, q/ε, R/L_T), where γ_E is the perpendicular flow shear and R/L_T is the normalised inverse temperature gradient scale. The extent to which it can be constructed from linear theory is discussed.

physics.plasm-ph↗

arXiv2011

Transport Bifurcation Induced by Sheared Toroidal Flow in Tokamak Plasmas

First-principles numerical simulations are used to describe a transport bifurcation in a differentially rotating tokamak plasma. Such a bifurcation is more probable in a region of zero magnetic shear than one of finite magnetic shear because in the former case the component of the sheared toroidal flow that is perpendicular to the magnetic field has the strongest suppressing effect on the turbulence. In the zero-magnetic-shear regime, there are no growing linear eigenmodes at any finite value of flow shear. However, subcritical turbulence can be sustained, owing to the transient growth of modes driven by the ion temperature gradient (ITG) and the parallel velocity gradient (PVG). Nonetheless, in a parameter space containing a wide range of temperature gradients and velocity shears, there is a sizeable window where all turbulence is suppressed. Combined with the relatively low transport of momentum by collisional (neoclassical) mechanisms, this produces the conditions for a bifurcation from low to high temperature and velocity gradients. The path of this bifurcation is mapped out using interpolation from a large number of simulations. Numerical simulations are also used to construct a parametric model which accurately describes the combined effect of the temperature gradient and the flow gradient over a wide range of their values. Using this parametric model, it is shown that in this reduced-transport state, heat is transported almost neoclassically, while momentum transport is dominated by subcritical PVG turbulence. It is further shown that for any given input of torque, there is an optimum input of heat which maximises the temperature gradient. The parametric model describes both the behaviour of the subcritical turbulence and the complicated effect of the flow shear on the transport stiffness. It may prove useful for transport modelling of tokamaks with sheared flows.

physics.plasm-ph↗

arXiv2011

Critically balanced ion temperature gradient turbulence in fusion plasmas

Scaling laws for ion temperature gradient driven turbulence in magnetized toroidal plasmas are derived and compared with direct numerical simulations. Predicted dependences of turbulence fluctuation amplitudes, spatial scales, and resulting heat fluxes on temperature gradient and magnetic field line pitch are found to agree with numerical results in both the driving and inertial ranges. Evidence is provided to support the critical balance conjecture that parallel streaming and nonlinear perpendicular decorrelation times are comparable at all spatial scales, leading to a scaling relationship between parallel and perpendicular spatial scales. This indicates that even strongly magnetized plasma turbulence is intrinsically three-dimensional.

physics.plasm-ph↗