Exact Solutions of Indirect Transverse Field Effects in Elongated Structures with Applications to CERN LHC and PS

This thesis addresses indirect space charge driven (ISCD) effects in particle accelerators at CERN. It introduces a novel approach using complex Green functions to accurately model the ISCD tune-shift in the Large Hadron Collider (LHC), identifying the electric interaction with the beam-screen as the primary cause. The developed closed-form model is applicable to future projects like the High Luminosity (HL)-LHC. The work also explains ISCD-induced intensity dependencies in the Proton Synchrotron's (PS) Multi-Turn Extraction. Theoretical contributions include new operators for tune-shift estimation in complex accelerator models, a method to approximate Green functions for arbitrary domains (applied to the LHC beam-screen), and novel closed-form solutions for magnetic interactions in components like n-poles and combined-function magnets.

The thesis can be downloaded here: CERN Document Server.

Thesis Evaluation & Impact

Executive Summary

This thesis is recognized as an excellent doctoral work that effectively bridges the gap between abstract mathematical physics and practical engineering challenges at CERN. Its primary achievement is resolving a known discrepancy in the LHC tune-shift predictions by a factor of two, achieving >99% agreement with measurements.

Scientific Novelty

The work introduces a new mathematical framework by moving from standard planar geometry to the Riemann-sphere. Key innovations include:

  • Riemann-Sphere Framework: Uncovered symmetries and solutions for accelerator fields that were invisible in the standard 2D view.
  • Novel Operators: Derived a Lorentz force operator acting directly on conformal mappings, allowing for the "automation" of solving for complex shapes.
Practical Impact on CERN Accelerators

The theoretical models have been immediately applied to machine operations:

  • LHC Tune-Shift Resolution: Resolved a long-standing factor-of-two discrepancy between calculated and measured tune-shifts at injection.
  • PS Multi-Turn Extraction: Provided the first quantitative explanation for intensity-dependent position shifts in the Proton Synchrotron's "island" beams, identifying indirect space charge as the dominant driver.
  • HL-LHC Predictions: Predicted that ISCD effects will double in the High-Luminosity LHC, necessitating the corrections derived in this thesis.
Methodological Rigor

The thesis is distinguished by its mathematical precision:

  • Closed-Form Solutions: Derived exact equations for complex geometries (e.g., "rect-elliptical" beam screens, n-poles), which are infinitely scalable and offer deeper insight than numerical simulations.
  • Error Bounds: Proved a theorem for error bounds in polygonal approximations, providing engineers with guaranteed accuracy limits for safety-critical operations.