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.

Bubble regime of plasma wakefield in 2D and 3D geometries

“…In order to find the longitudinal field E x (ξ) and the corresponding longitudinal force F x , we need to know the shape of the bubble's boundary y b (ξ). As it is known from the previous 3D models, 10,11 this shape can be selfconsistently found. The corresponding calculations for the 2D case are described next.…”

“…9 A more detailed phenomenological model makes it possible to describe the boundary of the bubble with a differential equation. 10 This phenomenological model has also been generalized for plasmas with nonuniform transverse profiles 11,12 , and it is also capable of describing beam loading effects 13,14 (i. e. the influence of accelerated electron bunches on the bubble). In the scope of the model, explicit expressions for the electromagnetic field components both inside and outside the bubble can be obtained.…”

“…The developed model is similar to the model of the bubble in the 3D geometry. [10][11][12] The paper is structured as follows. In Sec.…”

Analytic model for electromagnetic fields in the bubble regime of plasma wakefield in non-uniform plasmas

“…As shown in the previous works, 12,14,15 Eq. (14) for the bubble's boundary can be significantly simplified by assuming that the width of the electron sheath on the boundary is significantly smaller than the size of the bubble, i. e. ∆ r b .…”

“…12 Following the discovery of the advantages of plasmas with hollow channels in the bubble regime, 13 this analytic model has recently been generalized to describe plasmas with non-uniform transverse density profile. 14,15 The aforementioned theories focus mostly on the shape of the bubble and on the dynamics of relativistic accelerated particles, while paying less attention to the structure of electromagnetic field components inside the bubble and at its boundary. Knowledge of this structure can be of significant interest for the processes of particle injection and self-injection into the wakefield, 10,16 when the particles under consideration are not ultra-relativistic.…”