Comparison of Particle-in-Cell and Spectral Plasma Solver codes on weak whistler wave instability driven by temperature anisotropy

During periods of increased magnetospheric convection, fresh plasma is carried into the inner magnetosphere, leading to the velocity distribution function of energetic electrons becoming anisotropic. The temperature anisotropy of tens of keV electrons generates whistler-mode chorus waves, which play a crucial role in the ring current and radiation belt dynamics through wave-particle interactions. Self-consistent simulations of plasma waves is one of the biggest problems in the inner magnetosphere modeling. The conventional approach to simulate self-consistent plasma dynamics is the particle-in-cell (PIC) method which is frequently used to simulate whistler waves in the magnetosphere. PIC is a simple and robust method, however it has a major limitation which is a statistical noise which can nontrivially affect weak plasma instabilities and wave-particle resonances making it challenging to apply to considered problem. In this work, we present extensive comparison of whistler wave simulations with VPIC code against simulations with another first-principles code, the Spectral Plasma Solver (SPS). SPS is a continuous Vlasov solver which is based on spectral expansion of the velocity space with Asymmetrically Weighted Hermite Polynomials (AWHP). The spectral AWHP expansion allows for a significant reduction in the number of degrees of freedom required to represent velocity space, while still retaining kinetic effects. The noiseless nature of SPS makes it particularly suitable to deal with weak instabilities considered in this work. We investigate various aspects of simulations of weak whistler instabilities with the two codes and demonstrate that while PIC compares well with SPS and linear theory for larger anisotropies (strong instability), important discrepancies become apparent as the temperature anisotropy becomes smaller. Due to the high computational cost of weak whistler instabilities simulations with PIC codes, convergence studies are often unfeasible, and we argue that in these situations alternative approaches, like SPS, might be preferred.