Dynamic aperture and transverse proton diffusion in HERA

Abstract

The dynamic aperture caused by persistent-current nonlinear field errors is an important concern in the design of superconducting hadron storage rings. The HERA proton ring is the second superconducting accelerator in operation. In this lecture note, its measured dynamic aperture is compared with that inferred from comprehensive tracking studies. To understand the difference between prediction and measurement, a semi-analytical method is developed for evaluating transverse diffusion rates due to various processes, such as modulational diffusion or sweeping diffusion. This analysis makes use of parameters for high-order resonances in the transverse phase space, which are obtained by normal-form algorithms using differential-algebra software. The semi-analytical results are consistent with the measurements, and suggest that the actual dynamic aperture is caused by an interplay of tune modulation and nonlinear magnetic fields.

Analysis of the non-linear beam dynamics at top energy for the CERN Large Hadron Collider by means of a diffusion model

“…bounded, motion occurs. DA is one of the key quantities for the design of modern colliders based on superconducting magnets, which feature unavoidable non-linear field errors, such as the Tevatron [1,2,3], HERA [4,5,6,7], RHIC [8], the Superconducting Super Collider (SSC) [9,10], and LHC (see, e.g. Ref.…”

Advances on the modeling of the time evolution of dynamic aperture of hadron circular accelerators

“…In the domain of single-particle dynamics, the concept of dynamic aperture (DA), namely the extent of the phase space region where bounded motion occurs, has been the key observable to guide the design of several past (see, e.g. [1,2,3,4,5,6,7]), present (see, e.g. [8]), and future hadron machines (see e.g.…”

Diffusion in stochastically perturbed Hamiltonian systems with applications to the recent LHC dynamic aperture experiments

“…The dynamic aperture (DA) is the amplitude of the phase space region where stable motion occurs. It is one of the key quantities for the design of modern colliders based on superconducting magnets, such as Tevatron [3][4][5] , HERA [6][7][8][9] , RHIC 10 , the Superconducting Super Collider (SSC) 11,12 , and LHC (see e.g., Ref. 13 for a detailed overview).…”