Output of the eQL model using the strong (left panels) and weak (right panels) set of plasma parameters with realistic proton-to-electron mass ratio. Top panels: electron distribution function at different time instants in the direction parallel to the magnetic field. Grey vertical dashed lines correspond to v = 2v_the ≈ v_phz. Bottom panels: evolution supra-thermal electron density in Eq. (12). Vertical dashed line indicate the nonlinear time τ_NL in Eq. (16). Horizontal dotted gray lines indicate the results of Eq. (20). We note that time axes are different for the two simulations.