We propose a spectral Particle-In-Cell (PIC) algorithm that is based on the combination of a Hankel transform and a Fourier transform. For physical problems that have close-to-cylindrical symmetry, this algorithm can be much faster than full 3D PIC algorithms. In addition, unlike standard finite-difference PIC codes, the proposed algorithm is free of spurious numerical dispersion, in vacuum. This algorithm is benchmarked in several situations that are of interest for laser-plasma interactions. These benchmarks show that it avoids a number of numerical artifacts, that would otherwise affect the physics in a standard PIC algorithm -including the zero-order numerical Cherenkov effect.

Laser-plasma accelerators can produce high-quality electron beams, up to giga electronvolts in energy, from a centimetre scale device. The properties of the electron beams and the accelerator stability are largely determined by the injection stage of electrons into the accelerator. The simplest mechanism of injection is self-injection, in which the wakefield is strong enough to trap cold plasma electrons into the laser wake. The main drawback of this method is its lack of shot-to-shot stability. Here we present experimental and numerical results that demonstrate the existence of two different self-injection mechanisms. Transverse self-injection is shown to lead to low stability and poor-quality electron beams, because of a strong dependence on the intensity profile of the laser pulse. In contrast, longitudinal injection, which is unambiguously observed for the first time, is shown to lead to much more stable acceleration and higher-quality electron beams.