Quasi-linear theory in the non-resonant region

By solving for the changes 〈Δν〉 and 〈ΔνΔν〉 for a particle, it is shown that there is no diffusion equation for non-resonant particles when the electric field wave is damping. By indirect means it is then shown for this case that the appropriate quasi-linear solution for ƒ1(к, ν, t) is proportional to ∂ƒ0(ν, 0)/∂ν rather than ∂ƒ(ν, t)/∂ν.