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Title: Rate of chaotic action diffusion in weakly nonlinear 4D maps
Plain: Inside the region that looks stable, particles can still drift outward extremely slowly through thin chaotic layers; how fast is not known.
Precise: 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.
Settled by: Analytic or semi-analytic diffusion coefficients matching tracked action distributions over at least three decades of turn number.
Kind: well-posed
Answer type: value
References: (empty)
Literature status: open
Status note: (empty)
Posed since: (empty)