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.
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