Rate of chaotic action diffusion in weakly nonlinear 4D maps

For a 4D symplectic map of linear rotation with tunes $(Q_x, Q_y)$ plus thin sextupole and octupole kicks of strength $\epsilon$, with tune modulation $\Delta Q \sim 10^{-5} \text{ to } 10^{-4}$ at frequencies $50\,\mathrm{Hz} \text{ to } 10\,\mathrm{kHz}$ from power-supply ripple, compute the rate of chaotic transport in action (Arnold and modulational diffusion) at amplitudes below the short-term dynamic aperture as a function of $\epsilon$ and $\Delta Q$. Test against direct tracking to $10^{9}$ turns.

Analytic or semi-analytic diffusion coefficients matching tracked action distributions over at least three decades of turn number.