Topic/Type: 1. Plasma Simulation, Invited

### Gyrokinetic PIC Simulations of Magnetic Fusion Plasmas

W. W. Lee

Princeton Plasma Physics Laboratory, Princeton University, Princeton, NJ 08543 USA

Gyrokinetic particle-in-cell (GK-PIC) simulation of magnetic fusion plasmas has been in existence since the nineteen eighties.[1] With the advent of massively parallel computing capabilities and the improvements in algorithms in recent years, GK-PIC codes [2,3] based on global toroidal geometry has been contributing to the understanding of the confinement properties in tokamaks. In this talk, the numerical considerations pertinent to the integrated tokamak simulation of turbulence, neoclassical transport and global MHD effects will be discussed. First and foremost is the question of numerical noise. A recent paper based on the fluctuation-dissipation theorem which has extended our understanding from a quiescent plasma to a nonlinearly saturated one [4] will be used to interpret the global simulation results. The growing weight question for the $\small \delta f$ simulation, [5], i.e., what happens when the particle weights approach unity, can be answered by using a method based on the concept of multiscale expansion by bridging the full-F simulation with the $\small \delta f$ simulation, which we will discuss. Furthermore, the question of profile relaxation in the $\small \delta f$ simulation, which has been found to be unimportant, will be elaborated. With these issues resolved, together with the newly developed electromagnetic split-weight scheme, we should be able to simulate tokamak discharges that include spatial scales ranging from the electron skin depth to major radius. Finally, the gyrokinetic Poisson\'s equation in the long wavelength limit, which has been used routinely in the global simulations, has been proven to be valid despite of the recent controversy.[6] Moreover, it has been found that the stability property of the simulation plasma in the nonlinear stage depends crucially on the presence of the long wavelength zonal flow modes and the velocity space nonlinearity.[7] The latter is crucial for energy conservation in the simulation.

$\small ^*$ This work is presently supported by DoE Contract No. DE-AC02-09CH11466.

[1] W. W. Lee, Phys. Fluids {\bf 26}, 556 (1983); J. Comput. Phys. {\bf 72}, 243 (1987).

[2] Z. Lin, T. S. Hahm, W. W. Lee, W. M. Tang, and R. White, Science {\bf 281}, 1835 (1998).

[3] W. X. Wang, Z. Lin et al., Phys. Plasmas {\bf 13}, 092505 (2006).

[4] T. G. Jenkins and W. W. Lee, Phys. Plasmas {\bf 14}, 032307 (2007).

[5] S. E. Parker and W. W. Lee, Phys. Fluids B {\bf 5}, 77 (1993).

[6] W. W. Lee and R. A. Kolesnikov, Phys. Plasmas, {\bf 16}, 044506 (2009).

[7] W. W. Lee, S. Ethier et al., Computational Science & Discovery {\bf 1}, 015010 (2008).