Implementation of laser-plasma-based acceleration stages in user-oriented facilities requires the definition and deployment of appropriate diagnostic methodologies to monitor and control the acceleration process. An overview is given here of optical diagnostics for density measurement in laser-plasma acceleration stages, with emphasis on well-established and easily implemented approaches. Diagnostics for both neutral gas and free-electron number density are considered, highlighting real-time measurement capabilities. Optical interferometry, in its various configurations, from standard two-arm to more advanced common-path designs, is discussed, along with spectroscopic techniques such as Stark broadening and Raman scattering. A critical analysis of the diagnostics presented is given concerning their implementation in laser-plasma acceleration stages for the production of high-quality GeV electron bunches.

Highly nonlinear ellipsoid bubble regime of the laser wake-field acceleration with high-intensity laser pulse is considered with analytical and numerical calculations. The important property of this regime is the production of the mono-energetic high-quality electron beam. We introduce a new twofold ellipsoid structure of the bubble (egg shape) by referring to some published two-dimensional (2D) and 3D simulations. In this paper, a new analytical formalism is introduced, in which dimensions of the front part of the ellipsoid bubble are related to the laser pulse and plasma parameters. These relationships are in agreement with 2D particle-in-cell code results in recent work (Benedetti et al., 2013).