Result of a toy model wave-particle resonance after 50 gyration periods with an oblique wave with an amplitude of δB/B₀ = 0.001. As expected, also higher orders of resonances with n =  [ − 3, − 2, − 1,1,2] also developed. At this timestep Eq. (32) would again deviate significantly, because only few particles would fulfil the resonance condition, where others are still disturbed by the finite distortion of B₀ and thus interact nonresonantly, which produces the finite ballistic background.