The CERN LIU and HL-LHC program

Chapter 1

Introduction

1.1 Background

1.1.1 The CERN LIU and HL-LHC program

In the effort to an understanding of nature’s underlying principles, advances in modern scientific theories have been pushing the collision energy scale of particles further and further into terrains which are difficult, if not impossible, to study. The reason seems to be nature itself, as there are indications that, on the one hand, from a cosmological point of view the universe likely did evolve out of a state of very high energy-density and, on the other hand, from a microscopic point of view, that the coupling constants of the electromagnetic, the weak and the strong force are expected to be almost merging at collision energies of around 10¹³ T eV [Kaz01]. Unfortunately (or maybe fortunately), such energies are beyond the capabilities of any particle collider.

On the frontier of the highest possible particle collision energies mankind can currently produce lays the European Organization for Nuclear Research (CERN), as host of its Large Hadron Collider (LHC). CERN, founded in 1954, has currently 22 member states with around 2500 staff members and over 12200 users from 110 nationalities [CER19]. The LHC, as being the largest part in the CERN accelerator complex, is a 27kmcircular particle collider, built for the purpose of achieving the highest technically possible energies for fundamental high-energy physics research.

The ring was approved and built from around 1994 onwards in the tunnel of its predecessor, the Large-Electron-Positron Collider (LEP), and assembled in two stages. In its current second stage it can produce proton-proton collisions in four collision points with a center of mass energy of around 13 T eV. Two beams of particles are hereby circulating in two separated tubes inside a superconducting magnet system, and brought into collision at the interaction points. The scale of the entire complex is shown in Fig. 1.1, while a schematic view is given in Fig. 1.2.

The LHC was operated with success over the recent years, including the celebrated discovery of the Higgs-boson [Aad+12;Cha+12], the last sought piece of thestandard model depicted in Fig.

1.3. This was a major milestone in an understanding of nature’s fundamental principles. In order to further improve the performance of the LHC, major upgrades are scheduled within the coming years, starting from 2019 onwards, in which all injectors¹ – as well as the main ring – will receive improvements and element replacements.

The upgrade of the pre-accelerator complex is summarized under the name LHC Injectors Upgrade (LIU). LIU is required prior to an upgrade of the LHC, the High-Luminosity LHC (HL-LHC). The HL-LHC has the primary purpose to fully exploit the capabilities of the ring, using cutting-edge technology, with the goal to increase theluminosity (i.e. the number of collisions per second and per transverse area) by a factor of around ten [Apo+17].

1Rings through which the beam will be accelerated into the LHC are calledinjectors.

Figure 1.1: Aerial view of the CERN accelerator complex. c⃝CERN

Increasing the luminosity is highly desired, as it will lead to better statistics, in particular in regards of the detection of rare processes, and which will therefore improve our understanding of nature. Besides of exploring the properties of the Higgs boson, another goal of the scientific pro-gram will be the search for weakly interacting massive particles, in order to detect possible hints to physics beyond the standard model.

In order to reach high luminosities in the LHC, the pre-accelerator complex plays a crucial role, because in the chain of pre-accelerators the bunch characteristics of the LHC are determined: A high luminosity goal in the LHC collision points requires high-intensity beams in all involved ma-chines. However, the higher the intensity of the beam is set to, the stronger the repulsive forces of the individual particles will be due to the fact that they have the same electric charge. At some point thesespace charge forces are sufficiently strong enough to drive undesired beam instabilities

2This figure is a derivative of "Standard model of physics", http://texample.net/ c⃝ C. Burgard under the Creative Commons attribution license.

1.1. Background 3

Figure 1.2: Schematic view of the CERN accelerator complex. c⃝CERN

and other phenomena, which turn out to be major limitations for the operation of the machines.

Space charge is always present, but it is in particular dominant in the low-energy pre-accelerators, because its repulsive action takes place in the beam rest frame, i.e. under the effect of time dilation if observed from the laboratory frame of reference.

The CERN pre-accelerators consists of the linear accelerators LINAC3 for ions and LINAC4³ for protons, the Low Energy Ion Ring (LEIR) for ions, the Proton-Synchrotron-Booster (PSB) for protons, the Proton Synchrotron (PS) and finally the Super-Proton-Synchrotron (SPS), see Fig.

1.2. In all of those machines, simulations with high-intensity beams are necessary to determine the behavior of the beam due to the additional self-interaction of the particles.

For the purpose of simulating space charge effects, various simulation codes are at our disposal.

These codes are intended to solve the complex scenarios of interacting particles inside an accelera-tor over a reasonably long period of time. However, although they are sophisticated, they too have to rely on certain simplifications, and it is therefore important to determine whether the different models of the codes yield correct and consistent results. This is the point where this work comes into play. In particular we are going to analyze two specific space charge codes, which are called MAD-X and PyOrbit.

3LINAC4 is the replacement of LINAC2. LINAC2 was in operation at the time of this work.

R/G/B2/3

strongnuclearforce(color) electromagneticforce(charge) weaknuclearforce(weakisospin) gravitationalforce(mass)

charge colors mass (+6anti-quarks)(+6anti-leptons) 6quarks6leptons spin

12 fermions (+12 anti-fermions)

increasing mass→

5 bosons (+1 opposite chargeW)

standard matter unstable matter force carriers outside

standard model

1

2

3

Figure 1.3: The standard model of particle physics.²

1.1.2 Motivation

The simulation of a large number of interacting charged particles inside a storage ring is a chal-lenging task mainly because of two reasons: The first reason is the sheer amount of particles (at CERN usually in the order of 10¹¹to 10¹³) which require the invention of suitable models to reduce the amount of parameters to be processed, and usually to parallelize computations as much as possible. The second reason is the time span of the physical processes simulated versus the time step of the integrator. Formulated for a reader who is familiar with the subject:⁴ If the equations of motion are integrated in a straightforward manner, codes which are based on a non-Liouvillean model may lead to unphysical phenomena. A well-known example is the development of noise as a contribution to the beam entropy, which will affect the evolution of the beam emittances [Str96;

Str00;BF+15;KF15].

In accelerators, phenomena related to the interaction between charged particles or charged particles and the vacuum chamber walls are commonly abbreviated ascollective effects. The interaction of the particles fall mainly into two categories: direct and indirect effects. Direct effects are primarily caused by the Coulomb interaction between the particles inside the beam (usually described by an effective space charge field). Indirect effects are caused by the influence of image charges on the beam, which are induced in the wall of the beam pipe.

Codes dealing with space charge can be categorized in so-called adaptive codes and non-adaptive

4We will introduce some notions in this chapter later on.