Theory and simulations show harmonic Langevin PSDs approximate Paul trap x/y motion well only for small Mathieu q, with deviations exceeding factor of two at larger q, and permanent dipoles significantly alter those PSDs.
Also, the numerical PSD has a peak value that is approximately 40% lower than the Paul trap PSD Eq
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Simulations and theory of power spectral density functions for time dependent and anharmonic Langevin oscillators
Theory and simulations show harmonic Langevin PSDs approximate Paul trap x/y motion well only for small Mathieu q, with deviations exceeding factor of two at larger q, and permanent dipoles significantly alter those PSDs.