Velocity distribution function as a function of v_x and v_y averaged over x and calculated from the 1D hybrid simulations at two different times of the evolution. Top panel: initial development of the beams due to LD. Bottom panel: later development of the beams. A logarithmic scale is used to represent the distribution function for a better visualisation of the results. In this plot β_e = 6 × 10⁻² and β_p = 10⁻³ and corresponds to weak LD.