Argomenti di tesi proposti dal docente.
Proposal of a technique to measure the diffusion process in a circular particle accelerator
In recent years, intense research efforts have been devoted to the problem of describing the nonlinear dynamics in a circular particle accelerator using a Fokker-Planck equation that allows the effect of unavoidable fluctuations in the particle dynamics to be modelled. Provided it is possible to model the transverse and longitudinal dynamics using a Hamiltonian that describes the nonlinear motion, the functional form of the diffusion coefficient can be analytically derived from the results of the perturbation theory and it is possible to identify the free parameters.
The master thesis will consider the objective of studying the properties of the solution of the diffusion equation as a function of the free parameters of the diffusion coefficient, in view of devising a method to reconstruct the form of the diffusion equation by means of the results of a limited number of numerical simulations. The reconstruction technique should be robust again the presence of numerical errors artificially added to the simulation results. This should suggest a possible experimental protocol for the measurement of the diffusion coefficient in a real accelerator based on the proposed approach. The ultimate goal is to propose a technique that could be applied at the CERN LHC.
A. Bazzani, M. Giovannozzi and E. H. Maclean, Analysis of the non-linear beam dynamics at top energy for the CERN Large Hadron Collider by means of a diffusion model, Eur. Phys. J. Plus (2020) 135: 77
Manipulating the transverse beam distribution in presence of radiation damping and quantum excitation
In recent years, intense research efforts have been devoted to the problem of manipulating the transverse beam distribution by means of nonlinear beam dynamics. Currently, these techniques are used at the CERN PS to generate the high-intensity proton beams needed for the fixed-target programme at the CERN SPS Experimental Area.
The master thesis will consider the objective of extending the techniques developed for the proton beams to lepton beams in which the dynamics is affected by phenomena such as radiation damping and quantum excitation. The research activity will study the application of the adiabatic theory for Hamiltonian systems to the stochastic dynamics performed by the lepton beam and, in particular, the adiabatic resonance trapping that has been successfully used to perform a multi-turn beam extraction in proton machines. This study should be carried out using simple models describing the transverse betatronic motion in the presence of nonlinearities and radiation effects (damping end excitation). The ultimate goal is to complement the results obtained recently at synchrotron light sources, where these effects have been measured and simulated.
N. Carmignani, A. Franchi, M. Giovannozzi, Could synchrotron light sources benefit from the experience at CERN with beams split in horizontal phase space?, in Nonlinear Dynamics and Collective Effects in Particle Beam, World Scientific, ed. by S. Chattopadhyay, M. Cornacchia, S. Di Mitri, 298 (2019).
Space charge effects for transversely split beams
In recent years, intense research efforts have been devoted to the problem of manipulating the transverse beam distribution by means of nonlinear beam dynamics. Currently, these techniques are used at the CERN PS to generate the high-intensity proton beams needed for the fixed-target programme at the CERN SPS Experimental Area.
The master thesis will consider the objective of extending the techniques developed so far with the inclusion of intensity-dependent effects, namely direct and, possibly, also indirect space charge effects. The research activity will study the application of the adiabatic theory results for Hamiltonian systems to the Vlasov equation that deals with the effect of the long-range interactions of the charged particles with the electric field produced by their distribution. The study will include the derivation of models describing the dynamics of beams under the combined effect of nonlinearities and space-charge effects and their study by means of numerical simulations.
C. Benedetti; G. Turchetti, [https://cris.unibo.it/handle/11585/19413], Phys. Lett. A, 2005, 340, pp. 461 – 465
S. Gilardoni, M. Giovannozzi, and C. Hernalsteens, First observations of intensity-dependent effects for transversely split beams during multiturn extraction studies at the CERN Proton Synchrotron, Phys. Rev. ST Accel. Beams 16, 051001 (2013)
S. Machida, C. Prior, S. Gilardoni, M. Giovannozzi, A. Huschauer, and S. Hirlander, Numerical investigation of space charge effects on the positions of beamlets for transversely split beams, Phys. Rev. Accel. Beams 20, 121001 (2017)
