  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.

Plasma Physics