Two-dimensional Electrostatic Turbulence Research Articles

Experimental Verification of Entropy Cascade in Two-Dimensional Electrostatic Turbulence in Magnetized Plasma

The wave number spectrum (one-dimensional spectrum) of electrostatic potential fluctuations at sub-Larmor scales was measured in two-dimensional (2D) electrostatic turbulence in laboratory magnetized plasma. The spectrum at scales k([perpendicular])ρ(i)>1, where k([perpendicular]) and ρ(i) are the fluctuation wave number perpendicular to the magnetic field and ion Larmor radius, respectively, supports the existence of the k(-10/3) inertial range of the entropy cascade induced by nonlinear phase mixing. This indicates agreement with a theoretical prediction [A. A. Schekochihin et al., Plasma Phys. Controlled Fusion 50, 124024 (2008)] and the result of a 2D gyrokinetic simulation [T. Tatsuno et al., Phys. Rev. Lett. 103, 015003 (2009)]. The cutoff wave numbers of the spectrum, above which the entropy cascade is smeared by collisions, observed in this experiment were consistent with those in the theory.

Modelling the temperature plateau in RFX-mod single-helical-axis (SHAx) states

The core region of high-current RFX-mod reversed field pinch plasmas spontaneously organizes into high-temperature helical flux tubes with almost intact magnetic surfaces. Accordingly, radial diffusion due to magnetic chaos is expected to be vanishingly small. Notwithstanding this, the temperature profile within these structures is flat, suggesting instead a substantial level of heat transport inside them. In this work we propose a rather simplified model of two-dimensional electrostatic turbulence valid in the low-magnetic chaos region and suggest that the effective homogenization of temperature may come from self-consistently generated vortical drift motion.

Turbulent transport of fast ions in the Large Plasma Device

Strong drift wave turbulence is observed in the Large Plasma Device [H. Gekelman et al., Rev. Sci. Instrum. 62, 2875 (1991)] on density gradients produced by a plate limiter. Energetic lithium ions orbit through the turbulent region. Scans with a collimated ion analyzer and with Langmuir probes give detailed profiles of the fast ion spatial distribution and the fluctuating fields. The fast ion transport decreases rapidly with increasing fast ion gyroradius. Unlike the diffusive transport caused by Coulomb collisions, in this case the turbulent transport is nondiffusive. Analysis and simulation suggest that such nondiffusive transport is due to the interaction of the fast ions with stationary two-dimensional electrostatic turbulence.

Electron diffusion in a sheared unperturbed magnetic field and an electrostatic stochastic field

The electron diffusion induced by a two-dimensional electrostatic turbulence, in a sheared slab approximation of the toroidal magnetic geometry, is studied firstly using the decorrelation trajectory method (DCT), secondly by direct numerical simulation. The former semi-analytical method allows us to go beyond the Corrsin approximation, thus allowing for a non-classical analysis of the particle trapping phenomenon. The DCT results are compared to the transport properties of the electrons obtained by numerical simulations assuming an isotropic spectrum of electrostatic drift type turbulence that is Gaussian for small wavevectors and power-law k−3 for large wavevectors. The ‘radial’ and the ‘poloidal’ running and asymptotic diffusion coefficients of thermal electrons are obtained for physically relevant parameter values. The existence of enhanced diffusion in the poloidal direction is observed in the presence of magnetic shear. The agreement between the semi-analytical method and the purely numerical method is pointed out.

Equipartition and Transport in Two-Dimensional Electrostatic Turbulence

Turbulent equipartition is investigated for the nonlinear evolution of pressure driven flute modes in a plasma in an inhomogeneous magnetic field. Numerical solutions of the model equations on a bounded domain with sources and sinks show that the turbulent fluctuations give rise to up-gradient transport, a pinch flux, of heat or particles. The averaged equilibrium density and temperature profiles approach the profilesn B and T B 2=3 predicted by turbulent equipartition. Recently, a new approach has been suggested for predicting the quasi-steady profiles in tokamak plasmas [1, 2, 3, 4]. It is based on the existence of Lagrangian invariants in the presence of turbulence. The basic assumption is that the turbulent mixing causes the equipartition of these invariants over the accessible phase space, a state denoted Turbulent EquiPartition (TEP) [1]. Since the Lagrangian invariants depend on the magnetic fieldB, a homogeneous distribution of these invariants implies that if B is inhomogeneous, so are the density and the temperature. Therefore, the fluxes that drive the plasma towards TEP may be up-gradient. In a two-dimensional plasma model the corresponding mechanism is easily understood.

Velocity correlations in two-dimensional electrostatic turbulence in low-β plasmas

The Eulerian and Lagrangian correlation functions in low-frequency electrostatic turbulence in strongly magnetized plasmas are studied in two spatial dimensions. In this limit the ion velocity in the direction perpendicular to a homogeneous magnetic field is approximated by the E × B/B2velocity. For strictly flute-type fluctuations, a similar model is also used for the electron dynamics. Allowing, on the other hand, for a small B-parallel component of the perturbations, an isothermal Boltzmann distribution for the electrons can be justified while the two-dimensional ion description is retained. The present analysis is based on an approximation of the actual two-dimensional flow in terms of an autonomous system consisting of many overlapping and mutually convecting vortices. Simple analytical expressions for the full space—time-varying Eulerian correlation are derived solely in terms of plasma parameters. it is demonstrated that an extension of the arguments giving the foregoing results also allows for derivation of analytical expressions for the Lagrangian correlation function. The results are supported by a Monte Carlo simulation based on the model.

Two-dimensional electrostatic turbulence with variable density and pressure

Large-scale turbulence transverse to a uniform dc magnetic field is considered from the point of view of a two-fluid model of an electrostatic plasma of variable density. An approximation motivated by ’’geostrophic’’ techniques of dynamic meteorology is introduced. It is argued that the inverse cascade phenomenon should persist in the presence of variable pressure and density.