Theory of beam-driven nonlinear plasma wake and interior waves.

Abstract

A beam of relativistic charged particles propagating in a plasma can drive plasma electrons to oscillate and together form a wave whose phase velocity matches the velocity of the driving beam. These plasma waves realize state-of-the-art compact accelerators through plasma wakefield acceleration. Here, we formulate a one-dimensional analytic theory of beam-driven nonlinear plasma waves that is valid for positively and negatively charged particle beams propagating with arbitrary velocity. We find that nonlinear plasma waves can arise within the interior region of the driving beam, with wavelength and amplitude different from those of the plasma wakefield. In contrast to plasma wake waves, the interior waves are robust with respect to driver length variation. Our analytic results can be used to design current and future plasma accelerators, to understand their limitations due to wave breaking, and for applications in coherent light generation in plasma, such as relativistic mirrors formed by breaking plasma waves. Furthermore, we discuss the potential of our results to offer insights into the origin of ultrahigh-energy cosmic rays.