Entropy conservation as a constraint during Landau damping of a collisionless Langmuir wave

Landau damping is a collisionless wave-damping mechanism that has been well-studied across a variety of plasma environments. Since its initial prediction, Landau damping was detected and verified using multiple Laboratory experiments.(Malmberg et al., Phy. Rev. Letters.,13(6), 184,1964, Ida et al., Commun. Phys.,5,228,2022) A recent study confirmed signatures of Landau damping locally in the solar wind using single Magnetospheric Multiscale (MMS) spacecraft data employing field-particle correlation techniques (Chen et al., Nature Comm., 10, 740, 2019). It is known that conservation of energy implies that the internal energy increases as the wave undergoes Landau damping (Winterberg, Z. fur Naturforsch A,22,1682-9,1967). In this study, we argue that conservation of entropy in a closed, collisionless system provides another strong constraint on the evolution of the plasma during Landau damping. In particular, the decay of the density perturbation and the increase in temperature are incompatible in isolation with conservation of entropy, so the distribution function must also change shape in order to conserve entropy. We present a quantitative prediction of the change in shape of the distribution function as a function of system plasma parameters and the wave perturbation. We use a 1D-1V particle-in-cell (PIC) code to study Landau damping of a propagating collisionless Langmuir wave, and a parametric study validates the theoretical results.