Transport of Energetic Particles by Microturbulence in Magnetized Plasmas Wenlu Zhang (张文禄), 1,2, * Zhihong Lin (林志宏), 1 and Liu Chen (陈骝) 1,3 1 Department of Physics and Astronomy, University of California, Irvine, California 92697, USA 2 CAS Key Laboratory of Basic Plasma Physics, University of Science and Technology of China, Hefei, Anhui 230026, China 3 Institute for Fusion Theory and Simulation, Zhejiang University, Hangzhou, Zhejiang 310058, China (Received 20 May 2008; published 27 August 2008) Transport of energetic particles by the microturbulence in magnetized plasmas is studied in gyrokinetic simulations of the ion temperature gradient turbulence. The probability density function of the ion radial excursion is found to be very close to a Gaussian, indicating a diffusive transport process. The particle diffusivity can thus be calculated from a random walk model. The diffusivity is found to decrease drastically for high energy particles due to the averaging effects of the large gyroradius and orbit width, and the fast decorrelation of the energetic particles with the waves. DOI: 10.1103/PhysRevLett.101.095001 PACS numbers: 52.25.Fi, 52.35.Ra, 52.55.Fa, 52.65.Tt Energetic particles can be generated in magnetically confined plasmas by fusion reactions and auxiliary heating. They can be subjected to the diffusion by macroinstabil- ities [1], microtubulences [2], a stochastic magnetic field [3], and classical collisional and orbital effects [4]. The confinement of the energetic particles is a critical issue in the International Thermonuclear Experimental Reactor (ITER) [5], since the ignition relies on self-heating by the energetic fusion products. The diffusion of the ener- getic particles such as the cosmic rays by microscopic turbulence is also an important scientific issue in the space and astrophysical plasmas [6]. Earlier fusion experimental [4,7] and theoretical [8] studies indicated that energetic particles do not suffer a large transport due to the micro- turbulence excited by the pressure gradients of thermal particles. However, a recent fusion experiment [9] showed some evidence of the correlation between the excitation of the microturbulence and the redistribution of energetic ions produced by the neutral beam injection (NBI). Some recent theoretical [10] and computational [11] studies also sug- gested a significant transport level of the energetic particles driven by the microturbulence. To resolve this discrepancy, here we study the diffusion of the energetic particles by the microscopic ion tempera- ture gradient (ITG) [2] turbulence in large scale first- principles simulations of fusion plasmas using the global gyrokinetic toroidal code (GTC) [12]. The ion radial spread as a function of energy and pitch angle is measured in the steady-state ITG turbulence. The probability density function of the radial excursion is found to be very close to a Gaussian, indicating a diffusive transport from a random walk process. The radial diffusivity as a function of the energy and pitch angle can thus be calculated using the random walk model. We find that the diffusivity decreases drastically for high energy particles due to the averaging effects of the large gyroradius and banana width, and the fast decorrelation of the energetic particles with the ITG oscillations. By performing the integration in phase space, we can calculate the diffusivity for any distribution func- tion. The NBI ion diffusivity driven by the ITG turbulence is found to decrease rapidly for the born energy up to an order of magnitude of the plasma temperature and more gradually to a very low level for higher born energy. This result may explain the differences between the older ex- periments [4] with a higher born energy and the newer experiment [9] with a lower born energy (relative to the plasma temperature). Fully self-consistent ITG turbulence simulation.— This study employed a well bench-marked, massively parallel full torus gyrokinetic toroidal code (GTC) and used repre- sentative parameters of tokamak H-mode core plasmas which have a peak temperature gradient of thermal ions at a radial position r ¼ 0:5a with the following local parameters: R 0 =L T ¼ 6:9, R 0 =L n ¼ 2:2, q ¼ 1:4, ^ s  ðr=qÞðdq=drÞ¼ 0:78, T e =T i ¼ 1, and   a=R 0 ¼ 0:36. Here R 0 is the major radius, a is the minor radius, L T and L n are the temperature and density gradient scale lengths, respectively, T i and T e are the ion and electron tempera- ture, and q ¼ 0:854 þ 2:184ðr=aÞ 2 is the safety factor. In the full torus nonlinear simulation of a a ¼ 500 i tokamak with  i measured at r ¼ 0:5a, we calculated 800 transit times of 4  10 8 bulk marker particles (guiding centers), and interactions of these particles with self-consistent electrostatic potential represented on 4  10 7 spatial grid points to address realistic reactor-grade plasma parameters covering disparate spatial and temporal scales. A more complete simulation model is described in Ref. [13]. The simulation starts with very small random fluctuations which grow exponentially due to the toroidal ITG insta- bility as evident in the early part of the time history of the ion heat conductivity shown in the lower panel of Fig. 1. Zonal flows are then generated through modulational in- stability [14,15] and the ITG instabilities are saturated at the time of t ¼ 250L T =v i through random shearing by the zonal flows [16]. Finally, the nonlinear coupling of ITG- zonal flows leads to a fully developed turbulence after PRL 101, 095001 (2008) PHYSICAL REVIEW LETTERS week ending 29 AUGUST 2008 0031-9007= 08=101(9)=095001(4) 095001-1 Ó 2008 The American Physical Society