Impact of non-Gaussian beam profiles in the performance of hadron colliders

Abstract

At the Large Hadron Collider (LHC), the interplay between a series of effects, including intrabeam scattering (IBS), synchrotron radiation, longitudinal beam manipulations, two beam effects (beam-beam, e-cloud) and machine nonlinearities, can change the population of the core and tails and lead to non-Gaussian beam distributions, at different periods during the beam cycle. By employing generalized distribution functions, it can be demonstrated that the modified non-Gaussian beam profiles have an impact in the beam emittance evolution by itself and thereby to the collider luminosity. This paper focuses on the estimation of beam distribution modification and the resulting rms beam size due to the combined effect of IBS and synchrotron radiation by employing a Monte-Carlo simulation code which is able to track 3D generalized particle distributions (SIRE). The code is first benchmarked over classical semianalytical IBS theories and then compared with measurements from the LHC at injection and collision energies, including projections for the High-Luminosity LHC (HL-LHC) high brightness regime. The impact of the distribution shape on the evolution of the bunch characteristics and machine performance is finally addressed.

Electromagnetic interaction of colliding Q-Gaussian beams

“…For 𝑞 = 1, the Q-Gaussian distribution represents the usual Gaussian. For more on Q-Gaussian, see [11,12]. When an ultra-relativistic charged particle, with relativistic factor 𝛽 ≈ 1, and charge 𝑄 2 passes through (or near) a charged particle density 𝜌 1 at a zero crossing angle, it receives a total transverse momentum kick, which is defined as [2,13]:…”

“…The Q-Gaussian, see [9], describes the bunch profile for LHC and HL-LHC more realistically [8,10]. In [11] the effect of the non-Gaussian tails on the emittance evolution and intra-beam scattering was investigated using Q-Gaussian beams. In [12], we investigated the beam overlap of Q-Gaussian beams.…”

Linear acceleration emission of pulsar relativistic streaming instability and interacting plasma bunches

“…A.4, we chose the generalized Gaussian profile with the power exponent p = 6 in the expression e −x p to make the transition of the bunch and the surrounding plasma steeper and to separate the bunches more from the background plasma than for a Gaussian profile with p = 2. For the generalized Gaussian profile, we were inspired by laboratory measurements in electron beam colliders and laser wakefields, which also detected profiles similar to generalized Gaussian with p > 2 (Decker 1995;Papadopoulou et al 2020;Geng et al 2021;Liang et al 2022). Nonetheless, the study of how the density profile, for instance, the parameter p, specifically influences the properties of the emitted radiation is beyond the scope of this paper.…”

First Experimental Evidence of a Beam-Beam Long-Range Compensation Using Wires in the Large Hadron Collider

“…Eqs. (7) finally give the expression of the n th -multipole strengths for a DC wire, using the previous equations:…”

“…Obtaining a closed form for the luminosity is not trivial as different effects have to be taken into account. From [6] one can get the expression of the instantaneous luminosity produced by the collisions of two bunches with the same transverse Gaussian distribution (σ x , σ y ) (which is a valid assumption for the LHC and the HL-LHC [7,8]), for a given crossing angle θ c in the crossing plane and the beams and machine parameters:…”