Extrapolating dynamic aperture from a million to a billion turns · revision history

Revision 2

Accepted · core change · record

Changes against revision 1:

Title
Extrapolating dynamic aperture from a million to a billion turns
Plain
Computers can track particles for about a million turns, but colliders store beams for billions; the rule used to extrapolate the stable region is a conjecture.
Precise · changed · core
Revision 1: The dynamic aperture $D(N)$, the largest initial amplitude stable for $N$ turns of the 4D or 6D symplectic one-turn map of a hadron collider, is fitted by Nekhoroshev-type laws D(N) = D_inf + b/(log N)^kappa. Determine whether such a law fitted for $N \le 1e6$ predicts $D(N)$ and the resulting intensity decay at $N \sim 1e9$ (about 1e5 s of LHC operation) to within 10 percent, and derive $\kappa$ from the resonance structure of the map.
Revision 2: The dynamic aperture $D(N)$, the largest initial amplitude stable for $N$ turns of the 4D or 6D symplectic one-turn map of a hadron collider, is fitted by Nekhoroshev-type laws $D(N) = D_{\infty} + b/(\mathrm{log}\, N)^{\kappa}$. Determine whether such a law fitted for $N \le 10^{6}$ predicts $D(N)$ and the resulting intensity decay at $N \sim 10^{9}$ (about $10^{5}$ s of LHC operation) to within 10 percent, and derive $\kappa$ from the resonance structure of the map.
Settled by · changed · core
Revision 1: Direct tracking to 1e9 turns of a realistic lattice compared with the extrapolation, plus a derivation of $\kappa$ from normal-form or resonance analysis.
Revision 2: Direct tracking to $10^{9}$ turns of a realistic lattice compared with the extrapolation, plus a derivation of $\kappa$ from normal-form or resonance analysis.
Kind
well-posed
Answer type
value
References
(empty)
Literature status
partially-resolved
Status note · changed
Revision 1: Fitted scaling laws described LHC intensity and luminosity evolution in several fills (2018-2019 papers); a derivation of the exponent and a test at 1e9 turns are missing.
Revision 2: Fitted scaling laws described LHC intensity and luminosity evolution in several fills (2018-2019 papers); a derivation of the exponent and a test at $10^{9}$ turns are missing.
Posed since
1996

Decisions