Beam profile measurements in the LHC and its injector complex show heavy tails in both transverse planes. From standard profile measurements, it is not possible to determine if the underlying phase space distribution is statistically independent. A measurement campaign in the CERN PSB was carried out to introduce cross-plane dependence in bunched beams in controlled conditions, in view of characterizing the LHC operational beam distributions. The results of the measurement campaign demonstrate how heavy tails can be created via coupled resonance excitation of the lattice in the presence of space charge, in accordance with predictions from the fixed line theory. The coupled resonance introduces dependence between the different planes, which persists after the resonance excitation is removed.

The luminosity of particle colliders depends, among other parameters, on the transverse profiles of the colliding beams. At the LHC at CERN, heavy-tailed transverse beam distributions are typically observed in routine operation. The luminosity is usually modelled with the assumption that the 𝑥-𝑦 planes are independent (i.e. statistically uncorrelated particle distributions between the planes) in each beam. Analytical calculations show that the solution of inverting 1D heavy-tailed beam profiles to transverse 4D phase-space distributions is not unique. For a given transverse beam profile, the distributions can be dependent (i.e. statistically correlated) or independent in the transverse planes, even in the absence of machine coupling. In this work, the effect of transverse 𝑥-𝑦 dependence of the 4D phase space distribution on the luminosity of a particle collider is evaluated for heavy-tailed beams.

The beam transverse emittances play a critical role in high-energy colliders. Various measurement techniques are employed to measure them. In particular, the so-called luminosity emittance scans (or Van der Meer scans) are used in order to evaluate the convoluted beam emittances. This method assumes different emittances in the two planes but identical emittances in the two beams. In this paper, we propose an approach to remove this constraint. After having presented the new measurement protocol, we will discuss its potential and limits, including the statistical measurement error of the luminosity value as obtained from numerical studies.

The luminosity of particle colliders depends, among other parameters, on the transverse profiles of the colliding beams. At the LHC at CERN, heavy-tailed transverse beam distributions are typically observed in routine operation. The luminosity is usually modelled with the assumption that the 𝑥-𝑦 planes are independent (i.e. statistically uncorrelated particle distributions between the planes) in each beam. Analytical calculations show that the solution of inverting 1D heavy-tailed beam profiles to transverse 4D phase-space distributions is not unique. For a given transverse beam profile, the distributions can be dependent (i.e. statistically correlated) or independent in the transverse planes, even in the absence of machine coupling. In this work, the effect of transverse 𝑥-𝑦 dependence of the 4D phase space distribution on the luminosity of a particle collider is evaluated for heavy-tailed beams.

The beam transverse emittances play a critical role in high-energy colliders. Various measurement techniques are employed to measure them. In particular, the so-called luminosity emittance scans (or Van der Meer scans) are used in order to evaluate the convoluted beam emittances. This method assumes different emittances in the two planes but identical emittances in the two beams. In this paper, we propose an approach to remove this constraint. After having presented the new measurement protocol, we will discuss its potential and limits, including the statistical measurement error of the luminosity value as obtained from numerical studies.

Beam profile measurements in the LHC and its injector complex show heavy tails in both transverse planes. From standard profile measurements, it is not possible to determine if the underlying phase space distribution is statistically independent. A measurement campaign in the CERN PSB was carried out to introduce cross-plane dependence in bunched beams in controlled conditions, in view of characterizing the LHC operational beam distributions. The results of the measurement campaign demonstrate how heavy tails can be created via coupled resonance excitation of the lattice in the presence of space charge, in accordance with predictions from the fixed line theory. The coupled resonance introduces dependence between the different planes, which persists after the resonance excitation is removed.