Transverse beams stability studies at the Large Hadron Collider

A charged particle beam travelling at the speed of light produces large electromagnetic wake fields which, through interactions with its surroundings, act back on the particles in the beam. This coupled system may become unstable, resulting in a deterioration of the beam quality. Such effects play a major role in most existing storage rings, as they limit the maximum performance achievable. In a collider, the presence of a second beam significantly changes the dynamics, as the electromagnetic interactions of the two beams on each other are usually very strong and may, also, limit the collider performances. This thesis treats the coherent stability of the two beams in a circular collider, including the effects of the electromagnetic wake fields and of the beam-beam interactions, with particular emphasis on CERN's Large Hadron Collider. As opposed to other colliders, this machine features a large number of bunches per beam each experiencing multiple long-range and head-on beam-beam interactions. Existing models describing the beams stability need to be extended accordingly. The beam-beam interactions are very non-linear, as a result, different particles in the beams oscillates with slightly different frequencies, which generates Landau damping of coherent motion. A numerical integrator is developed in order to estimate the effect of Landau damping on potentially unstable coherent modes of oscillation. As the characteristics of the machine and the beams vary along the operational cycle of the Large Hadron Collider, the beam-beam forces and consequently the effect of Landau damping may vary significantly. It is shown that some configurations are particularly critical. Measurements of coherent instabilities during these operational phases, as well as in dedicated experiments, are presented and compared to the model. While most observations are in agreement with the model, some observed instabilities remain unexplained. A mechanism is proposed as an explanation for these instabilities. It is shown that the distribution of particles in the beam can be distorted in the presence of external noise and that non-measurable variations of the distribution functions can lead to significant deterioration of the Landau damping strength. Multiparticle tracking simulations are used to demonstrate this effect in realistic conditions. The coherent modes of oscillation of the coupled system including the two beams and the electromagnetic wake fields is discussed by extending an existing linear model introduced earlier to describe single bunches encountering a single beam-beam interaction in order to describe the beams in the Large Hadron Collider, i.e. involving multiple bunches and multiple beam-beam interactions. It is shown that under certain circumstances, a resonant action of the beam-beam forces and the electromagnetic wake fields may lead to strong instabilities. An experiment was performed to test these effects in the Large Hadron Collider, showing a good agreement with the models. Mitigation techniques against these instabilities are investigated, the effect of Landau damping is discussed by comparing the linear model with multiparticle tracking simulations. An operational solution to relax the limitations due to coherent instabilities, taking advantage of the stabilising effect of the head-on beam-beam interactions, is discussed based on the models developed and tested experimentally

The Online Model for the Large Hadron Collider

The control of the high intensity beams of the CERN Large Hadron Collider is particular challenging and requires a good modeling of the machine. In recent years efforts were devoted to the design of a software infrastructure aimed at mimicking the behavior of the LHC. An online model of the machine, based on the accelerator design tool MAD-X, has been developed to support the commissioning and the operation of the LHC. This model is integrated into the Java-based LHC development framework and provides the full computing power of MAD-X, including the best knowledge of the machine aperture and magnetic models. In this paper, we present the status of the MAD-X online application and illustrate how it has been used during the LHC commissioning. Possible future implementations are also discussed

Status of JMAD, the Java API for MADX

MadX (Methodical Accelerator Design) is the de-facto standard software for modeling accelerator lattices at CERN. This feature-rich software package is implemented and still maintained in the programming languages C and FORTRAN. Nevertheless the controls environment of modern accelerators at CERN, e.g. of the LHC, is dom- inated by Java applications. A lot of these applications, for example, for lattice measurement and fitting, require a close interaction with the numerical models, which are all defined by the use of the proprietary MadX scripting lan- guage. To close this gap an API to MadX for the Java pro- gramming language (JMad) was developed. JMad was first presented to the public about one year ago. In the mean- time, a number of improvements were done, and additional MadX features (e.g., tracking) were made available for Java applications. Additionally, the graphical user interface was improved and JMad was released as open source software. This paper describes the current status and some new fea- tures of the project, as well as some usage examples

Simulation of Linear Beam Parameters to Minimize the Duration of the Squeeze in the LHC

The betatron squeeze allows to increase the luminosity of a collider by reducing the β function at the interaction points. This operation has shown to be very critical in pre- vious colliders. In this state of mind, the squeezing was performed extremely safely during the first year of oper- ation of the Large Hadron Collider, at the expense of the duration of the process. As the turnaround time is a rele- vant parameter for the integrated luminosity, a squeeze of shorter duration is proposed for 2011 and further. MadX simulation of linear beam parameters based on settings ex- tracted from the LHC control system are used to justify the proposal. Further optimization of the squeeze setting gen- eration is also discussed

Beam Based Optimization Of The Squeeze In The LHC

The betatron squeeze is a critical operational phase for the LHC because it is carried out at top energy, with the maximum stored energy and with reduced aperture mar- gins in the superconduting triplets. A stable operation with minimum beam losses must be achieved in order to ensure a safe and efficient operation. The operational experience at the LHC showed that this is possible. The operation in 2010 is reviewed. In particular, orbit, tune and chromatic- ity measurements are investigated and correlated to beam losses. Different optimizations are then proposed towards a more efficient and robust operation. The improvements obtained for the operation in 2011 are presented

A systematic measurement analyzer for LHC operational data

The CERN Accelerator Logging Service stores data from hundreds of thousands of parameters and measurements, mostly from the Large Hadron Collider (LHC). The systematic measurement analyzer is a Java-based tool that is used to visualize and analyze various beam measurement data over multiple fills and time intervals during the operational cycle, such as ramp or squeeze. Statistical analysis and various manipulations of data are possible, including correlation with several machine parameters such as β^{*} and energy. Examples of analyses performed include checks of collimator positions, beam losses throughout the cycle and tune stability during the squeeze which is then used for feed-forward purposes.peer-reviewe

Toolchain for Online Modeling of the LHC

The control of high intensity beams in a high energy, su- perconducting machine with complex optics like the CERN Large Hadron Collider (LHC) is challenging not only from the design aspect but also for operation towards physics production. To support the LHC beam commissioning, ef- forts were devoted in the design and implementation of a software infrastructure aimed at using the computing power of the beam dynamics code M AD - X in the framework of the JAVA-based LHC control and measurement environment. Alongside interfaces to measurement data as well as to set- tings of the control system, the best knowledge of machine aperture and optic models is provided. In this paper, we will present the status of the toolchain and illustrate how it has been used during commissioning and operation of the LHC. Possible future implementations will be discussed

Commissioning of Ramp and Squeeze at the LHC

The energy ramp and the betatron squeeze at the CERN Large Hadron Collider (LHC) are particularly critical oper- ational phases that involve the manipulation of beams well above the safe limit for damage of accelerator components. In particular, the squeeze is carried out at top energy with reduced quench limit of superconducting magnets and re- duced aperture in the triplet quadrupoles. In 2010, the commissioning of the ramp from 450 GeV to 3.5 TeV and the squeeze to 2 m in all the LHC experiments have been achieved and smoothly became operational. In this paper, the operational challenges associated to these phases are discussed, the commissioning experience with single- and multi-bunch operation is reviewed and the overall perfor- mance is discusse

Observation of Coherent Beam-Beam effects in the LHC

Early collisions in the LHC with a very limited num- ber of bunches with high intensities indicated the presence of coherent beam-beam driven oscillations. Here we dis- cuss the experimental results and compare with the expec- tations

Beam-beam amplitude detuning with forced oscillations

Recently, relations were established between the coefficients of free and forced amplitude detuning polynomial expansions. The forced oscillations were considered only in a single plane. In this paper we extend and generalize previous results by developing analytical equations that transform the free amplitude detuning function into the amplitude detuning involving forced oscillations in both transverse planes. These are used to obtain closed approximated formulas for the beam-beam amplitude detuning with forced oscillations. Formulas are compared to single and multiparticle simulations