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The self-organization of structures in a tokamak plasma as it undergoes an H-mode transition shows properties similar to simpler shear flow configurations. We will describe recent dynamical studies of plasma shear flows, including the idea of tracking the edge of chaos that separates two bistable states, computing the nonlinear minimal seed that can lead to turbulence, finding the attractor solution on the edge and seeing how starting from this solution we can understand the stability of relative period orbits that permeate the turbulent basin of attraction. We present a modus operandi developed for these simple configurations that can be adapted to understand the H-mode transition. [ABSTRACT FROM AUTHOR]

For a magnetised plasma in a straight magnetic guide field, we derive a set of four-dimensional kinetic equations, which can capture electromagnetic turbulence in the drift kinetic limit. To do so, we start from the gyrokinetic equations, employ a Laguerre decomposition in the perpendicular velocity direction, retaining only the dominant gyroaverage contributions and only the first two Laguerre moments that source the electromagnetic fluctuations. The model conserves free energy, and can describe electromagnetic turbulence for a plasma at the transition between fluid and gyrokinetic regimes ($k_\perp \rho _i\approx 1$ range of scales), as dominant finite-Larmor-radius (FLR) effects are considered. In addition to the three dimensions in positions space, we retain the parallel velocity dependence, which we describe via a Hermite representation. Employing this system, but without any other physics-based assumptions for the plasma species that can bias results, will allow us to investigate how fluid effects transition into the kinetic range, and analyse the interplay between spatial and velocity space mixing for electromagnetic plasma turbulence. [ABSTRACT FROM AUTHOR]

The ALLIANCE (ALLIANCE - spectrAL soLver for kInetic plAsma turbuleNCE) code is developed to solve a new set of four-dimensional electromagnetic drift-kinetic equations in slab geometry [1]. 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. • Four-dimensional equations to study plasma turbulence are presented in the form applicable for numerical studies. • Numerical tests proving convergence of linear and nonlinear solver are shown. • Linear run showing the linear phase mixing is shown. • Nonlinear run showing the ability of the system to develop turbulence is shown. • Performance tests results are shown. [ABSTRACT FROM AUTHOR]

In a proton–electron magnetized plasma, we analyze turbulence at kinetic scales captured by a gyrokinetic formalism. The interval of scales spans the range between the proton and the electron gyroradii, while the use of the proper mass ratio between the two species ensures a realistic scale separation for the nonlinear couplings. The simulation is pertinent to astrophysical conditions, employing a straight field line magnetic geometry for the guide field, a plasma β of one, and a temperature ratio between the two species of unity. We investigate the intermittency of the distribution functions in the perpendicular direction, measured over the phase space as a way to account for the velocity space structures generated via Landau damping as well as for the nonlinear spatial mixing (i.e., the turbulent cascade). The analysis makes use of a Hermite decomposition in the parallel velocity. Electron structures are found to be strongly intermittent compared to weakly intermittent protons. Moreover, we find evidence linking intermittency with phase mixing and electron Landau damping, as intermittent electron structures also exhibit strong parallel velocity structures. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In magnetized plasma turbulence, the couplings of perpendicular spatial scales that arise due to the nonlinear interactions are analyzed from the perspective of the free-energy exchanges. The plasmas considered here, with appropriate ion or electron adiabatic electro-neutrality responses, are described by the gyrokinetic formalism in a toroidal magnetic geometry. Turbulence develops due to the electrostatic fluctuations driven by temperature gradient instabilities, either ion temperature gradient (ITG) or electron temperature gradient (ETG). The analysis consists in decomposing the system into a series of scale structures, while accounting separately for contributions made by modes possessing special symmetries (e.g., the zonal flow modes). The interaction of these scales is analyzed using the energy transfer functions, including a forward and backward decomposition, scale fluxes, and locality functions. The comparison between the ITG and ETG cases shows that ETG turbulence has a more pronounced classical turbulent behavior, exhibiting a stronger energy cascade, with implications for gyrokinetic turbulence modeling. [ABSTRACT FROM AUTHOR]