Comparison of Measured and Computed Dynamic Aperture for the SPS and the Hera Proton Ring

Abstract

Nonlinear magnetic fields in conjunction with tune modulation can lead to chaotic particle motion and thereby limit the dynamic aperture of hadron storage rings. This is of particular interest for the LHC at injection energy where the field errors of the superconducting magnets and the beam size have their maximum.The SPS dynamic aperture experiment was performed to study a controlled nonlinear machine under the influence of tune modulation. In parallel long-term tracking simulations were done to test to which extend computer programs can predict the dynamic aperture under those conditions. In a complementary experiment at the HERA proton ring the dynamic aperture was measured at injection energy under normal operating conditions. The computer simulations for these measurements included a very detailed model of the nonlinear magnetic fields which were measured for each individual magnet.

Diffusion due to Beam-Beam Interaction and Fluctuating Fields in Hadron Colliders

“…The dynamics are qualitatively different however when the time-dependence, both deterministic and stochastic, of parameters is included. The effects of deterministic tune modulation are well studied and removing modulation lines from the betatron spectrum reduces particle loss from the tails of the beam [1]. Random fluctuations in the tune, closed orbit and beam size are also present in accelerators.…”

Overview of single-particle nonlinear dynamics

“…In [37] the influence of two ripples on a simplified lattice model (Hènon map) has been analysed, using the concept of sidebands and overlapping. The effectiveness of the ripple correction to improve beam lifetime in the HERA has been shown in [38]. Different mechanisms that lead to transverse proton diffusion have been analysed in [39], where a diffusion equation and resonance parameters evaluated through perturbative theory were used to understand which mechanism could explain diffusion in the HERA.…”

Dynamic aperture computation for the as-built CERN Large Hadron Collider and impact of main dipoles sorting

“…In the design phase, the dynamic aperture (DA), the amplitude of the region in phase space where stable motion occurs, has been a key quantity for the specification of the performance of the CERN LHC; as is also true for all modern colliders and storage rings, such as Tevatron [1][2][3][4], HERA [5][6][7][8][9], RHIC [10], or the Superconducting Super Collider (SSC) [11,12]. The case of synchrotron light sources, damping rings or, in general, lepton machines is somewhat different and is not considered here; the presence of strong damping due to synchrotron radiation, implies that only the so-called "short-term" dynamic aperture, i.e.…”

“…It has also demanded an increased effort in the field of massive numerical simulations to gain insight to the DA characteristics, and direct measurements in existing machines (see, e.g., Refs. [9,[19][20][21] for the case of hadron machines) and that comparisons be made between measurements and simulations (see, e.g., Ref. [22] for a review of this topic).…”