Doctoral theses
Current Record: 1 of 2177

Identifier 
000442691 
Title 
Nonlinear dynamics modelling in accelerators with the use of symplectic integrators 
Alternative Title 
Μοντελοποίηση της μηγραμμικής δυναμικής σε επιταχυντές με τη χρήση συμπλεκτικών ολοκληροτών 
Author

Σκουφάρης, Κυριάκος Α.

Thesis advisor

Τσιρώνης, Γεώργιος
Τομαράς, Θεόδωρος
Papaphilippou, Yannis

Abstract 
This PhD thesis elaborates the particle dynamics for a large number of revolutions
(long time integration) in synchrotrons (circular particle accelerators) like the Large
Hadron Collider (LHC) and its upcoming High Luminosity upgrade (HLLHC). A fast
introduction to the CERN accelerator complex is presented in Chapter 1. In Chapter 2,
using the powerful tools of the Hamiltonian formalism and the Poisson bracket Lie algebra,
the mathematical framework that will be used in the following Chapters is developed.
For any Hamiltonian problem, the use of symplectic transfer maps is mandatory for
any long term integration study. In Chapters 3 and 4 two differed symplectic integration
methods are presented. The first one is better suited for heavy simulations like the study
of the bunch dynamics while the other one for simulations that require very good accuracy
like the single particle dynamics.
The computational cost for long term bunch dynamics analysis (e.g. study of the
space charge or beambeam effects) can be quite large especially for machines like the
LHC and HLLHC (more that 10^{16} operations per revolution are required). In order to
speed up this type of simulations, differed tricks like the parallelcomputing, the use of
macroparticles and reduced lattices can be applied. In Chapter 3 a method to produce
simplified versions of the original nonlinear lattices is presented. This versatile symplectic
integration scheme (effective lattice) is a sequence of linear sections that are separated
by combined nonlinear kicks and can reproduce all the linear properties of the original
lattice while retains an adequate accuracy for the nonlinear ones with the least possible
elements. The developed transfer map is quite ease to be adjusted for the needs of differed
rings and it is made available as a refined replacement of the simplified rotation matrix
that is often used in multiparticle studies that requiring a fast beam transport routine.
For the evaluation if the different configurations of an accelerator are operational,
a set of long term single particle tracking studies is needed. In Chapter 4 a new family
of high order symplectic integrators C S AB A_{ν} & C SB AB_{ν} is used for the calculation of
the Hamiltonian flows in different accelerator lattices. A benefit of theses symplectic
integrators (when they can be applied) is the presence of only forward integration steps
independent of the order of accuracy. In addition to that, the C S AB A_{ν} & C SB AB_{ν} integrators are found to be more accurate for similar or smaller integration cost than other
symplectic integration schemes that are well established in the accelerator community.
The Chapter 5 of this thesis, deals with an operational problem of the HLLHC which
is the mitigation of the beambeam longrange (BBLR) interactions. These BBLR kicks
can significantly reduce the performances of the collider thus, the use of DC wires as a
compensatory devise is studied. Analytical expressions for the resonance driving terms
and the tune spread with amplitude, driven by the BBLR interactions and the wires
electromagnetic field, are derived. Using these results as a guideline for the numerical
simulations, it is demonstrated that with a proper optimization of the DC wires, without
violating the machine protection restrictions, the long range beambeam interactions can
be very well mitigated. Also, new nominal and ultimate scenarios of the HLLHC with
smaller crossing angle are found. These scenarios are operational (good lifetime) only
with the use of wire compensators and can be used as complementary to the original ones
for improving the integrated luminosity and the operational flexibility of the machine.
Finally, the last chapter (Chapter 6) is devoted to the conclusions of this thesis.

Language 
English 
Subject 
Beambeam long range interactions 

HLLHC 

LHC 

Particle accelerators 
Issue date 
20211011 
Collection

School/DepartmentSchool of Sciences and EngineeringDepartment of PhysicsDoctoral theses


Type of WorkDoctoral theses

Permanent Link 
https://elocus.lib.uoc.gr//dlib/a/9/e/metadatadlib16337783889171892889.tkl

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