On solving the Thomas Bargman-Michel-Telegdi equation using the Bogoliubov Krylov method of averages and the calculation of the Berry phases

Several proposals aimed at measuring the Electric Dipole Moment (EDM) for charged particles require very precise simulations and understanding of the systematic errors that can contribute to a spin buildup mimicking the EDM signal to be detected. In what follows, one used the Bogoliubov-Krylov-Mitropolski method of averages to solve the T-BMT equation and calculate the Berry phases arising for a proton EDM storage ring. The formalism employed proved to be particularly useful to determine the evolution of the spin at the observation point, i.e. at the location of the polarimeter. Several selected cases of lattice imperfections were simulated and benchmarked with the analytical estimates. This allowed the proof of the convergence of the numerical simulations and helped gain better understanding of the systematic errors

Les méthodes d'accélération circulaire de forte puissance et les réacteurs sous-critiques pilotés par un accélérateur de particules (ADS-R)

High power proton accelerators allow providing, by spallation reaction, the neutron fluxes necessary in thesynthesis of fissile material, starting from Uranium 238 or Thorium 232. This is the basis of the concept ofsub-critical operation of a reactor, for energy production or nuclear waste transmutation, with the objective ofachieving cleaner, safer and more efficient process than today’s technologies allow.Designing, building and operating a proton accelerator in the 500-1000 MeV energy range, CW regime,MW power class still remains a challenge nowadays. There is a limited number of installations at presentachieving beam characteristics in that class, e.g., PSI in Villigen, 590 MeV CW beam from a cyclotron, SNS inOakland, 1 GeV pulsed beam from a linear accelerator, in addition to projects as the ESS in Europe, a 5 MWbeam from a linear accelerator.Furthermore, coupling an accelerator to a sub-critical nuclear reactor is a challenging proposition: some ofthe key issues/requirements are the design of a spallation target to withstand high power densities as well asensure the safety of the installation.These two domains are the grounds of the PhD work: the focus is on the high power ring methods inthe frame of the KURRI FFAG collaboration in Japan: upgrade of the installation towards high intensityis crucial to demonstrate the high beam power capability of FFAG. Thus, modeling of the beam dynamicsand benchmarking of different codes was undertaken to validate the simulation results. Experimental resultsrevealed some major losses that need to be understood and eventually overcome.By developing analytical models that account for the field defects, one identified major sources of imperfectionin the design of scaling FFAG that explain the important tune variations resulting in the crossing of severalbetatron resonances. A new formula is derived to compute the tunes and properties established that characterizethe effect of the field imperfections on the transverse beam dynamics. The results obtained allow to developa correction scheme to minimize the tune variations of the FFAG. This is the cornerstone of a new fixed tunenon-scaling FFAG that represents a potential candidate for high power applications.As part of the developments towards high power at the KURRI FFAG, beam dynamics studies have toaccount for space charge effects. In that framework, models have been installed in the tracking code ZGOUBIto account for the self-interaction of the particles in the accelerator. Application to the FFAG studies is shown.Finally, one focused on the ADSR concept as a candidate to solve the problem of nuclear waste. In orderto establish the accelerator requirements, one compared the performance of ADSR with other conventionalcritical reactors by means of the levelized cost of energy. A general comparison between the different acceleratortechnologies that can satisfy these requirements is finally presented.In summary, the main drawback of the ADSR technology is the high Levelized Cost Of Energy comparedto other advanced reactor concepts that do not employ an accelerator. Nowadays, this is a show-stopper forany industrial application aiming at producing energy (without dealing with the waste problem). Besides, thereactor is not intrinsically safer than critical reactor concepts, given the complexity of managing the targetinterface between the accelerator and the reactor core.Les accélération de faisceaux de forte puissance et le bombardement d'une cible de spallation permettent d'atteindre les flux requis pour application aux réacteurs sous-critiques pilotés par un accélérateur de particules (ADSR).Parmi les methodes d'acceleration, on trouve les accélérateurs circulaires, en particuler les FFAG et les cyclotrons. Le travail de cette these porte sur l'évaluation de ces methodes pour la production de faisceaux de protons de classe multi-mégawatts, y compris la participation à des collaborations d'études internationales de design. Une evaluation de la methode ADSR comme candidat potential pour resoudre le probleme des dechets nucleaires est finalement etablie

On solving the Thomas Bargman-Michel-Telegdi equation using the Bogoliubov Krylov method of averages and the calculation of the Berry phases

Several proposals aimed at measuring the Electric Dipole Moment (EDM) for charged particles require very precise simulations and understanding of the systematic errors that can contribute to a spin buildup mimicking the EDM signal to be detected. In what follows, one used the Bogoliubov-Krylov-Mitropolski method of averages to solve the T-BMT equation and calculate the Berry phases arising for a proton EDM storage ring. The formalism employed proved to be particularly useful to determine the evolution of the spin at the observation point, i.e. at the location of the polarimeter. Several selected cases of lattice imperfections were simulated and benchmarked with the analytical estimates. This allowed the proof of the convergence of the numerical simulations and helped gain better understanding of the systematic errors

Geometric phase effect study in electric dipole moment rings

Several proposals to measure a possible small electric dipole moment (EDM) of charged particles aligned with the spin and the well-known magnetic dipole moment (MDM) are based on the concept to circulate bunches with an initial polarization in the horizontal plane and to observe the buildup of a vertical spin component caused by the EDM. Most proposals aim at operating the ring with “frozen spin,” such that, with an MDM only, the spin remains aligned with the trajectory. The signature of a finite EDM is the buildup of a vertical spin component. Machine imperfections may lead as well to a vertical spin buildup, which can be misinterpreted as an EDM and thus limit the sensitivity of the experiment. For that reason, a good understanding of spin dynamics is mandatory to estimate and limit such systematic errors in the measurement. In this paper, a coordinate system attached to the trajectory is introduced to expand the spin. This is of particular interest for fully electric EDM rings operated at the “magic energy” to satisfy the frozen spin condition. The procedure is used for a straightforward analysis of geometric phase and other second order effects, which limit the possible sensitivity, i.e., the smallest EDM which can be detected in presence of systematic effects

Tune compensation in nearly scaling fixed field alternating gradient accelerators

In this paper, we investigate the stability of the particle trajectories in fixed field alternating gradient accelerators (FFAs) in the presence of field errors. The emphasis is on the scaling radial sector FFA type: A collaboration work is ongoing in view of better understanding the properties of the 150 MeV scaling FFA at Kyoto University Institute for Integrated Radiation and Nuclear Science in Japan and progress toward high-intensity operation. Analysis of certain types of field imperfections revealed some interesting features that required the development of an analytical model based on the scalloping angle of the orbits. This helped explain some of the experimental results as well as generalize the concept of a scaling FFA to a nonscaling one for which the tune variations obey a well-defined law. Based on this, a compensation scheme of tune variations in imperfect scaling FFAs is presented. This is the cornerstone of a novel concept of a fixed tune FFA in which the scaling is not achieved at every azimuthal position of the ring but rather in an average sense.In this paper, we investigate the stability of the particle trajectories in Fixed Field Alternating Gradient (FFAG) accelerators in the presence of field errors: The emphasis is on the scaling FFAG type: a collaboration work is on-going in view of better understanding the properties of the 150 MeV scaling FFAG at KURRI in Japan, and progress towards high intensity operation. Analysis of certain types of field imperfections revealed some interesting features about this machine that explain some of the experimental results and generalize the concept of a scaling FFAG to a non-scaling one for which the tune variations obey a well defined law. A compensation scheme of tune variations in imperfect scaling FFAGs is presented. This is the cornerstone of a novel concept of a non-linear non-scaling fixed tune FFAG that we present and discuss in details in the last part of this paper

Systematic Effects Limiting the Sensitivity of "Magic Energy" Proton EDM Rings

Proposals to measure a possible Electric Dipole Moment (EDM) of protons in an electro-static storage ring are studied by a world-wide community. The machine is operated at the so-called "magic energy" to satisfy the "frozen spin" condition such that, without imperfections and with the well known magnetic moment of the particle, the spin is always oriented parallel to the direction of movement. The effect of a finite EDM is a build-up of a vertical spin component. Any effect, other than a finite EDM, leading as well to a build-up of a vertical spin limits the sensitivity of the experiment. Such "systematic effects" are caused by machine imperfections, such as magnetic fields inside the magnetic shield surrounding the ring, and misalignments of electro-static elements or of the RF cavity. Operation of the machine with counter-rotating beams helps mitigating some of the effects. The most dangerous effects are those, which cannot be disentangled from an EDM by combining measurements from both counter-rotating beams, such as an average residual radial magnetic field penetrating the magnetic shield or a combination of magnetic fields and misalignments of electric elements

Systematic Errors of a ”frozen Spin” EDM measurement with electric and magnetic Fields due to imperfect Alignment of Fields

Many of the rings proposed to measure the Electric Dipole Moment (EDM) of charged particles rely on a combination of magnetic and electric fields bending the beam to fulfil the ”frozen spin” condition. Imperfect alignment of the two fields bending the beam is known to rotate the spin from the longitudinal into the vertical direction. This effect is very similar to the signature of a finite EDM and, thus, a potential limitation for the sensitivity of the measurement. The concept of a ”spin transparent” quadrupole is to superimpose magnetic and electric contributions for focusing elements as well to increase the spin coherence time. A vertical offset between the two quadrupole contributions leads as well to rotations of the spin from the longitudinal to the vertical direction. In this report, simple expressions to compute the angular frequencies of these rotations around a radial axis are given

The PSI meson target facility and its upgrade IMPACT-HIMB

The high intensity proton accelerator complex (HIPA) at the Paul Scherrer Institute (PSI) delivers a 590 MeV CW proton beam with currents up to 2.4 mA (1.4 MW). Besides two spallation targets for thermal/cold neutrons (SINQ) and for ultracold neutrons (UCN), the beam feeds two meson production targets Target M and Target E. The targets consist of graphite wheels of effective thickness 5 mm (M) and 40/60 mm (E). The target stations M and E are of quite different design; however, both of them rotate at 1 Hz to dissipate the heat (20 kW/mA for the 40 mm target E) efficiently. Recent progress was made by a new type of bearings and a new target geometry able to increase the rate of surface muons by up to 50 %. This is also foreseen for the upgrade of the target station M within the High Intensity Muon Beam (HIMB) initiative aiming to increase the surface muons available for experiment by two orders of magnitude. HIMB is part of IMPACT (Isotope and Muon Production with Advanced Cyclotron and Target Technology), an application for the Swiss Roadmap of Research Infrastructure