The Radial Propagation of Heat in Strongly Driven Non-Equilibrium Fusion Plasmas

Heat transport is studied in strongly heated fusion plasmas, far from thermodynamic equilibrium. The radial propagation of perturbations is studied using a technique based on the transfer entropy. Three different magnetic confinement devices are studied, and similar results are obtained. "Minor transport barriers" are detected that tend to form near rational magnetic surfaces, thought to be associated with zonal flows. Occasionally, heat transport "jumps" over these barriers, and this "jumping" behavior seems to increase in intensity when the heating power is raised, suggesting an explanation for the ubiquitous phenomenon of "power degradation" observed in magnetically confined plasmas. Reinterpreting the analysis results in terms of a continuous time random walk, "fast" and "slow" transport channels can be discerned. The cited results can partially be understood in the framework of a resistive Magneto-HydroDynamic model. The picture that emerges shows that plasma self-organization and competing transport mechanisms are essential ingredients for a fuller understanding of heat transport in fusion plasmas.Research sponsored in part by the Ministerio de Economía y Competitividad of Spain under Project No. ENE2015-68206-P and ENE2015-68265-P. This work has been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training program 2014-2018 and 2019-2020 under Grant Agreement No. 633053. The views and opinions expressed herein do not necessarily reflect those of the European Commission

Comparison of BES measurements of ion-scale turbulence with direct, gyrokinetic simulations of MAST L-mode plasmas

Observations of ion-scale (k_y*rho_i <= 1) density turbulence of relative amplitude dn_e/n_e <= 0.2% are available on the Mega Amp Spherical Tokamak (MAST) using a 2D (8 radial x 4 poloidal channel) imaging Beam Emission Spectroscopy (BES) diagnostic. Spatial and temporal characteristics of this turbulence, i.e., amplitudes, correlation times, radial and perpendicular correlation lengths and apparent phase velocities of the density contours, are determined by means of correlation analysis. For a low-density, L-mode discharge with strong equilibrium flow shear exhibiting an internal transport barrier (ITB) in the ion channel, the observed turbulence characteristics are compared with synthetic density turbulence data generated from global, non-linear, gyro-kinetic simulations using the particle-in-cell (PIC) code NEMORB. This validation exercise highlights the need to include increasingly sophisticated physics, e.g., kinetic treatment of trapped electrons, equilibrium flow shear and collisions, to reproduce most of the characteristics of the observed turbulence. Even so, significant discrepancies remain: an underprediction by the simulations of the turbulence amplituide and heat flux at plasma periphery and the finding that the correlation times of the numerically simulated turbulence are typically two orders of magnitude longer than those measured in MAST. Comparison of these correlation times with various linear timescales suggests that, while the measured turbulence is strong and may be `critically balanced', the simulated turbulence is weak.Comment: 27 pages, 11 figure

Theory of the Spatio-Temporal Dynamics of Transport Bifurcations

The development and time evolution of a transport barrier in a magnetically confined plasma with non-monotonic, nonlinear dependence of the anomalous flux on mean gradients is analyzed. Upon consideration of both the spatial inhomogeneity and the gradient nonlinearity of the transport coefficient, we find that the transition develops as a bifurcation front with radially propagating discontinuity in local gradient. The spatial location of the transport barrier as a function of input flux is calculated. The analysis indicates that for powers slightly above threshold, the barrier location $x_b(t) \sim ( D_n t (P-P_c)/P_c)^{1/2},$ where $P_c$ is the local transition power threshold and $D_n$ is the neoclassical diffusivity . This result suggests a simple explanation of the high disruptivity observed in reversed shear plasmas. The basic conclusions of this theory are insensitive to the details of the local transport model.Comment: 21 page Tex file, 10 postscript file

Mesoscopic transport in KSTAR plasmas: avalanches and the E×BE \times B staircase

The self-organization is one of the most interesting phenomena in the non-equilibrium complex system, generating ordered structures of different sizes and durations. In tokamak plasmas, various self-organized phenomena have been reported, and two of them, coexisting in the near-marginal (interaction dominant) regime, are avalanches and the $E \times B$ staircase. Avalanches mean the ballistic flux propagation event through successive interactions as it propagates, and the $E \times B$ staircase means a globally ordered pattern of self-organized zonal flow layers. Various models have been suggested to understand their characteristics and relation, but experimental researches have been mostly limited to the demonstration of their existence. Here we report detailed analyses of their dynamics and statistics and explain their relation. Avalanches influence the formation and the width distribution of the $E \times B$ staircase, while the $E \times B$ staircase confines avalanches within its mesoscopic width until dissipated or penetrated. Our perspective to consider them the self-organization phenomena enhances our fundamental understanding of them as well as links our findings with the self-organization of mesoscopic structures in various complex systems

Non-linear effects in electron cyclotron current drive applied for the stabilization of neoclassical tearing modes

Due to the smallness of the volumes associated with the flux surfaces around the O-point of a magnetic island, the electron cyclotron power density applied inside the island for the stabilization of neoclassical tearing modes (NTMs) can exceed the threshold for non-linear effects as derived previously by Harvey et al, Phys. Rev. Lett. 62 (1989) 426. We study the non-linear electron cyclotron current drive (ECCD) efficiency through bounce-averaged, quasi-linear Fokker-Planck calculations in the magnetic geometry as created by the islands. The calculations are performed for the parameters of a typical NTM stabilization experiment on ASDEX Upgrade. A particular feature of these experiments is that the rays of the EC wave beam propagate tangential to the flux surfaces in the power deposition region. The calculations show significant non-linear effects on the ECCD efficiency, when the ECCD power is increased from its experimental value of 1 MW to a larger value of 4 MW. The nonlinear effects are largest in case of locked islands or when the magnetic island rotation period is longer than the collisional time scale. The non-linear effects result in an overall reduction of the current drive efficiency for this case with absorption of the EC power on the low field side of the electron cyclotron resonance layer. As a consequence of the non-linear effects, also the stabilizing effect of the ECCD on the island is reduced from linear expectations