δf and particle simulations of parametric instabilities

The δf and particle simulation methods are presented and compared for parametric instabilities in a 1D unmagnetized plasma. The δf simulation method used here is based on the linearized Vlasov equation. The simulation growth rates from both methods roughly agree with growth rates obtained from a fluid theory. Doubling the number of characteristics in the δf simulations does not significantly alter the growth rates. Doubling the number of particles in the particle simulation does alter the growth rates indicating that particle noise is interfering with the physics. The δf simulation method was also compared to Vlasov theory for parametric instabilities in a ID magnetized plasma. The simulations generally agree with the theory.