Non-linear theory of a cavitated plasma wake in a plasma channel for special applications and control

Abstract

We introduce a complete semi-analytical model for a cavitated electron wake driven by an electron beam in a radially inhomogeneous plasma. The electron response to the driver, dynamics of electrons in a thin sheath surrounding the cavity, as well as accelerating and focusing fields inside the cavity are calculated in the quasistatic approximation. Our theory holds for arbitrary radial density profiles and reduces to known models in the limit of a homogeneous plasma. A free-propagating blow-out in an evacuated channel experiences longitudinal squeezing, qualitatively the same as observed in particle-in-cell simulations for the laser pulse-driven case [Pukhov et al., Phys. Rev. Lett. 113, 245003 (2014)]. Our model also permits qualitative interpretation of the earlier observed cancellation of the focusing gradient in the cavity [Pukhov et al., Phys. Rev. Lett. 113, 245003 (2014)]. In this work, we show the underlying mechanism that causes the radial fields in the vacuum part of a channel to become defocussing.