“…In standard PIC simulation (Birdsall & Langdon, 1985), the size of each cell has to be smaller than the Debye length in order to avoid numerical instability. Recently, numerical techniques based on hybrid simulations have been extensively applied for the study of beam-plasma interactions (Welch et al, 2001;Davies, 2003;Honrubia et al, 2005;Campbell et al, 2005;Evans, 2006;Solodov et al, 2009;Zhou et al, 2009). In this work, we shall not consider the initial laser-cone interaction, which has been investigated by many authors (Gibbon, 2005;Cai et al, 2009;Wu et al, 2010).…”