Comparison of 1-D PIC simulations with GBDR and Langmuir waves observations in front of the Saturnian bow shock.

Plasma waves are commonly observed in front of planetary shocks. These waves are typically generated via the beam instability due to a drift velocity between low density electron beams and thermal velocity of the background plasma. We focus on simulations of solar wind plasma conditions resulting to observed spectra with varying spectral structures. We compare results of 1-D electrostatic PIC simulations with a solution of the Generalized Buneman Dispersion Relation (GBDR) which was derived from the linear dispersion theory and with observations of the Wideband instrument onboard Cassini at Saturn. We study applicability of 1-D electrostatic PIC algorithms and their modifications for simulations of the plasma wave phenomena. We compare different methods of particle weighting, cell splitting, distribution generating and higher-order methods of temporal discretization. We show that proper distribution generating and particle weighting procedures lead to mitigation of numerical noise in cases of low density electron beams and that higher-order methods of temporal discretization lead to lower numerical dispersion errors (shift and blur of modes).