Long global gyrokinetic simulations: Source terms and particle noise control

Abstract

In global gyrokinetic simulations it takes a long time for the turbulence to reach a quasisteady state, and quantitative predictions about the quasisteady state turbulence have been difficult to obtain computationally. In particular, global particle-in-cell gyrokinetic simulations have been inefficient for long simulations due to the accumulation of noise. It is demonstrated that a simple Krook operator can effectively control noise; it also introduces an unphysical dissipation, which damps the zonal flows and can significantly affect simulation results even when the relaxation time is very long. However, it is possible to project out the effects of the Krook operator on the zonal flows. This permits noise accumulation to be controlled while preserving the physics of interest; simulations are then run to determine the level of quasisteady state transport and the variation across the ensemble of turbulent dynamics. Convergence is demonstrated both in the number of computational particles and the unphysical relaxation time.

Parallel filtering in global gyrokinetic simulations

“…Now that these problems have been overcome, a nonlinear ∆m scan is necessary. It is a tedious task for decaying simulations (when the temperature gradient is allowed to relax): 320M particles are needed to converge a Cyclone simulation at ∆m = 5 [37], when a noise-control algorithm is used [26]. The situation becomes easier for nearly-fixed-gradient simulations, as the signal-to-noise ratio can be maintained high enough with relatively few markers (80M for the previous example).…”

“…This is a difficult task as bursts are chaotic: the turbulence has a so-called intrinsic variability. This phenomenon has been studied in [26] and [38] for ORB5 simulations: identical simulations differing only by the initialization are performed, and are compared by applying a moving time-average of width ∆t w . A standard deviation over the ensemble of simulations of about 15% is found for ∆t w = 500a/c s .…”

“…τ ( E) = − df 0 dt 1 (10) S N C ( z, t) is the noise-control operator [26]. It is composed of a Krook term −γ K δf ( z, t) and a correction term such that S N C ( z, t) does not alter an arbitrary set of moments.…”

Neoclassical physics in full distribution function gyrokinetics

“…This latter point has important practical implications for a newer generation of gyrokinetic codes which resolve the full distribution function, [38][39][40][41][42][43][44] amongst which the GYSELA 38 and XGC1 45 codes featured here. Self-consistent evolution of the distribution function is key to these models.…”

Particle-in-wavelets scheme for the 1D Vlasov-Poisson equations

“…Note that the kinetic energy appearing in E(t) is approximated by a discrete sum over the particles. Variations remain small for the two schemes, and are especially low for the PIW scheme with 2 19 particles.…”