D. R. Hatch

Gyrokinetic prediction of microtearing turbulence in standard tokamaks

First global gyrokinetic simulations of microtearing instabilities in ASDEX Upgrade geometry provide increasing evidence for the existence of these modes in standard tokamaks. It is found that even in only moderately large devices, nonlocal effects like profile shearing are negligible, supporting the use of an efficient flux-tube approach. Nonlinear gyrokinetic simulations show that the resulting level of magnetic electron heat flux can be experimentally relevant.

Role of subdominant stable modes in plasma microturbulence

In gyrokinetic simulations, thousands of degrees of freedom are available to contribute to the fluctuation spectrum. For wavevectors with a single linear instability, the unstable eigenmode accounts for only one of these degrees of freedom. Little has been known about the role of the remaining fluctuations in the turbulent dynamics. In this paper, these fluctuations are characterized as modes in mode decompositions of gyrokinetic distribution functions from nonlinear simulations. This analysis reveals the excitation of a hierarchy of damped modes at the same perpendicular scales as the driving instabilities. Two effects of these subdominant modes are described: First, these damped modes define a potent energy sink, creating a situation where energy drive and energy dissipation peak at the same perpendicular scales. Second, damped modes with tearing parity (even parity about the outboard midplane for A|| fluctuations) are driven to significant amplitudes and facilitate the development of magnetic stochasti...

Magnetic stochasticity and transport due to nonlinearly excited subdominant microtearing modes

Subdominant, linearly stable microtearing modes are identified as the main mechanism for the development of magnetic stochasticity and transport in gyrokinetic simulations of electromagnetic ion temperature gradient driven plasma microturbulence. The linear eigenmode spectrum is examined in order to identify and characterize modes with tearing parity. Connections are demonstrated between microtearing modes and the nonlinear fluctuations that are responsible for the magnetic stochasticity and electromagnetic transport, and nonlinear coupling with zonal modes is identified as the salient nonlinear excitation mechanism. A simple model is presented, which relates the electromagnetic transport to the electrostatic transport. These results may provide a paradigm for the mechanisms responsible for electromagnetic stochasticity and transport, which can be examined in a broader range of scenarios and parameter regimes.

Phase space scales of free energy dissipation in gradient-driven gyrokinetic turbulence

A reduced four-dimensional (integrated over perpendicular velocity) gyrokinetic model of slab ion temperature gradient-driven turbulence is used to study the phasespace scales of free energy dissipation in a turbulent kinetic system over a broad range of background gradients and collision frequencies. Parallel velocity is expressed in terms of Hermite polynomials, allowing for a detailed study of the scales of free energy dynamics over the four-dimensional phase space. A fully spectral code – the DNA code – that solves this system is described. Hermite free energy spectra are significantly steeper than would be expected linearly, causing collisional dissipation to peak at large scales in velocity space even for arbitrarily small collisionality. A key cause of the steep Hermite spectra is a critical balance – an equilibration of the parallel streaming time and the nonlinear correlation time – that extends to high Hermite number n. Although dissipation always peaks at large scales in all phase space dimensions, small-scale dissipation becomes important in an integrated sense when collisionality is low enough and/or nonlinear energy transfer is strong enough. Toroidal full-gyrokinetic simulations using the Gene code are used to verify results from the reduced model. Collision frequencies typically found in present-day experiments correspond to turbulence regimes slightly favoring large-scale dissipation, while turbulence in low-collisionality systems like ITER and space and astrophysical plasmas is expected to rely increasingly on small-scale dissipation mechanisms. This work is expected to inform gyrokinetic reduced modeling efforts like Large Eddy Simulation and gyrofluid techniques.

On secondary and tertiary instability in electromagnetic plasma microturbulence

Zonal flows, widely accepted to be the secondary instability process leading to the nonlinear saturation of ion temperature gradient modes, are shown to grow at higher rates relative to the linear mode amplitude as the plasma pressure β is increased—thus, confirming that zonal flows become increasingly important in the turbulent dynamics at higher β. At the next level of nonlinear excitation, radial corrugations of the distribution function (zonal flow, zonal density, and zonal temperature) are demonstrated to modify linear growth rates moderately through perturbed-field, self-consistent gradients: on smaller scales, growth rates are reduced below the linear rate. In particular, excitation of kinetic ballooning modes well below their usual threshold is not to be expected under normal conditions. These findings strengthen the theory of the non-zonal transition [M. J. Pueschel et al., Phys. Rev. Lett. 110, 155005 (2013)].

Aspects of Linear Landau Damping in Discretized Systems

Basic linear eigenmode spectra for electrostatic Langmuir waves and drift-kinetic slab ion temperature gradient modes are examined in a series of scenarios. Collisions are modeled via a Lenard-Bernstein collision operator which fundamentally alters the linear spectrum even for infinitesimal collisionality [Ng et al., Phys. Rev. Lett. 83, 1974 (1999)]. A comparison between different discretization schemes reveals that a Hermite representation is superior for accurately resolving the spectra compared to a finite differences scheme using an equidistant velocity grid. Additionally, it is shown analytically that any even power of velocity space hyperdiffusion also produces a Case-Van Kampen spectrum which, in the limit of zero hyperdiffusivity, matches the collisionless Landau solutions.

Quasilinear transport modelling at low magnetic shear

Accurate and computationally inexpensive transport models are vital for routine and robust predictions of tokamak turbulent transport. To this end, the QuaLiKiz [Bourdelle et al., Phys. Plasmas 14, 112501 (2007)] quasilinear gyrokinetic transport model has been recently developed. QuaLiKiz flux predictions have been validated by non-linear simulations over a wide range in parameter space. However, a discrepancy is found at low magnetic shear, where the quasilinear fluxes are significantly larger than the non-linear predictions. This discrepancy is found to stem from two distinct sources: the turbulence correlation length in the mixing length rule and an increase in the ratio between the quasilinear and non-linear transport weights, correlated with increased non-linear frequency broadening. Significantly closer agreement between the quasilinear and non-linear predictions is achieved through the development of an improved mixing length rule, whose assumptions are validated by non-linear simulations.

Electron heat transport from stochastic fields in gyrokinetic simulationsa)

GYRO is used to examine the perturbed magnetic field structure generated by electromagnetic gyrokinetic simulations of the CYCLONE base case as βe is varied from 0.1% to 0.7%, as investigated by J. Candy [Phys. Plasmas 12, 072307 (2005)]. Poincare surface of section plots obtained from integrating the self-consistent magnetic field demonstrates widespread stochasticity for all nonzero values of βe. Despite widespread stochasticity of the perturbed magnetic fields, no significant increase in electron transport is observed. The magnetic diffusion, dm [A. B. Rechester and M. N. Rosenbluth, Phys. Rev. Lett 40, 38 (1978)], is used to quantify the degree of stochasticity and related to the electron heat transport for hundreds of time slices in each simulation.

Properties of high-β microturbulence and the non-zonal transition

The physics underlying the non-zonal transition [M. J. Pueschel et al., Phys. Rev. Lett. 110, 155005 (2013)] are explored in detail, and various studies are presented which support the theory that critically weakened zonal flows are indeed responsible for the failure of ion-temperature-gradient-driven turbulence at high plasma β to saturate at typical transport values. Regarding flux-surface-breaking magnetic fluctuations and their impact on zonal flows, numerical approaches to obtaining zonal flow residuals are elaborated on, and simulation results are shown to agree with analytical predictions, corroborating the interpretation that flux-surface-breaking magnetic fluctuations cause the transition. Consistently, the zonal-flows-related energetics of the turbulence are found to change fundamentally when exceeding the threshold.

Global and local gyrokinetic simulations of high-performance discharges in view of ITER

One of the key challenges for plasma theory and simulation in view of ITER is to enhance the understanding and predictive capability concerning high-performance discharges. This involves, in particular, questions about high-beta operation, ion temperature profile stiffness, and the physics of transport barriers. The goal of this contribution is to shed light on these issues by means of physically comprehensive ab initio simulations with the global gyrokinetic code GENE, applied to discharges in TCV, ASDEX Upgrade, and JET-with direct relevance to ITER.