Simulating ultrarelativistic beam-plasma instabilities with a quasistatic particle-in-cell code

Quasistatic particle-in-cell (PIC) codes are increasingly employed to study laser or plasma wakefield accelerators. By decoupling the slow dynamics of the driver (a laser or ultrarelativistic particle beam) from the fast plasma response, these codes can reduce the computational time by several orders of magnitude compared to conventional PIC codes. In this work, we demonstrate that quasistatic PIC codes can also be utilized to investigate relativistic beam-plasma instabilities, with a focus on the oblique two-stream instability (OTSI). For this purpose, we have developed a 2D quasistatic PIC code, QuaSSis, based on a new numerical scheme that can handle transversely periodic boundary conditions, a capability absent in previous quasistatic codes. The accuracy of QuaSSis is benchmarked first against standard PIC simulations performed with the CALDER code, and then against an analytical spatiotemporal model of the OTSI. Physically, this instability grows exponentially from initial fluctuations in the particle charge or current densities. Since the numerical noise inherent to PIC simulations can mimic these fluctuations to some extent, its control is crucial to seed the beam-plasma instability at the desired amplitude. Common methods for tuning this noise involve modifying the resolution or adding filters, but these can be computationally costly when aiming at very low noise levels. Here, we show that this noise can be finely controlled by properly initializing the positions and weights of the macroparticles.