Coupled moment expansion model for the dynamics in a beam–plasma system

Abstract

A new technique is developed to study beam dynamics in an overdense plasma. This technique is an alternative to, and extension of, the well-known envelope equation formalism, and it can be used in systems with nonlinear forces. It is based on a systematic moment expansion of the Vlasov equation. In contrast to the envelope equation, which is derived assuming constant rms beam emittance, this coupled moment expansion (CME) model allows the emittance to vary through coupling to higher order moments. The CME model is implemented in slab geometry in the absence of return currents. The evolution of the low order moments of the distribution function are followed with ∼100 ordinary differential equations. The CME simulation yields rms beam sizes,velocity spreads, and emittances that are in good agreement with particle-in-cell simulations for a wide range of system parameters. New analytical results for the second-order moments in the phase-mixed state are obtained. Unlike previous results, these connect the final values of the second-order moments with the initial beam mismatch. These analytical estimates are in good agreement with the CME model and particle-in-cell simulations.