Rate of chaotic action diffusion in weakly nonlinear 4D maps · revision history

Revision 2

Accepted · core change · record

Changes against revision 1:

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 · changed · core
Revision 1: 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.
Revision 2: 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.
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)

Decisions