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Fluid simulations, which are considerably simpler and faster, have beenemployed to study the behavior of the wakefield driven by a relativistic rigidbeam in a 2-D cold plasma. When the transverse dimensions of the beam arechosen to be much larger than its longitudinal extent, a good agreement withour previous 1-D results [\textcolor{red}{\it Physics of Plasmas 22, 073109(2015)}] are observed for both under-dense and over-dense beams. When the beamis overdense and its transverse extent is smaller or close to the longitudinalextension, the 2-D blow-out structure, observed in PIC simulations andanalytically modeled by Lu et al. [\textcolor{red}{\it Phys. Rev. Lett., 96,165002 (2006)}] are recovered. For quantitative assessment of particleacceleration in such a wake potential structure test electrons are employed. Itis shown that the maximum energy gained by the test electrons placed at theback of the driver beam of energy $\sim 28.5$ GeV, reaches up to $2.6$ GeV in a10 cm long plasma. These observations are consistent with the experimentalresults presented in ref. [\textcolor{red}{\it Phys. Rev. Lett. 95, 054802(2005)}]. It is also demonstrated that the energy gained by the test electronsget doubled ($\sim 5.2$ GeV) when the test particles are placed near the axisat the end of the first blowout structure.

2-D fluid simulation of a rigid relativistic electron beam driven wakefield in a cold plasma