• synchrotron light source
• optimization
• ESRF
• Accelerator physics
• Touschek lifetime

The lifetime of the electron beam in a storage ring is a measure of how fast the electrons are being lost. This is an important parameter in third generation synchrotron light sources for a number of reasons. First of all, the intensity of radiation seen in an experiment, at the end of a beamline, is proportional to the electron beam current. Further, as the current changes, there are important effects on the x-ray optics along the beamline. Changes in heat-load can effect the transport and focusing properties of the beamline. For these reasons, more electrons must be injected when the current drops below some threshold value.
The electron beam lifetime determines the injection frequency. If the lifetime is long enough, the injections can be done less frequently. The injection disturbs the stability of the stored beam, it increases the radiation losses and it increases the energy consumption of the facility, because the linac and the synchrotron booster must be turned on during the injection.
When the lifetime is too short, the top-up injection is needed. The top-up injection is a very frequent injection of electrons into the storage ring, one every few minutes, and it is done without interrupting the x-ray flux and the users’ experiments. Top-up injection needs a high injection efficiency.
In the ESRF storage ring, the top-up injection is not used now. In the low emittance ESRF upgrade storage ring, the top-up injection will be used, because the very low horizontal emittance, from the actual εx = 4 nm to εx = 150 pm, will result in a very short Touschek lifetime.
The Touschek effect is the main limitation in the beam lifetime in third generation synchrotron light sources. It is a single scattering between two electrons of the bunch. The collision can transfer momentum from transverse to longitudinal motion and both the electrons can exceed the momentum acceptance, in which case they are lost. The Touschek scattering probability is larger when the charge density is high, so when emittances and β functions are small and the current is high.
The Touschek effect depends on many electron beam and machine parameters: the RF voltage, the bunch current, the bunch length, the beam emittances and the momentum acceptance. The small horizontal emittance storage rings, necessary to have a high brilliance x-ray source, have small β-functions and horizontal dispersion and strong focusing magnets. The natural chromaticity of low emittance rings is very high and strong sextupole magnets are needed to correct it.
High nonlinear fields from sextupoles cause a high amplitude-dependent tune variation. The large tune shift with amplitude causes many resonance crossings for off-axis particles and therefore a small dynamic aperture. The small dynamic aperture causes a small injection efficiency.
The positive chromaticity, needed for the bunch stability, and the strong nonlinear fields give large tunes variation with momentum. This can cause the strong resonance crossing of off-momentum particles and therefore a small momentum acceptance. The small momentum acceptance causes a short Touschek lifetime.
Momentum acceptance is determined by RF voltage and longitudinal dynamic acceptance, which depends on the sextupole setting.
A model able to predict the Touschek lifetime, given the lattice, the current, the emittances, the RF voltage, the size of the vacuum chamber, is useful to optimize the parameters of the present ESRF lattice and the new low emittance ESRF upgrade lattice.
In this thesis, a model able to predict lifetime of the beam has been developed and tested with measurements and it has been used to optimize parameters and sextupole settings. The model is also used for the new lattice lifetime studies.
In chapter 1, a brief description of the ESRF facility and on its upgrade program is given.
In chapter 2, the Touschek lifetime derivation, from the Møller scattering differential cross section, is presented. The effects of the spin polarization in the Touschek lifetime are also treated.
In chapter 3, the measurements of some parameters, relevant for the Touschek lifetime, done for the ESRF storage ring, are reported. The RF voltage calibration factor between the readout value and the real voltage applied to the cavity is measured from the synchrotron tune and the synchronous phase measurements. A bunch lengthening with current model, derived from measurements, is presented. The momentum acceptance computation, using a 6-D particle tracking code, is described.
In chapter 4, the lifetime measurements are described: the vacuum lifetime, that must be measured before all the Touschek lifetime measurements; the effect of the spin polarization on the Touschek lifetime and the spin polarization time; the Touschek lifetime versus the RF voltage; the Touschek lifetime versus the horizontal scraper position.

In chapter 5, the optimization of the sextupole setting is described: the multiobjective generic algorithm used is described, the results of the optimization and the measurements are reported.
In chapters 6 and 7, the Touschek lifetime model, described in previous chapters, is used to study the Touschek lifetime of the low emittance ESRF upgrade lattice. The bunch length model and the emittance growth due to the intrabeam scattering are used to predict the Touschek lifetime of the new lattice for different modes.
In first appendix, an overview of the beam physics in an electron storage ring is given. In the first section, the single particle dynamics without synchrotron radiation is treated. In the second section, the effects of synchrotron radiation on the single particle dynamics are reported. In the third section two current dependent effects, related to the beam lifetime, are treated: the bunch lengthening effect due to the longitudinal wakefield and the intrabeam scattering.
In second appendix, a matlab code, developed during the thesis work and used to simulate the spin depolarization with a kicker, is described.
In third appendix, two possible momentum compaction factor measurements are presented.
In fourth appendix, the effect of synchrotron motion on the dynamic aperture computation is described.