Verification that electrons are isothermal and protons adiabatic for ion-acoustic waves in unmagnetized collisionless PIC simulation plasma

Ion acoustic waves in collisionless plasma have a phase speed determined by the adiabatic constants of electrons and protons. Typically, the isothermal equation of state is assumed for electrons, resulting in an adiabatic constant γe=1, while the adiabatic equation of state with one degree of freedom is applied to protons, yielding γp=3. This selection has been experimentally validated in plasmas with hot electrons and cool ions. Here, we investigate whether this remains true in particle-in-cell (PIC) simulations, which generally exhibit noise levels significantly higher than those in real plasma. By comparing the power spectrum of simulation noise to the thermal noise spectrum and the dispersion relation of ion acoustic waves, we confirm that γe=1 and γp=3 are good approximations for the adiabatic constants that determine dispersive properties of ion acoustic waves in unmagnetized PIC simulation plasma with proton temperatures well below the electron temperature.