Turbulent Transport of Trapped-Electron Modes in Collisionless Plasmas Yong Xiao and Zhihong Lin Department of Physics and Astronomy, University of California, Irvine, California 92697, USA (Received 31 December 2008; published 19 August 2009) Global gyrokinetic particle simulations of collisionless trapped-electron mode turbulence in toroidal plasmas find that electron heat transport exhibits a device size scaling with a gradual transition from Bohm to gyro-Bohm scaling. A comprehensive analysis of spatial and temporal scales shows that the turbulence eddies are predominantly microscopic because of zonal flow shearing, but the presence of mesoscale structures drives a nondiffusive component in the electron heat flux due to the weak nonlinear detuning of the precessional resonance that excites the linear instability. DOI: 10.1103/PhysRevLett.103.085004 PACS numbers: 52.35.Ra, 52.30.Gz, 52.35.Qz, 52.65.y The anomalous heat loss in magnetic fusion plasmas is widely believed to arise from the microscopic turbulence excited by drift wave instability [1]. The understanding of and thus the ability to control ion heat transport have been drastically improved thanks to intensive studies of the ion temperature gradient (ITG) turbulence in fusion experi- ments, theory, and simulation. In contrast, electron heat transport is less understood, even though it is more impor- tant for burning plasmas such as ITER [2] since fusion products (energetic  particles) mostly heat the electrons. A prominent candidate for the electron heat transport in high temperature toroidal plasmas is collisionless trapped- electron mode (CTEM) [1] turbulence with a characteristic eddy size of the ion gyroradius ( i ). Despite a renewed interest [3–6], the nonlinear physics and transport proper- ties of the CTEM turbulence remain poorly understood. We report here the device size scaling of the electron heat transport, as well as the underlying saturation mechanism and nondiffusive transport process from the largest ever gyrokinetic particle simulations. The device size scaling of turbulent transport is one of the most important issues when predicting confinement properties of the large device ITER by extrapolating data from current devices. Tokamak experiments have reported both Bohm and gyro-Bohm scaling [7] for the ion heat transport, but more consistently gyro-Bohm scaling for the electron heat transport. Here, the gyro-Bohm scaling refers to a normalized heat conductivity independent of the de- vice size, whereas it increases with the device size in the Bohm scaling [1]. First-principles turbulence simulation can provide important physical insights on the size scaling [8] and avoid the difficulties of the empirical scaling in isolating a specific type of the turbulence and in varying the device size while keeping all other dimensionless parame- ters fixed. Our large scale simulations of the CTEM turbu- lence using the global gyrokinetic toroidal code (GTC) [9] find that the electron heat transport exhibits a gradual transition from the Bohm to gyro-Bohm scaling when the device size is increased. The deviation from the gyro-Bohm scaling could be induced by large eddies [10], turbulence spreading [8], and a nondiffusive transport process [11,12]. In our simu- lations, radial correlation function shows that the CTEM turbulence eddies are predominantly microscopic (a few  i ) but with a significant component in the mesoscale (tens of  i ). The macroscopic, linear streamers (hundreds of  i ) are mostly destroyed by the zonal flow shearing, which is found to be important in saturating the linear instability and in regulating the turbulence evolution and transport process. The mesoscale eddies form in a competing pro- cess between the breaking of the macroscopic streamers by the zonal flows and the merging of the microscopic eddies. A comprehensive analysis of kinetic and fluid time scales finds very weak nonlinear detuning of the toroidal precessional resonance of the magnetically trapped elec- trons that drives the linear CTEM instability. Thus the trapped electrons behave as fluid elements in the transport process, and their ballistic radial drifts across the meso- scale eddies drive a nondiffusive component in the electron heat flux. In contrast, the ions cannot drift across the mesoscale eddies due to the parallel wave-particle decor- relation [13,14], which is not operational for trapped elec- trons because of the bounce averaging by the fast parallel motion. The nondiffusive electron heat flux, together with the turbulence spreading, leads to an electron heat con- ductivity dependent on the device size, i.e., a breaking of the gyro-Bohm scaling. In the GTC simulations, the ion is treated by the gyro- kinetic equation while the electron by the drift kinetic equation. A fluid-kinetic hybrid electron model [15] is ap- plied to improve the numerical efficiency for the electron dynamics. The following DIII-D H-mode parameters [16] are used for the nonlinear CTEM simulation: R 0 =L Te ¼ 6:9, R 0 =L Ti ¼ R 0 =L n ¼ 2:2, T e =T i ¼ 1, m i =m e ¼ 1837, q ¼ 0:58 þ 1:09r=a þ 1:09ðr=aÞ 2 , where a is the minor radius of the tokamak. The circular cross section model is used in the simulation with the magnetic field defined by B ¼ B 0 =½1 þðr=aÞ cos. Linear simulations [16] show that this case is a pure CTEM turbulence instability with a maximum linear growth rate  max ¼ 0:25v i =L n , where v i ¼ ffiffiffiffiffiffiffiffiffiffiffiffi T i =m i p is the ion thermal speed. The field mesh for the electrostatic potential consists of 32 parallel grids and a PRL 103, 085004 (2009) PHYSICAL REVIEW LETTERS week ending 21 AUGUST 2009 0031-9007= 09=103(8)=085004(4) 085004-1 Ó 2009 The American Physical Society