ALLIANCE: Spectral solver for kinetic plasma turbulence

The ALLIANCE code is developed to solve a new set of four-dimensional electromagnetic drift-kinetic equations in slab geometry [J. Plasma Phys. 88 905880117 (2022)]. The nonlinear equations are useful for the study of magnetized plasma systems at scales comparable to, or larger than the ion gyroradius. In particular, it is suited for the study the kinetic turbulent cascade in astrophysical plasma, while preserving finite Larmor radius effects at the fluid-kinetic transition. The equations solved are in spectral Fourier-Laguerre-Hermite form, a pseudo-spectral approach is used for the nonlinear terms, and the code is parallelised over multiple directions. After a presentation of the code, validation runs are shown, and benchmarks for serial and parallel computations are presented

The anisotropic redistribution of free energy for gyrokinetic plasma turbulence in a Z-pinch

For a Z-pinch geometry, we report on the nonlinear redistribution of free energy across scales perpendicular to the magnetic guide field, for a turbulent plasma described in the framework of gyrokinetics. The analysis is performed using a local flux-surface approximation, in a regime dominated by electrostatic fluctuations driven by the entropy mode, with both ion and electron species being treated kinetically. To explore the anisotropic nature of the free energy redistribution caused by the emergence of zonal flows, we use a polar coordinate representation for the field-perpendicular directions and define an angular density for the scale flux. Positive values for the classically defined (angle integrated) scale flux, which denote a direct energy cascade, are shown to be also composed of negative angular sections, a fact that impacts our understanding of the backscatter of energy and the way in which it enters the modeling of sub-grid scales for turbulence. A definition for the flux of free energy across each perpendicular direction is introduced as well, which shows that the redistribution of energy in the presence of zonal flows is highly anisotropic

On the locality of MHD turbulence scale fluxes

The scale locality of energy fluxes for magnetohydrodynamics (MHD) is investigated numerically for stationary states of turbulence. Two types of forces are used to drive turbulence, a kinetic force that acts only on the velocity field and a kinetic-inductive forcing mechanism, which acts on the velocity and magnetic fields alike. The analysis is performed in spectral space, which is decomposed into a series of shells following a power law for the boundaries. The triadic transfers occurring among these shells are computed and the fluxes and locality functions are recovered by partial summation over the relevant shells. Employing Kraichnan locality functions, values of 1/3 and 2/3 for the scaling exponents of the four MHD energy fluxes are found. These values are smaller compared with the value of 4/3 found for hydrodynamic turbulence. To better understand these results, an in depth analysis is performed on the total energy flux.Comment: submitted to Physics of Plasmas, 10 pages, 8 figure

Sub-grid-scale effects in magnetised plasma turbulence

In the present paper, we use a coarse-graining approach to investigate the nonlinear redistribution of free energy in both position and scale space for weakly collisional magnetised plasma turbulence. For this purpose, we use high-resolution numerical simulations of gyrokinetic (GK) turbulence that span the proton-electron range of scales, in a straight magnetic guide field geometry. Accounting for the averaged effect of the particles' fast gyro-motion on the slow plasma fluctuations, the GK approximation captures the dominant energy redistribution mechanisms in strongly magnetised plasma turbulence. Here, the GK system is coarse-grained with respect to a cut-off scale, separating in real space the contributions to the nonlinear interactions from the coarse-grid-scales and the sub-grid-scales (SGS). We concentrate on the analysis of nonlinear SGS effects. Not only that this allows us to investigate the flux of free energy across the scales, but also to now analyse its spatial density. We find that the net value of scale flux is an order of magnitude smaller than both the positive and negative flux density contributions. The dependence of the results on the filter type is also analysed. Moreover, we investigate the advection of energy in position space. This rather novel approach for GK turbulence can help in the development of SGS models that account for advective unstable structures for space and fusion plasmas, and with the analysis of the turbulent transport saturation.Comment: 15 figures Accepted for publication by Journal of Plasma Physic

A nonlinear approach to transition in subcritical plasmas with sheared flow

In many plasma systems, introducing a small background shear flow is enough to stabilize the system linearly. The nonlinear dynamics are much less sensitive to sheared flows than the average linear growthrates, and very small amplitude perturbations can lead to sustained turbulence. We explore the general problem of characterizing how and when the transition from near-laminar states to sustained turbulence occurs; a model of the interchange instability being used as a concrete example. These questions are fundamentally nonlinear, and the answers must go beyond the linear transient amplification of small perturbations. Two methods that account for nonlinear interactions are therefore explored here. The first method explored is edge tracking, which identifies the boundary between the basins of attraction of the laminar and turbulent states. Here, the edge is found to be structured around an exact, localized, traveling wave solution; a solution that is qualitatively similar to avalanche-like bursts seen in the turbulent regime. The second method is an application of nonlinear, non-modal stability theory which allows us to identify the smallest disturbances which can trigger turbulence (the minimal seed for the problem) and hence to quantify how stable the laminar regime is. The results obtained from these fully nonlinear methods provides confidence in the derivation of a semi-analytic approximation for the minimal seed

Simple advecting structures and the edge of chaos in subcritical tokamak plasmas

In tokamak plasmas, sheared flows perpendicular to the driving temperature gradients can strongly stabilize linear modes. While the system is linearly stable, regimes with persistent nonlinear turbulence may develop, i.e. the system is subcritical. A perturbation with small but finite amplitude may be sufficient to push the plasma into a regime where nonlinear effects are dominant and thus allow sustained turbulence. The minimum threshold for nonlinear instability to be triggered provides a criterion for assessing whether a tokamak is likely to stay in the quiescent (laminar) regime. At the critical amplitude, instead of transitioning to the turbulent regime or decaying to a laminar state, the trajectory will map out the edge of chaos. Surprisingly, a quasi-traveling-wave solution is found as an attractor on this edge manifold. This simple advecting solution is qualitatively similar to, but simpler than, the avalanche-like bursts seen in earlier turbulent simulations and provides an insight into how turbulence is sustained in subcritical plasma systems. For large flow shearing rate, the system is only convectively unstable, and given a localised initial perturbation, will eventually return to a laminar state at a fixed spatial location