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.
This involves doing the calculation in a frame rotating with the frequency w0 [12],[6]
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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.