Fixing E-field divergence in strongly nonlinear wakefields in homogeneous plasma

Available analytical wakefield models for the bubble and the blow-out regime of electron-plasma acceleration perfectly describe important features like shape, fields, trapping ratio, achievable energy, energy distribution and radial emittance. As we show, for wakefields with an extremely small amplitude these models fail to describe the accelerating electric field and its divergence in the wakefield rear. Since prominent parameter regimes like the Trojan horse regime of photocathode injection exhibit this feature, it is of great importance to work out analytical models that fix this problem; one possible model is introduced in this work. Using a phenomenological theory, we are able to better describe the divergence of the electric field and the bubble shape.