Stability of energy-conserving PIC algorithms with smoother interpolations and more accurate Poisson solves

We have performed periodic, one-dimensional particle-in-cell (PIC) simulations to test explicit energy-conserving PIC algorithms with a variety of properties: continuous interpolated electric fields, continuous first derivatives of the interpolated electric field, Lagrangian-derived field solves, and second- and forth-order accurate field solves. We present numerical measurements of the stability, accuracy, and noise for each method, as well as comment on the generalizability to complex boundary conditions. In all cases, we find that the algorithm suffers from a cold-beam instability when v_thermal < v_drift and when v_drift < v_critical where v_critical is some algorithm-dependent critical velocity. Notably, all algorithms are stable to grid-heating (v_drift = 0) instabilities. This work confirms the semi-analytic work of Barnes and Chacon (2021), and extends their results by considering algorithms that have continuous first derivatives of the interpolated electric field and algorithms with a variety of field solves. We present an argument for the general failure of field solves to prevent cold-beam instabilities and derive v_critical analytically for some algorithms.