Rate of chaotic action diffusion in weakly nonlinear 4D maps
In plain words
Inside the region that looks stable, particles can still drift outward extremely slowly through thin chaotic layers; how fast is not known.
Precise statement
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 $\Delta Q \sim 1e-5 \text{ to } 1e-4$ 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 1e9 turns.
What would settle it
Analytic or semi-analytic diffusion coefficients matching tracked action distributions over at least three decades of turn number.