Defining optical injector parameters for optimal acceleration bunches

The standard regime for Laser Wake Field Acceleration (LWFA) requires femto-second timing between the driving laser pulse and the injected electron bunch to be accelerated in order to properly match the injected electron and the phase of the accelerating field. Additionally, the injected electron bunch must be short compared to the wavelength of the accelerating plasma wave to reduce distortion of the accelerated electron bunch. This timing requirement necessitates use of an all-optical injector. Several schemes for creating the injection electrons have been proposed including Laser Induced Poderomotive Acceleration (LIPA), Self-Modulated Laser Wakefield Acceleration (SMLWFA), and illumination of solid targets e.g., wires. Each of these schemes operate on a different mechanism. However, each of these mechanisms for creating injection electrons produces a broad, roughly Maxwell-Boltzmann, electron energy distribution with some "effective temperature". This paper presents a methodology for defining an optimal initial electron energy distribution, in conjunction with the details of the LWFA to be used, in order to provided a specified accelerated electron bunch distribution. For instance, for a given laser power and accelerating plasma density a specific approximate Hamiltonian function can be identified. Given this Hamiltonian and a desired distribution for the energy spread and phase for the accelerated electrons, an initial energy distribution and phase for the electrons can be identified. These initial conditions can be used to deduce an optimal effective temperature and bunch length for the optical injection beam. Results of both analytic analysis and simulations will be presented and implications for planned LWFA experiments and NRL will be discussed.