Tesi di laurea

Design beamlines using a machine learning approach

OVERVIEW

The National Center for Oncological Hadrontherapy (CNAO, Pavia) is one of the four cancer treatment facilities in Europe delivering proton and carbon ion beams for cancer treatment.
For the beamline optics design, the conventional trial-and-error approach is based on a few alternating-gradient structures and it yields too many starting points and too many designs to optimize individually by hand.
The thesis activity consists of simulating possible beamline design using the Machine Learning approach. The aim is to explore new optic possibilities and reduce dimensions and costs. The lattice will be reproduced in MAD-x, a well-established code for charged particle optics design developed by CERN, and PyTorch library in python will be employed for machine learning analysis
Starting from basic lattice segments, it is possible to initialize a neural network that can be used to explore a large number of segment combinations. The aim is to build a possible set of lattice designs and look for the best solutions.

SPECIFICATIONS

Expected duration of activity (including thesis write-up): 12 Months
Preferred technical skills: fundamentals of accelerator physics, fundamentals of mechanical statistics, basic knowledge of coding (python)
Most suited curriculum studiorum of the candidate: physics, engineer
Required soft skills: attitude to problem solving, will to take initiative, eagerness to learn, openness to discussions.
References: guglielmo.frisella@cnao.it  marco.pullia@cnao.it, enrico.felcini@cnao.it

STEPS

1.    Simulated Lattice algorithm
a.    Define optic parameters for lattice elements
b.    Generate new lattice segment
c.    Propagate the test particle using transfer matrices.
d.    Repeat until the desired length is achieved

2.    Machine learning approach using PyTorch
a.    Randomly initialize a population of neural networks
b.    Build the associated lattices by propagating a test particle through each neural network
c.    Evaluate the optical functions of each lattice
d.    Rank the performance of the networks using constrained-dominated sorting
e.    Pick candidates to produce new offsprings
f.    Introduce random mutations
g.    Sort combined population and pick top candidates for next iteration

Characterization of Strongly-bent Superconducting 4T dipoles using Taylor Analysis and Particle Tracking tools

OVERVIEW

In the framework of the HITRIplus and SIG projects in collaboration with the CNAO foundation, a European effort is put in place to design and build short and strongly-bent superconducting dipoles. Such magnets require an appropriate description and representation to be used in traditional beam optics codes.
Although it is common practice to describe dipoles in transfer lines with a linear hard edge model, this approximation is suitable and useful as long as the length of the magnet's heads is negligible with respect to its magnetic length and the non-linear components of the magnetic field can be neglected. If these conditions are not fulfilled, the transport of the beam through the magnet requires a more complex representation.
The thesis activity consists of using particle tracking to derive linear and non-linear components of a magnetic field and represent them in accelerator codes effectively.
First, the linear transfer matrices of optics elements are extracted using the results from particle tracking in the field map and a minimization algorithm is employed to evaluate the main parameters of these elements.
Second, a non-linear model is implemented to optimize the results with respect to the particle tracking in the field map.
Finally, these results are benchmarked using the well-established Taylor analysis.
The approach developed in this work aims to provide a suitable representation of short and strongly-bent dipoles, to represent the field map in accelerator codes, such as MAD-X, an optimized code for charged particle optics design developed by CERN.

SPECIFICATIONS

Expected duration of activity (including thesis write-up): 9-12 Months
Preferred technical skills: fundamentals of accelerator physics, fundamentals of mechanical statistics, basic knowledge of coding (Matlab)
Most suited curriculum studiorum of the candidate: physics, engineer
Required soft skills: attitude to problem solving, will to take initiative, eagerness to learn, openness to discussions.
References: guglielmo.frisella@cnao.it  marco.pullia@cnao.it, enrico.felcini@cnao.it

STEPS

1.    Particle Tracking Algorithm
a.    Tracking particles in the 3D field map using Runge-Kutta algorithm.
b.    The linear transfer matrix is evaluated using a least-square fitting.
c.    Linear Lattice Representation (e.g. combined function dipole, dipole edges, and drifts).
d.    Non Linear Lattice Representation.

2.    Taylor expansion series analysis
a.    Taylor analysis of the magnetic field map.
b.    Evaluation of field components.
c.    Benchmarked against particle tracking