Effects of an artificial source in global gyrokinetic simulations

Global gyrokinetic simulations without a source do not reach a steady state due to profile relaxation. Since the physical velocity-dependent source is usually not known with sufficient accuracy, artificial sources are used that prevent profile relaxation and ensure a steady state. To compare the turbulent fluxes from simulation with experiment, the simulation result must be insensitive to the artificial source. This problem is of fundamental importance for the validation of the gyrokinetic model. Several of the common forms of energy/particle source have been implemented in the GEM ????-PIC code.   Nonlinear simulations with kinetic electrons are carried out varying the source form and the source rate. It is found that the ion heat flux increases linearly with the source rate when the source rate is small and becomes less sensitive for larger source rates. When the source rate is near 10% of the maximum linear growth rate, the dependence of the flux on the source rate becomes significant with variations depending on the form of the source.  We also investigate the closely related problem of marker distribution in PIC simulations. We show that, in partially-linearized PIC simulations, the marker density necessarily evolves away from the initially loaded marker distribution. Such evolution invalidates the typically used weight evolution equation in the ????-method. Techniques to mitigate this problem are presented.