“…Recently, some research groups, e.g., Kostyukov et al, 4 Lotov, 6 Lu et al, 9,10 and Xie et al 14 have made some analysis on the bubble core fields as well as bubble front fields and concluded a linear scaling law of bubble core fields on coordinates. It seems that the validity of this linear law have been confirmed by many particle-incell ͑PIC͒ simulations, however, the slopes of the linear fields always have some discrepancies between PIC and theoretical results, in particular for the transverse electromagnetic fields.…”