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Size Scaling of Turbulent Transport in Magnetically Confined Plasmas

Z. Lin, S. Ethier, T. S. Hahm, W. M. Tang

2002
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Physical Review Letters
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Transport scaling with respect to device size in magnetically confined plasmas is critically examined for electrostatic ion-temperature-gradient turbulence using global gyrokinetic particle simulations. It is found, by varying device size normalized by ion gyroradius while keeping other dimensionless plasma parameters fixed, that fluctuation scale length is microscopic in the presence of zonal flows. The local transport coefficient exhibits a gradual transition from a Bohm-like scaling for
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... ke scaling for device sizes corresponding to present-day experiments to a gyro-Bohm scaling for future larger devices. Transport levels in magnetically confined plasmas are generally observed to be well above those associated with collisional relaxation processes. This anomalous transport is believed to arise from microscopic turbulence driven by pressure gradients. The balance between turbulent transport and heating power determines the performance of magnetic fusion plasmas. Therefore, an accurate prediction of the expected transport level is critical for the design of fusion reactors. At present, the reactor design studies [1] rely on extrapolations of turbulent transport properties from present-day tokamak experiments to larger devices. These estimates are based in large part on some forms of empirical scaling, particularly device size scaling, for the global energy confinement time. These empirical scaling estimates are not always compatible with theoretical constraints from transformation invariants of fundamental plasma equations [2] . In this work, transport scaling with respect to device size is critically examined using first-principles gyrokinetic particle simulations for electrostatic toroidal ion temperature gradient (ITG) turbulence [3], which is a leading candidate to account for anomalous ion thermal transport in the tokamak core region. These large scale nonlinear simulations have recently been enabled by advances in efficient algorithms and by effective utilization of tera-scale massively parallel computers. In the absence of a fundamental, first-principles turbulence theory, heuristic, mixing length rules are often utilized to estimate size scaling of turbulent transport [3] . This approach invokes a random walk type of picture for diffusive processes using the scale length of turbulent eddies as the step size and the linear growth time of the instability as the step time. It predicts that if the eddy size increases with device size, the transport scaling is Bohm-like, i.e., local ion heat diffusivity is proportional to x B cT͞eB. Here c, T, e, B are, respectively, speed of light, electron temperature, electric charge of electrons, and magnetic field amplitude. On the other hand, if the eddy size is microscopic (on the order of the ion gyroradius), the transport scaling is gyro-Bohm, i.e., local ion heat diffusivity is proportional to x GB r ء x B . Here, r ء r i ͞a is the ion gyroradius r i normalized by the tokamak minor radius a. If transport is not diffusive (e.g., large transport events dominate the contribution to energy fluxes) the scaling can also be Bohm-like. Most theories [3] and local (or flux-tube) direct simulations [4] of ITG turbulence predict a gyro-Bohm scaling for ion transport since they assume fluctuations on a microscopic scale length and ignore pressure gradient profile variations. The gyro-Bohm scaling is often the implied scaling in reactor designs [1], and is clearly beneficial for larger devices since it predicts that transport coefficient decreases when the device size increases. However, trends from experimental observations have been more complicated. Transport scalings in low confinement regimes (L mode) have always been observed to be Bohm or worse than Bohm in major tokamaks [5, 6] . In particular, dimensionless scaling studies on the DIII-D tokamak found that ion transport and energy confinement time exhibit Bohm-like behavior, while fluctuation characteristics suggest a gyro-Bohm scaling [7] for transport. In the high confinement regime (H mode), transport scalings have been reported to be either Bohm [8] or gyro-Bohm in limited operational parameter space [6] . The uncertainty here may, in part, reflect the difficulty in varying r ء while keeping all other dimensionless parameters fixed (e.g., Mach number of toroidal rotation in H mode). An effective tool for scaling studies is full torus gyrokinetic particle simulations [9] . In these large scale calculations, kinetic effects and global profile variations are treated rigorously, and r ء can be varied over a wide range while all other dimensionless parameters are fixed. In previous global gyrokinetic simulations of electrostatic ITG turbulence, Bohm-like transport scaling was observed due to radially elongated eddies associated with the global structure of linear toroidal eigenmodes [10]. However, those scaling studies did not properly deal with turbulencedriven zonal flows. Our more realistic simulations in which zonal flows are self-consistently included found that the global mode structure is destroyed by the random shearing action of the zonal flows. This results predominantly in the reduction of the radial correlation length and subsequently the turbulence level [11] . This finding that the shearing of zonal flows is the dominant saturation mechanism represents a new nonlinear paradigm that is fundamentally 195004-1

doi:10.1103/physrevlett.88.195004
pmid:12005641
fatcat:phnkwa6s55fn3iqpjqx3hi5k34