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Register a new userWavelet transforms and their applications to MHD and plasma turbulence: a review
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Wavelet analysis and compression tools are reviewed and different applications to study MHD and plasma turbulence are presented. We introduce the continuous and the orthogonal wavelet transform and detail several statistical diagnostics based on the wavelet coefficients. We then show how to extract coherent structures out of fully developed turbulent flows using wavelet-based denoising. Finally some multiscale numerical simulation schemes using wavelets are described. Several examples for analyzing, compressing and computing one, two and three dimensional turbulent MHD or plasma flows are presented.
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This review puts the developments of the last few years in the context of the canonical time line (Kolmogorov to Iroshnikov-Kraichnan to Goldreich-Sridhar to Boldyrev). It is argued that Beresnyaks objection that Boldyrevs alignment theory violates the RMHD rescaling symmetry can be reconciled with alignment if the latter is understood as an intermittency effect. Boldyrevs scalings, recovered in this interpretation, are thus an example of a physical theory of intermittency in a turbulent system. Emergence of aligned structures brings in reconnection physics, so the theory of MHD turbulence intertwines with the physics of tearing and current-sheet disruption. Recent work on this by Loureiro, Mallet et al. is reviewed and it is argued that we finally have a reasonably complete picture of MHD cascade all the way to the dissipation scale. This picture appears to reconcile Beresnyaks Kolmogorov scaling of the dissipation cutoff with Boldyrevs aligned cascade. These ideas also enable some progress in understanding saturated MHD dynamo, argued to be controlled by reconnection and to contain, at small scales, a tearing-mediated cascade similar to its strong-mean-field counterpart. On the margins of this core narrative, standard weak-MHD-turbulence theory is argued to require adjustment - and a scheme for it is proposed - to take account of the part that a spontaneously emergent 2D condensate plays in mediating the Alfven-wave cascade. This completes the picture of the MHD cascade at large scales. A number of outstanding issues are surveyed, concerning imbalanced MHD turbulence (for which a new theory is proposed), residual energy, subviscous and decaying regimes of MHD turbulence (where reconnection again features prominently). Finally, it is argued that the natural direction of research is now away from MHD and into kinetic territory.
A unique method of driving Alfvenic turbulence via an oscillating Langevin antenna is presented. This method of driving is motivated by a desire to inject energy into a finite domain numerical simulation in a manner that models the nonlinear transfer of energy from fluctuations in the turbulent cascade at scales larger than the simulation domain.. The oscillating Langevin antenna is shown to capture the essential features of the larger scale turbulence and efficiently couple to the plasma, generating steady-state turbulence within one characteristic turnaround time. The antenna is also sufficiently flexible to explore both strong and weak regimes of Alfvenic plasma turbulence.
JOREK is a massively parallel fully implicit non-linear extended MHD code for realistic tokamak X-point plasmas. It has become a widely used versatile code for studying large-scale plasma instabilities and their control developed in an international community. This article gives a comprehensive overview of the physics models implemented, numerical methods applied for solving the equations and physics studies performed with the code. A dedicated section highlights some of the verification work done for the code. A hierarchy of different physics models is available including a free boundary and resistive wall extension and hybrid kinetic-fluid models. The code allows for flux-surface aligned iso-parametric finite element grids in single and double X-point plasmas which can be extended to the true physical walls and uses a robust fully implicit time stepping. Particular focus is laid on plasma edge and scrape-off layer (SOL) physics as well as disruption related phenomena. Among the key results obtained with JOREK regarding plasma edge and SOL, are deep insights into the dynamics of edge localized modes (ELMs), ELM cycles, and ELM control by resonant magnetic perturbations, pellet injection, as well as by vertical magnetic kicks. Also ELM free regimes, detachment physics, the generation and transport of impurities during an ELM, and electrostatic turbulence in the pedestal region are investigated. Regarding disruptions, the focus is on the dynamics of the thermal quench and current quench triggered by massive gas injection (MGI) and shattered pellet injection (SPI), runaway electron (RE) dynamics as well as the RE interaction with MHD modes, and vertical displacement events (VDEs). Also the seeding and suppression of tearing modes (TMs), the dynamics of naturally occurring thermal quenches triggered by locked modes, and radiative collapses are being studied.
Regular oscillations of the central electron temperature have been observed by means of ECE and SXR diagnostics during non-inductively driven discharges on Tore Supra. These oscillations are sustained by LHCD, do not have a helical structure and, therefore, cannot be ascribed as MHD phenomena. The most probable explanation of this oscillating regime (O-regime) is the assumption that the plasma current density (and, thus, the q-profile) and the electron temperature evolve as a non-linearly coupled predator-pray system. The integrated modelling code CRONOS has been used to demonstrate that the coupled heat transport and resistive diffusion equations admit solutions for the electron temperature and the current density which have a cyclic behaviour. Recent experimental results in which the O-regime co-exists with MHD modes will be presented. Because both phenomena are linked to details of the q-profile, some interplay between MHD and oscillations may occur. The localisation of magnetic islands allows to obtain an accurate picture of the q-profile in the plasma core. In some case, MHD-driven reconnection helps in maintaining a weakly inverted q-profile that is found to be, in the CRONOS simulations, a necessary condition to trigger the oscillations.
The current understanding of MHD turbulence envisions turbulent eddies which are anisotropic in all three directions. In the plane perpendicular to the local mean magnetic field, this implies that such eddies become current-sheet-like structures at small scales. We analyze the role of magnetic reconnection in these structures and conclude that reconnection becomes important at a scale $lambdasim L S_L^{-4/7}$, where $S_L$ is the outer-scale ($L$) Lundquist number and $lambda$ is the smallest of the field-perpendicular eddy dimensions. This scale is larger than the scale set by the resistive diffusion of eddies, therefore implying a fundamentally different route to energy dissipation than that predicted by the Kolmogorov-like phenomenology. In particular, our analysis predicts the existence of the sub-inertial, reconnection interval of MHD turbulence, with the Fourier energy spectrum $E(k_perp)propto k_perp^{-5/2}$, where $k_perp$ is the wave number perpendicular to the local mean magnetic field. The same calculation is also performed for high (perpendicular) magnetic Prandtl number plasmas ($Pm$), where the reconnection scale is found to be $lambda/Lsim S_L^{-4/7}Pm^{-2/7}$.
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