The missing GeV gamma-ray cascade signal of distant Blazars implies either the deflection of the pair beam by intergalactic magnetic fields or, alternatively, an energy loss of the beam due to the beam-plasma instability. A recent study demonstrated that the instability feedback on a simplified 1D beam profile reduces the instability growth severely. Here we study the feedback on the realistic 2D beam distribution. We solve the Fokker-Planck diffusion equation with initially dominant angular diffusion, then we analyse the other terms using the widened beam distribution. We found that the energy loss of the beam due to the growth of the instability and its momentum diffusion feedback on the beam is small compared to the inverse Compton cooling rate. We found also that another angular diffusion term, which is initially negligible, might become relevant and narrows the beam particles with Lorentz factors less than $10^{6}$. Finally, we have included the production of new pairs due to the gamma-ray annihilation along the beam axis. We found that the unstable waves saturate so that the beam widening balances the injection at the production angles and the beam keeps expanding. However, it is essential to include the inverse Compton cooling in the beam transport equation to understand the physical effects of this balance.